Loraine Kennedy

OUTSOURCED URBAN GOVERNANCE AS A STATE RESCALING STRATEGY IN HYDERABAD, INDIA

In the years since liberalization, state power has been rescaled in India's polity and this is both a cause and consequence of greater inter-state competition for footloose capital. In this context, some state governments are designing special regulatory tools to attract and concentrate investments by easing 'doing business' for private investors and leveraging land resources-primarily in their largest cities. Equally important, they ensure public investments are channelled to these select spaces and that resources are available for maintaining high standards of infrastructure. In Hyderabad, the 'Industrial Area Local Authority' (IALA) is a powerful tool that allows privatised management by state and nonstate actors of recently constructed productive spaces, mainly concentrating globalised service sector activities, including by collecting local tax revenues and various development charges to be spent exclusively within the industrial area. In this way, governance and fiscal functions are outsourced to non-elected bodies, outside the purview of democratic institutions. By essentially replacing municipal authorities, the IALA framework produces new forms of governance at the same time that it generates fragmentation of the institutional fabric of urban spaces. In effect, it creates a tool for by-passing urban politics, or in the case of periurban spaces does not allow an urban politics to emerge. Building on recent research, this paper examines the implications of IALAs in Hyderabad on urban governance and local state sovereignty.

INTRODUCTION: OUTSOURCING URBAN GOVERNANCE

The period since the 1970s has seen the burgeoning of new institutional forms aimed at tackling the myriad challenges of urban governance and development in an era of neoliberal governmentality. Derived from the hybridization of public and private actors and interests, new models of urban governance, whether public-private partnerships or place-based instruments like business improvement districts, have drawn their raison d'être from perceived and documented government failures in providing public goods, infrastructure and services.

Ranked as the number one destination for public-private partnership (PPP) investment flows since 2006 by World Bank data (Planning Commission 2013:18), India has been at the forefront of institutional experimentation on the public-private interface at least since 1991. The emerging institutional arrangements range all the way from special purpose vehicles (SPVs) to guide megaproject development to the long-standing prototypes of the company town, repurposed to meet contemporary requirements in integrated industrial townships. The SPV model, for example, was deployed not only in the previous Congress-led government's National Investment and Manufacturing Zones but also in the current BJP-led government's flagship Smart Cities scheme, where the plan to appoint Chief Executive Officers for selected Smart Cities as a parallel structure of authority alongside the elected municipal framework has met with disquiet [START_REF] Idiculla | Will Smart Cities stifle local democracy? Scroll[END_REF].

The outsourcing of key powers and functions that traditionally fell under the rubric of government has newfound momentum under the current dispensation, with its slogan of "minimum government, maximum governance" [START_REF] Ruparelia | Minimum Government, Maximum Governance': The Restructuring of Power in Modi's India[END_REF][START_REF] Modi | Minimum Government, Maximum Governance[END_REF]. But the evolution of these privatized forms of governance can be traced back to the contradictory dynamics that came into focus in the 1990s. The 74 th Constitutional Amendment granted recognition and democratic legitimacy to local governments in urban areas. This advance in decentralized governance unfolded, however, against the backdrop of IMF-supported programme of liberalization, which created new entrepreneurial imperatives for subnational states and fostered the rise of speculative forms of governance [START_REF] Goldman | Speculative Urbanism and the Making of the Next World City[END_REF][START_REF] Mahadevia | Branded and Renewed? Policies, Politics and Processes of Urban Development in the Reform Era[END_REF]. While on the one hand, these forces reflected and necessitated the reconfiguration of the state's powers and functions across national, sub-national and local scales, they also gave a unique cast to [START_REF] Harvey | From managerialism to entrepreneurialism: the transformation in urban governance in late capitalism[END_REF] conceptualization of entrepreneurialism as the motive force of urban governance in the neoliberal epoch, as sub-national state (provincial) governments rather than city governments came to take on the mantle of entrepreneurialism, leaving the task of managing the after-effects of growth to local bodies [START_REF] Kennedy | The Politics of Economic Restructuring in India: Economic Governance and State Spatial Rescaling[END_REF].

If the ideal of subnational entrepreneurialism found propulsive impetus in the South Indian state of Andhra Pradesh, its realization depended in large degree on the regime of the Industrial Area Local Authority (IALA), applied in industrial parks and estates across the erstwhile state of Andhra Pradesh as well as present-day Telangana. 1 A specialized governance instrument that devolves the powers and functions of rural and urban local bodies to a state government agency, the IALA represents a fairly elaborate template for outsourced urban governance in contemporary India. In the establishment of a de facto private government in select industrial areas, the IALA shows kinship with other forms of corporate urbanism, such as the industrial township (Sood 2015). It also bears close resemblance to global models for outsourcing public goods provision such as the Economic Development Zones and the Business Improvement Districts (BIDs), which starting from Canada have proliferated around North America, Europe, Asia and Africa [START_REF] Warner | Club goods and local government: questions for planners[END_REF]. In South Africa, for instance, these are called City Improvement Districts (CID) [START_REF] Dubresson | Urbanisme entrepreneurial, pouvoir et aménagement. Les City Improvement Districts au Cap[END_REF][START_REF] Peyroux | City Improvement Districts in Johannesburg. An examination of the local variations of the BID model[END_REF].

While scholars have been particularly attentive to the BID phenomenon over the last few decades, the Indian case has remained overlooked, partly because it departs on some dimensions from the canonical international paradigm. The ability to levy higher property tax rates to finance infrastructural improvements is central to the BID's definition. For example, Hoyt and Gopal-Agge (2007:946) define the BID as "privately directed and publicly sanctioned organizations that supplement public services within geographically defined boundaries by generating multiyear revenue through a compulsory assessment on local property owners and/or businesses." In South Africa, "CID were funded by additional taxes on top of existing municipal levies and were intended, not to replace the municipality but to manage additional services under contractual concession arrangements, and to facilitate local development" (Dubresson: 2008: 3). In contrast, the IALA like other Indian models of corporate urbanism, seeks to replace rather than supplement the municipality; it outsources both tax powers and spending powers to the "special purpose enclave" itself, thereby transforming it into a 'local authority'. This paper seeks to position the restructuring of state power around the IALA within a broader understanding of the state spatial rescaling processes that have characterized contemporary Hyderabad, and that are indicative of India-wide trends. Processes of state rescaling are known to produce institutional reconfigurations; here, we examine recent reterritorialisation efforts aimed at scaling up the municipality to a metropolitan region. The aim is to analyse the repercussions of these processes of institutional and territorial restructuring on governance and on the larger socio-spatial dimensions of the urban fabric. Two hitherto overlooked modes of institutional fragmentation need particular attention. The first aspect of concern is the fiscal fragmentation introduced into municipal finances, as a result of the territorial and political reorganization of tax collection powers around the IALA regime. The second, related dimension interrogates the politics of bypass embodied in this instrument. How do regimes of exception produced through 'zoning technologies' [START_REF] Ong | Neoliberalism as exception: mutations in citizenship and sovereignty[END_REF]) such as the IALA reconfigure accountability and local sovereignty?

This paper draws on interviews with key informants and close examination of organizational documents both offline and online. We conducted interviews with over 35 key informants over the period August 2015 to January 2017. These included retired senior bureaucrats, planners, officials from various departments within the Telangana government, as well as members and representatives of industry federations and IALA service societies. We also met officials at various levels of the municipal corporation (circle offices and the head office), and the metropolitan planning authority.

Following the enactment of the Right to Information Act 2005, government and semigovernmental agencies are required to appoint Public Information Officers and respond to information requests by the public. Given this push to transparency, Telangana state government agencies, as well as the municipality provide considerable data and information online, though it is on occasion out-dated, incomplete or incorrect. In the latter cases, we attempted to follow up with interviews with relevant informants.2 In addition we also scanned closely relevant news and media reports as well as press releases. Finally, field visits of selected industrial areas in Greater Hyderabad allowed us to observe the material conditions of IALAs and collect their geographical coordinates for mapping their location ( see Figure 1).

The paper is organized as follows: The next section delineates the analytical approach undergirding this paper and positions state rescaling theorization in relation to the Indian and Hyderabad contexts. The following section elaborates on the opposed logics of integration and institutional fragmentation embodied in recent rounds of territorial reorganisation in Hyderabad. Next, the IALA instrument is described in detail before critically examining the fiscal and political fragmentation it has generated. The paper then situates the case of Hyderabad within a wider trend of bypass, and underscores the conflicts and contradictions in processes of state rescaling in India. The last section traces the IALA's role in the city's growth engine and outlines the implications of the politics of bypass and exception for democratic governance.

THE RESCALING PERSPECTIV E

The development of megaprojects in the form of new industrial estates and corridors has contributed to restructuring urban economies and shaping urban space in metropolitan Hyderabad, most strikingly in the erstwhile peripheral areas of the city [START_REF] Kennedy | Regional industrial policies driving peri-urban dynamics in Hyderabad, India[END_REF][START_REF] Ramachandraiah | The makeover of Hyderabad: Is it the 'Model' IT city?[END_REF]Das 2015a;[START_REF] Das | Making of high-tech Hyderabad: Mapping neoliberal networks and splintering effects[END_REF]. This pattern, observed in other large Indian cities since the mid-1990s [START_REF] Shaw | Metropolitan restructuring in post-liberalized India: Separating the global and the local[END_REF], has contributed to spatial and institutional fragmentation [START_REF] Shatkin | Planning privatopolis: representation and contestation in the development of urban integrated mega-projects[END_REF][START_REF] Ren | Urban governance, mega-projects and scalar transformations in China and India[END_REF][START_REF] Follmann | Urban mega-projects for a 'world-class' riverfront -The interplay of informality, flexibility and exceptionality along the Yamuna in Delhi, India[END_REF]Bon 2015;Anand and Sami 2016;[START_REF] Kennedy | Greenfield Development as Tabula Rasa. Rescaling, Speculation and Governance on India's Urban Frontier[END_REF].

To interpret the links between overarching political economic processes and urban spaces, and to capture how the understanding of these links influences public policy, the literature on state restructuring or rescaling appears particularly relevant. This body of theory, largely inspired by critical urban geography and French regulation theory, focuses on how states adapt to changes in capitalism by reconfiguring their relation to space and territory (Brenner et al 2003;[START_REF] Brenner | New state spaces: urban governance and the rescaling of statehood[END_REF]. Developed primarily in reference to North Atlantic capitalism,3 it has sought to explain how nation-states shifted from a Keynesian-inspired model, based on "uniform and centrally managed policies, aimed at the redistribution of assets, income and employment opportunities and infrastructure in order to create socially cohesive national space economies" [START_REF] Klink | Development Regimes, Scales and State Spatial Restructuring: Change and Continuity in the Production of Urban Space in Metropolitan Rio de Janeiro, Brazil[END_REF](Klink : 1169)), to a supply-side model targeting investments and promotional policies in favour of specific types of spaces. Thus, in contrast to 'spatial Keynesianism' subsequent policies were characterized by "the proliferation of customized and downscaled institutional arrangements aimed at the creation of competitive urban economies" (ibid). Urban spaces in particular have been targeted as strategic production sites, concentrating human and physical resources most capable of creating value and well connected through quality telecommunications and transport infrastructure. Increasingly, cities are leveraged as growth engines in regional and national economies, a trend observed in both advanced and emerging economies.

This body of theory builds on conceptions of scale that are not restricted to spatial aspects. Here, a scale has political and social texture and emerges or consolidates as a result of social processes that involve an appropriation of space. In this perspective, the emphasis shifts to the 'scalar dimensions of political and social practices' rather than focusing on phenomena occurring at various ready-made scales (e.g., local, national, global, etc.) [START_REF] Moisio | Political geographies of the state and scale[END_REF]. Importantly, rescaling or shifting scales is always a contested process and new or recalibrated scales are understood as an outcome of struggles for influence and power [START_REF] Swyngedouw | Globalisation or "glocalisation"? Networks, territories and rescaling[END_REF]. In India, endogenous political development in conjunction with market reforms have given rise to state spatial rescaling; new state spaces are produced via a contested process by socio-political forces emanating from various geographical scales [START_REF] Kennedy | The Politics of Economic Restructuring in India: Economic Governance and State Spatial Rescaling[END_REF].

Across the globe, as cities have increasingly become strategic sites for growth, issues about urban governance have come to the fore. This has prompted debates about multiscalar governance arrangements, territorial reorganisation, the devolution of fiscal powers to local bodies, and the merits of powerful executives and directly elected mayors (see [START_REF] Sivaramakrishnan | Urban Development and Metro Governance[END_REF]. In India, despite the reforms instituted by the 74 th amendment, even the largest cities have not seen a significant increase in powers [START_REF] Ghosh | A Comparative Overview of Urban Governance in Delhi, Hyderabad, Kolkata, and Mumbai[END_REF]).

State governments remain the key actors in urban space; moreover, many have asserted their intention to act as a substitute for the local government [START_REF] Kennedy | The Shift to City-Centric Growth Strategies: Perspectives from Hyderabad and Mumbai[END_REF]. In other words, in the reordering of jurisdictions that has occurred in the last couple of decades, subnational states have seen their jurisdictions enlarged [START_REF] Kennedy | The Politics of Economic Restructuring in India: Economic Governance and State Spatial Rescaling[END_REF]. If this has not been the case with local (municipal) governments, it is largely because state governments have resisted devolving powers and resources. At the same time, they have actively participated in rescaling state space by multiplying policy interventions in their largest cities, including in ways that have been described as 'predatory' [START_REF] Mahadevia | Branded and Renewed? Policies, Politics and Processes of Urban Development in the Reform Era[END_REF] and speculative [START_REF] Goldman | Speculative Urbanism and the Making of the Next World City[END_REF].

Fundamentally, rescaling processes imply a change in the spatial frame of reference underpinning state action. This can be expressed through a formal reconfiguration of jurisdictions, rescaling in a 'narrow' sense, which refers to "the changing organization of state territoriality in the modern inter-state system; the evolving role of borders, boundaries, and frontiers; and the changing intra-national geographies of state territorial organization and internal administrative differentiation" (Brenner et al. 2003: 6). The creation of Greater Hyderabad in 2007 through the merging of territories is one such example, and will be further discussed below.

In contrast, the 'integral' sense of state space covers a wider range of state spatial strategies that attempt to shape the geographies of socio-economic activities (Brenner et al. 2003). It refers to the myriad ways in which social and economic activities and relations are re/deregulated and re-organized in order to achieve state objectives, which may or may not involve territorial reorganization. These strategies have scope to restructure local economies, by shaping which sectors are promoted, the types of employment created and the sites where firms can locate. In many Indian cities, including Hyderabad, state strategies aim to provide 'world class' infrastructure to investors and often take the form of enclaves [START_REF] Shatkin | Planning privatopolis: representation and contestation in the development of urban integrated mega-projects[END_REF][START_REF] Follmann | Urban mega-projects for a 'world-class' riverfront -The interplay of informality, flexibility and exceptionality along the Yamuna in Delhi, India[END_REF]Sood 2015). Often, these areas are governed by a set of special "streamlined" rules, ranging from building regulations to tax codes. Hence these strategies create not only spatial but also institutional fragmentation. The IALA instrument provides a compelling illustration of this state strategy, further discussed below.

TERRITORIAL REORGANISATION AND STATE RESCALING I N HYDERABAD

In the mid-2000s, the Andhra Pradesh government unilaterally decided to expand the boundaries of the municipality of Hyderabad and create the Greater Hyderabad Municipal Corporation (hereafter GHMC, Greater Hyderabad or municipal government). Although the elected councillors opposed the expansion, GHMC was created by decree through a Government Order in 2007. 4 It was formed by merging 12 surrounding municipalities and eight villages (gram panchayats), increasing the area of the municipality by more than four times, from 172 km 2 to 725 km 2 , and almost doubling the population. This decision to territorially reorganize the municipality, i.e., rescaling in the narrow sense, can be interpreted as part of a larger restructuring strategy on the part of the state government [START_REF] Kennedy | The Politics of Economic Restructuring in India: Economic Governance and State Spatial Rescaling[END_REF]. It came after about a decade of policies that aggressively sought to develop specific places in Hyderabad's urban peripheries, most remarkably in Rangareddy district, located on the western edge of the core city [START_REF] Kennedy | Regional industrial policies driving peri-urban dynamics in Hyderabad, India[END_REF][START_REF] Ramachandraiah | The makeover of Hyderabad: Is it the 'Model' IT city?[END_REF][START_REF] Das | Making of high-tech Hyderabad: Mapping neoliberal networks and splintering effects[END_REF]). There, the state government directly promoted or provided support for private development of large-scale industrial projects, starting with HITEC City, one of its flagship projects, a first step in the creation of a cluster of export-oriented service sector activities that has been pursued, for instance with the Nanakramguda IT Park and Financial District. Here, international investors have set up and equipped globally connected platforms, like the Waverock Special Economic Zone, developed by a US-based company (see Photo 1).

Photo 1. Waverock SEZ, Nanakramguda IT Park, Hyderabad. (Photo A. Sood, 2015) The two stated rationales for instituting Greater Hyderabad were to strengthen the city's civic administration in order to provide public services, and to scale-up economic development in the metropolitan region. 5 Regarding the latter, expanding the metropolitan area was seen as a means to better engage with globalisation processes; export-oriented information technologies and bio-technologies are explicitly mentioned in the Government Order. This resonates entirely with the state government's efforts to use Hyderabad as a 'platform' for connecting the region to the global economy, articulated in the late 1990s in the Vision 2020 roadmap (Government of Andhra Pradesh 1999).

In the wake of the merger of surrounding local bodies, political and administrative sub-units were redrawn and staffing patterns reconfigured. The new administrative set-up was conceived as a three tier structure: a head office at the apex level, five zonal offices, each headed by a Commissioner, and finally 'circles', each headed by a Deputy Commissioner. As of October 2016 there were 30 circles (increased from 18, then 24). This was the number recommended by an expert committee formed to offer guidance on the rationalisation of the staffing pattern. In its 2011 report, the committee recommended hiring 2607 new administrative posts (in addition to the existing 2399) to enhance governance and accountability while improving service delivery. 6 Although the recommendations received approval both from the municipal council and the state government, the new posts were not filled, the most probable reason being that the Telangana agitation was intensifying in late 2013 and those in favour of bifurcation wanted all new hiring to take place under a new administration, more favourable to Telangana natives. 7 Then Greater Hyderabad commissioner Somesh Kumar in on record saying "It is not proper to take major decisions at this time. We will wait for the bifurcation process to be completed".8 However, in January 2016, nearly two years after bifurcation, recruitments had still not taken place. Staffing at the municipality remains not only grossly insufficient compared to the population of the city, but also highly skewed, with very few senior and middle level officers in relation to lowlevel employees. This pattern makes for a hierarchical model of urban management where senior level officers concentrate the bulk of power and responsibility.

In terms of planning, the Urban Development Authority was 'upgraded' in 2008 and transformed into the Metropolitan Development Authority. With jurisdiction over 7257 square kilometres, it is the 3rd largest urban planning authority in the country after the National Capital Region and Bengaluru Metropolitan Region. However, it was evident from interviews with planners that the capacity of the organization had not been proportionately empowered to keep pace with the new mandate, perhaps the most egregious illustration being that the statutory land use Master Plan for the metropolitan area was not prepared in-house but instead outsourced to an agency in Ahmedabad. 9 In conformity with the 74th CAA, a metropolitan planning committee has been set up in Hyderabad, but it is comprised primarily of officials, with the Chief Minister at its head. According to one of India's foremost urban experts, "The Hyderabad [Metropolitan Development Authority] is a super body with a significant mandate but singularly lacks political participation and, therefore, legitimacy and accountability" [START_REF] Sivaramakrishnan | Megacity governance: The current hierarchical model is neither sacred nor eternal[END_REF].

It can be noted that this tendency to bypass representational bodies, for instance by delaying elections, is a recurring pattern in Andhra Pradesh/Telangana politics. There were several long gaps in which municipal elections were not held in Hyderabad (1973-1986; 1991-2002) and more recently 2-year gaps: after the creation of Greater Hyderabad (2007)(2008)(2009) and after the formation of Telangana (2014 and2016). It is worth noting that significant municipal reforms (property tax, service delivery systems) that were implemented in the 1990s, notably under Chandrababu Naidu's TDP government, took place in the absence of an elected municipal council [START_REF] Kennedy | New Forms of Governance in Hyderabad[END_REF]. These deficits of democracy form part of the overall political backdrop of this region, against which current rescaling strategies must be analysed.

Significantly, the upgraded metropolitan planning authority encompassed, in addition to the existing planning area, three other entities: Hyderabad Airport Development Authority, Cyberabad Development Authority and Buddha Poornima Project Authority (Hussain Sagar Lake development). These three special authorities had been created in the late 1990s under Naidu's government as part of an effort to expedite particular large-scale projects, identified for their strategic importance. They are emblematic of a certain type of state spatial rescaling, i.e., ad hoc policy instruments that define specific regulatory frameworks for the realization of specific projects, effectively removing them from the purview of normal government departments [START_REF] Kennedy | The Politics of Economic Restructuring in India: Economic Governance and State Spatial Rescaling[END_REF]. Jurisdiction over these areas was delegated to a government agency, which took charge of all the traditional functions of the local government: general maintenance of the area, new infrastructure development and tax collection. As this suggests, this governance structure was modelled on the IALA, presented in the following section.

MAPPING THE CONTOURS OF THE IALA

The IALA was established in 1994, shortly before Chandrababu Naidu's election as Chief Minister. It is an instrument that devolves the statutory powers and functions of local bodies to a semi-autonomous agency of the state government, viz., the industrial infrastructure corporation, for selected industrial areas that are designated as IALAs. The rationale for the IALA was the local bodies' putative neglect of industrial areas; the notification of an IALA ensures stable access to resources. Concretely, it devolves powers to assess, levy and collect taxes and various fees, sanction building permits, remove encroachments and to enjoy spending powers mainly with regard to management and maintenance of infrastructure and civic services. The demarcation of particular areas as IALAs and the notification of specific powers and functions to be devolved are activated through executive fiat in the form of Government Orders. Notwithstanding, it is interesting to note that provisions for devolving powers and functions were embedded in local government legislation passed in 1994 for rural areas (Panchayati Raj Act) and similar 'exceptions' were also introduced into laws governing urban areas (Municipalities Act, Hyderabad Municipal Corporation Act). The table in the Appendix provides a listing of devolved powers and functions.

At the local scale, each IALA has an internal self-governance structure in the form of a "service society", which regroups the owners of the firms located in the IALA [START_REF] Sood | A political Economy of Premium networked space? Unpacking the IALA in Hyderabad[END_REF]. The society elects a managing committee, whose members meet each month to take decisions on day-to-day issues regarding the basic services provided by the society, as well as infrastructure maintenance. They work closely with the Commissioner assigned to each IALA, the authority in charge of assessment and collection of property taxes, approval of building rules and of providing civic services in the IALA area. This decentralised, semiautonomous governing structure resonates with that found in BIDs/CIDs in other countries.

The exact number of IALAs falling within Greater Hyderabad's boundaries remains a matter of contestation. While municipal officials cited a number of 19, industry associations listed 16. Our own mapping concluded there are 17 IALAs located wholly within city boundaries (see Figure 1). 10 Whereas these discrepancies suggest problems of transparency, field surveys indicated numerous instances of ambiguity at various levels within the local and regional administration, including uncertainty about the exact spatial boundaries covered by a given IALA, whether residential areas were included or not, whether a given IALA had indeed forwarded its share of taxes to the municipality, etc.

Until the bifurcation of the state in 2014, the IALAs in Greater Hyderabad were controlled by the Andhra Pradesh Industrial Infrastructure Corporation (APIIC). Currently, it is the Telangana State Industrial Infrastructure Corporation (TSIIC) is the territorial successor, in function and institutional form, to the APIIC for the districts comprising Telangana state. Through its control over IALAs, the TSIIC's territorial jurisdiction can be said to 'overlap' with that of Greater Hyderabad. The deployment of the IALA instrument within Greater Hyderabad creates tension as its goes against efforts to integrate the municipal space and forge an effective political scale within the expanded boundaries. It contributes to institutional fragmentation instead of building cohesion. The IALAs are also contested because they deprive the municipality of much needed fiscal revenue.

MUNICIPAL VS STATE GOVERNMENT: CONTESTING RESCALED TAX POWERS

Property tax, calculated on the basis of estimated rental values, is the single largest source of revenue in Hyderabad, like in most Indian cities. "Town Planning charges" are the second most important budgetary item. These have been very buoyant in Hyderabad, bringing in revenue that amounts to approximately 50% of that of property tax. In 2014-15, receipts from Town Planning were INR 5.3 billion11 , compared to property tax revenues of INR 10.9 billion. Among Town Planning receipts the two most important heads are building permits and impact fees, levied on certain roads, followed by betterment charges and Building development charges. As this suggests, a booming real estate sector has the potential to bring significant revenue to local government. However, Greater Hyderabad is not currently fully harvesting the fruits of property development and building activities because of the IALAs. As mentioned, the provisions governing IALAs allow for significant tax revenue and building fees to be collected and kept internally. Under the rules, only part of the property tax collected is turned over to the municipality (35% initially, although this has been increased for some IALAs) and the rest is maintained within the IALA to be used on maintenance and other improvements, at the discretion of the managing committee. 12In conducting research for this paper, we learned that many of the IALAs do not in fact share tax revenues and town planning fees with the municipality. In January 2016, municipal officials stated that in 2014-15 they had collected INR 70 million in shared property tax from IALAs, against 600 million that was owed to them. Only the Shamshabad (international airport) and Cyberabad areas, both recently developed, remitted a share of the taxes they had collected. 13 By some estimates, INR 1.5 billion is the amount of property tax currently withheld via the IALA mechanism, a figure we were unable to cross-check. As a proportion of the municipality's total revenues, this represents a very significant amount. To illustrate the tax-generating scope of some of the newly integrated areas, Serilingampally (Circle 11), where the Cyberabad and Nanakramguda IALAs are located, collected more than INR 1 billion in 2014-15 (out of 10.9 billion total for Greater Hyderabad). 14The municipal government is naturally displeased about this state of affairs. In theory at least, the revenue generated within the industrial areas could be used to improve service levels, one of the major challenges facing the current administration, thereby helping it to integrate the recently annexed areas into the more established city core. The municipal government has protested against the non-payment of taxes and tax arrears from IALAs and, more importantly, has publicly disputed the principle of maintaining IALAs within the municipal area on grounds that it fragments local state space. In 2010 the municipal council passed resolutions contesting the delegation of powers to the IALAs and appealing for the dismantlement of the IALAs and their re-integration into the municipality's jurisdiction. These challenge the statutory basis of the IALAs' powers, arguing that it was the Municipalities Act of 1994 that delegated these powers and not the law that created Greater Hyderabad (the GHMC Act) [START_REF] Sood | A political Economy of Premium networked space? Unpacking the IALA in Hyderabad[END_REF]. The municipal government has formally requested that the state government allow it to take over the industrial areas currently administered under the IALA formula. In a press report, the municipal government is quoted as saying the IALAs represent "a parallel power centre by giving building permissions and collecting property tax",15 a viewpoint also expressed in interviews with officials in the municipal authority. 16 Recovering jurisdiction over the IALAs would be a game-changer for the municipality, given the proportion of tax revenues they generate in relation to the municipality's total budget. As this makes clear, the local government (GHMC) contests the state government's claim to administer the industrial areas within municipal territory. It strives to assert its sovereignty over its official territory, basically challenging the state government to honour its promise of making the metropolitan city a genuine political scale. So far the municipal government has not succeeded in convincing the concerned state government department (Municipal Administration) to act in its favour. Doing so would involve countering the weight of the Industries & Commerce Department, and its powerful Industrial Infrastructure Corporation (TSIIC), which comes under the direct supervision of the Chief Secretary to the government. Within the state government there are no doubt conflicting positions and tensions.

BYPASS AND THE POLITICS OF EXCEPTION

The Cyberabad Development Area and the HITEC City project laid the groundwork for the application of specialized governance regimes on the fast-growing western expanse of the city. . In particular, the carving out of IALA territory from the then Serilingampally municipality provided an early preview of the contestations that came to mark the relationship between the IALA and successive municipal governments. In 2007 as many as 120 properties were taken from Serilingampally to constitute the present-day Nanakramguda IALA. To quote a press report, that territorial reorganization put the municipality in the "strange situation" of losing tax revenue yet still being held responsible to provide services to those areas.17 Reflecting on this fiscal and institutional fragmentation, one official was quoted as saying: "It is as if islands have come into existence here". This skewed fiscal allocation in favour of economic actors reflects the deeper logics animating "entrepreneurialism" in Greater Hyderabad. Many of the civil servants and planners we interviewed believed that the municipal framework remains inadequate to the task of building a global city. One retired bureaucrat, speaking informally, argued that the making of Cyberabad was in some respects too important to be left to the municipal administration [START_REF] Sood | A political Economy of Premium networked space? Unpacking the IALA in Hyderabad[END_REF]. He noted that Hyderabad had been bankrupt up until the municipal finance reforms of the late 1990s and early 2000s spearheaded by the state government. In his view, it was necessary to integrate planning, financing and governance in one agency and the municipality lacked this kind of capacity. But more importantly, according to this interviewee, the municipality's problem was its inability to think "big", as evidenced by the fact it was still building flyovers with the large revenue surpluses it had recently accrued. Another planner argued that project approvals with the municipal authority remained mired in long-winded procedures and red-tape, if not expectations of kickbacks [START_REF] Sood | A political Economy of Premium networked space? Unpacking the IALA in Hyderabad[END_REF].

Fundamental to these perspectives was a view of the city as a corporate entity; urban management was in this way an application of corporate management principles. The industrial infrastructure corporation (APIIC/TSIIC), as an ostensibly 'public sector' agency18 , perfectly fit the bill for the entrepreneurial organ of the state. Most critically, this agency could respond to needs of enterprises in the IT parks and other industrial parks and estates in a way that the municipal corporation's democratic mechanisms could not. Resonating with policy documents on the IALA concept, entrepreneurs spoke of "self-governance" as a key rationale and impetus behind the devolution of panchayat and municipal powers. The municipalities and panchayats were attentive to the demands of residents; in contrast, the IALA addressed itself to the requirements of growing enterprises. The IALA's role as special purpose enclaves suggests that it has been deployed by state-level technocrats as an instrument for planning in opposition to the trajectory towards decentralization contained in the 74 th Constitutional Amendment, in some ways in keeping with logics of bypass [START_REF] Sood | A political Economy of Premium networked space? Unpacking the IALA in Hyderabad[END_REF][START_REF] Kennedy | The Politics of Economic Restructuring in India: Economic Governance and State Spatial Rescaling[END_REF][START_REF] Idiculla | New Regimes of Private Governance. The Case of Electronics City in Periurban Bengaluru[END_REF]) and exceptionality [START_REF] Follmann | Urban mega-projects for a 'world-class' riverfront -The interplay of informality, flexibility and exceptionality along the Yamuna in Delhi, India[END_REF]. As [START_REF] Kennedy | The Politics of Economic Restructuring in India: Economic Governance and State Spatial Rescaling[END_REF] has argued for the strongly guarded ramparts of HITEC City, these enclaves serve as a vehicle for bypass, seeking to keep "competitive regions" protected from the realities of democratic contestation embodied in municipal government. At the same time, their administration through privatised forms of governance amounts to removing them from the pubic oversight, despite the fact that such enclaves benefit from public resources. These include investments in basic infrastructure and services but more importantly access to land, acquired using state government machinery or made available from existing land reserves under the stewardship of the state.

A second form of bypass is equally salient: the IALAs have played a critical role as sites of regulatory easing, with respect to matters such as building approvals. For example, in cases of buildings above 18 metres, the IALA Commissioner remains closely involved in expediting building approval applications. In fact, the procedure documents pledge that applications will be processed and sanction awarded or denied within 14 days. One interviewee who was closely associated with the industrial infrastructure corporation in the western reaches of the city appealed to the logic of bypass, arguing that the municipality's approval procedure for building plans was both long-winded and corrupt and often served to block projects [START_REF] Sood | A political Economy of Premium networked space? Unpacking the IALA in Hyderabad[END_REF]. 19Nonetheless, the evidence presented in this paper also indicates another reading. As the oft-repeated narrative of the IALAs as sites of self governance by smaller entrepreneurs reveals, the outsourcing of governance in these enclaves also creates new articulations of collectivity for the enterprises that "reside" in the industrial parks. The transfer of powers and functions among the actors that constitute the IALA -the service societies, the state government and the industrial infrastructure corporation itself -becomes subject to contestations. Together they form a parallel centre of power. Thus, far from the politics-free zones envisaged by state-level technocrats, the IALAs remain mired in the contestations that mark the "political economy of resource sharing" in metropolitan Hyderabad [START_REF] Sood | A political Economy of Premium networked space? Unpacking the IALA in Hyderabad[END_REF].

GREATER HYDERABAD VS IALAS: DEMOC RACY VERSUS SELF-GOVERNANCE?

As indicated above, the municipality contests the devolution of its statutory powers over industrial areas within its territorial jurisdiction. However, the state government has not seriously considered rolling back its use of the IALA instrument. Industry groups strongly support the state government's position. IALA office-bearers in an industrial area located in the eastern edge of the city made a provocative point about the nature of their battle against the reintegration of the Hyderabad IALAs into the municipality. They noted that the municipality's reintegration campaign was targeted less at older industrial parks, than at the newer IT Parks in Cyberabad Zone, where both property tax collections and the scope for deepening revenues was higher [START_REF] Sood | A political Economy of Premium networked space? Unpacking the IALA in Hyderabad[END_REF]). Yet, it was the SMEs and "middle class" local entrepreneurs/industrialists who led the battle against the Greater Hyderabad's claims. The schism, they argued, arose because the enterprises located in the older industrial parks had more to lose if control of infrastructure and upkeep passed out of the hands of the service societies. In fact, one interviewee suggested that in these IALAs, entrepreneurs were willing to go to any lengths, including resort to violence if necessary, to preserve the status quo.

What exactly is the most important stake for enterprises in the IALAs? In contrast to the SMEs that populate legacy industrial parks, companies locating in Cyberabad zone IALAs are far more autonomous in terms of basic services delivery [START_REF] Sood | A political Economy of Premium networked space? Unpacking the IALA in Hyderabad[END_REF]. Not only does the Cyberabad Zone house the campuses and regional headquarters of prominent IT and financial services multinationals and corporations ranging from HSBC to Microsoft, Infosys and Wipro, it is also home to an unusually large number of Special Economic Zones and business parks. Not surprisingly, average plot sizes here are far larger than those in older industrial areas and in those catering to SMEs. Nonetheless, an equally important issue may be property tax collections and how they affect SMEs. Enterprise owners fear tax hikes under a municipal regime.

IALA service society members interviewed as part of this study all complained about proposed hikes on property taxes via new assessments, and occasionally rate increases. More broadly, the industry federations have disputed estimates of potential property tax collections in the IALAs. To understand this disjunction, it is useful to note once again that not only has the industrial infrastructure corporation been the nodal agency for collection of taxes in the IALAs but that property tax assessments often depend on interpretation of the tax code. For example, in one case brought to our notice, an industrial area located in a former village incorporated into Greater Hyderabad was classified in 2007-08 rental assessment gazette as a "slum", though property values in the area had risen manifold. While in this case, the lack of revision of property tax rates may partially be to blame, municipal revenue officials also pointed to examples where industrial park properties were incorrectly classified by IALA managers. These ambiguities arise from the fragmentation of authority and oversight in the management of these areas, and from the lack of an effective mechanism for mediating contested claims.

One IALA service society member provided another perspective on the stakes, noting the precarious market conditions faced by SMEs in sectors such as engineering, where the closing down of major public sector units had killed local demand. Given the uncertain economic fortunes of these enterprises, the industrial infrastructure corporation tended to be more understanding and flexible in property tax demands than could be expected of the municipality [START_REF] Sood | A political Economy of Premium networked space? Unpacking the IALA in Hyderabad[END_REF]. In this way, the IALA appears to act as a 'buffer' between the municipal authority and enterprises located in the municipal area, raising important questions about local state sovereignty. This illustrates the importance of informal practices afforded by the IALA instrument, which leave scope for traditional forms of authority to prevail over formal rules and regulations. This perfectly demonstrates Roy's theory of informality existing "at the very heart of the state and [as] an integral part of the territorial practices of state power" (Roy 2009: 85). 20 Enterprises expect indulgence from the industrial infrastructure corporation, and interviews suggest they do indeed receive it e.g., via favourable assessments and deferment of tax obligation.

The battle for jurisdiction over industrial areas appears to be on-going although if the Telangana Industrial Policy is to be believed, the state government, or at least the Department of Industries has made its stance clear [START_REF] Sood | A political Economy of Premium networked space? Unpacking the IALA in Hyderabad[END_REF]. 21 It promises:

As a part of providing a hassle-free environment for the industrial units, the concept of Industrial Area Local Authority (IALA) will be strengthened. All new Industrial Parks that will be set up by the TSIIC will be covered under the IALA system. All existing TSIIC Industrial Parks which do not have an IALA will adopt the IALA system (Government of Telangana 2014: 16).

The "hassle-free" epithet exposes the rationale driving the extension of the IALA instrument, i.e., ease conditions for business, and equates municipal governance with "hassle".

Yet, this seemingly decisive statement was not the end of the matter. April 2015 saw a further round of claims and counter-recriminations between the municipality and "IALA representatives". It was reported that the then Greater Hyderabad Commissioner had submitted a plan in March 2015 to the State's Chief Secretary to merge 16 IALAs into the municipal area, and that the municipal government had made forcible advance claims on IALA property tax collections for the year 2015-16. 22 The IALA Federation organized another press meet and appointed a panel to liaise and advocate on the matter to the government. 23 At the time of this study, interviewed industry representative reiterated their argument for local "self governance" but matters appear to be in abeyance.

CONCLUSION

This paper examined emerging forms of governance in Hyderabad that rely on privatised management of select industrial spaces. Through executive orders and legislative amendments the subnational state government of Andhra Pradesh, and subsequently Telangana, effectively removed industrial enclaves from the purview of the municipality of Hyderabad. A large number of the latter's statutory powers and functions were effectively outsourced to an ad hoc entity, the "Industrial Area Local Authority", under the control of the powerful infrastructure development corporation (APIIC/TSIIC).

We argued that the IALA instrument represents a compelling example of a rescaling strategy on the part of the state government, allowing it to appropriate select productive spaces in the metropolitan city. This reconfiguration of state power is an expression of a wider strategy playing out over the last few decades aimed at shaping the geographies of industrial development in this region. Although state rescaling strategies can take broadly similar forms across space, their specific rationales and outcomes necessarily depend on local contexts and contingencies. The transformations underway in Indian cities have been shaped by historically inscribed forms of power relationships. Municipal governments have not experienced a significant enhancement of their prerogatives within the country's overall territorial organisation despite formal decentralization reforms and despite intense processes of spatial restructuring occurring in urban spaces over the last few decades. This is primarily because subnational state governments, in charge of urban legislation within their territories, have been disinclined to implement reforms and are especially reluctant to leave economic development in the hands of local administrations. The creation of Greater Hyderabad in 2007 was motivated by the recognition that metropolitan-scale governance was necessary to accompany economic restructuring and related urban expansion. Yet, in practice the state government has undermined the municipality's fiscal and administrative capacity. The systematic application of the IALA instrument removed the most vibrant economic areas from the municipality's jurisdiction.

Like other neoliberal-inspired instruments designed to administer "zones of exception", IALAs facilitate the circumvention of rules and regulations; they are tools to allow exceptional forms of governance (and presumably to supply exceptional levels of services). So though the decentralised, semi-autonomous governing structure of the IALA broadly resembles that of the BID/CID found in other countries, its rationale and functioning are distinct. It does not seek to supplement local government but to replace it. Our analysis has shown that it is above all a regional state strategy the primary goal of which is to ease doing business, including through administrative and territorial "flexibility", what [START_REF] Roy | Why India cannot plan its cities: Informality, insurgence and the idiom of urbanization[END_REF] has called 'calculated' informality. IALAs offer flexibility to enterprises with respect to their obligation to pay local taxes, both the amounts and the timeframe. Although the official policy framework clearly intended that a percentage of tax revenues from IALAs were to be shared with the local body, the state government has not enforced this responsibility.

As a state spatial rescaling strategy that effectively outsources the governance of industrial areas, IALAs represent a reconfiguration of local politics. By effectively removing territory from the purview the local state, they contribute to institutional fragmentation at the local scale, creating a patchwork of fiscal and regulatory regimes governed by different authorities. Yet, even as the IALA disconnects from and bypasses the local, it allows integration into political and economic circuits at other scales. As an instrument of a state government parastatal agency, the IALA draws its legitimacy from and serves the purposes of the state government; IALA's highest officers have a direct hotline to the chief minister. Likewise, the IALA instrument has been systematically deployed in the newer industrial areas, where it is showcased as an effective platform for linking firms to global markets. These firms, many of which are global concerns or domestic firms producing for global markets, no doubt find the IALA convenient as a 'single-window' for fiscal and administrative matters.

The local state (municipality) contests the devolution of its statutory powers over economic spaces within its territorial jurisdiction and has demanded their reintegration. More than a symbolic struggle over territory and sovereignty, the municipality is deprived of a large proportion of tax revenue. This case illustrates in a compelling fashion the tensions and contradictions between the "narrow" forms of state rescaling implicated in the creation of Greater Hyderabad through the massive expansion of its boundaries and the more "integral" reorganisation of state space represented by the IALAs. Although by no means settled, the shifting terrain of this contest suggests the ways in which local sovereignty and accountability are undercut by state rescaling strategies that reconfigure territorial organisation through enclaves and exceptional forms of governance.

Hyderabadis take pride in the new, globally-connected industrial areas of their city, which are widely perceived as proof that Hyderabad is successfully meeting the challenge of creating wealth and employment. Cutting them out from the municipal fabric and removing them from the collective oversight of elected officials is to symbolically separate the shining new Hyderabad from the old business as usual city. Municipal authorities are mounting resistance to the state government's rescaling strategy but it remains to seen whether they will succeed in reclaiming the territory and statutory functions that have been outsourced to the "Industrial Area Local Authorities". are grateful to two anonymous reviewers for their detailed evaluation and constructive advice for improving the article.

APPENDIX A: POWERS AND FUNCTIONS DEVOLVED

Fig. 1 .

 1 Fig. 1. Location of IALAs in Hyderabad. Source: TSIIC commissioners data; Revised GHMC Circle map 2016; HMDA map; map created by Shreya Basu, with Ashima Sood. Note: Dots representing IALAs are not drawn to scale. HMDA boundary is approximate. Legend abbreviations: TSIIC: Telangana State Industrial Infrastructure Corporation; ORR: Outer Ring Road; GHMC: Greater Hyderabad Municipal Corporation; HMDA: Hyderabad Metropolitan Development Area.

TO THE IALA Act Relevant Sections Nature of Powers and Functions AP Panchayati Raj Act, Section 147

  Adapted from APIIC website. Available online: http://www.apiic.in/industrial-area-local-authority/ Last accessed July 10, 2018.

			60 to 69, 71 and 72		Provisions relating to Taxation and Finance
			93 to 103, 120 to 123		Provisions relating to Public Safety, Convenience and
						Health; (including encroachments and obstructions)
			126 to 129, 131,	General and Miscellaneous (Gram Panchayats)
			132,134; To 142 and 145	Provisions; (including naming of streets; licensing of
						"professions"; inspection, appeal and others)
			254 to 257 and 267		Miscellaneous Provisions (recovery of arrears,
						inspections, etc)
	AP Municipalities Act,	85 to 95; 114-119; 120;	Provisions relating to Property Tax, Tax on
	Section 389-B		124; Rules 1-38 of	advertisements, duty on transfer of property
			Schedule-II	of	AP
			Municipalities Act, 1965
			134 to 145			Provisions relating to water supply
			146 to 155			Provisions relating to lighting, public and private
						drainage
			164 to 170			Provisions relating to scavenging
			171 to 183			Provisions relating to public streets
			184 to 193			Provisions relating to private streets and
						encroachments on streets
			197, 198			Prohibition against making holes and causing
						obstruction in streets; License for work on buildings
						likely to cause obstruction (as public safety)
			357 to 368			Provisions relating to powers of entry and inspection,
						enforcing	license	proceedings,	payment	of
						compensation etc
	Hyderabad Municipal	197 to 203; 204 to 206;	Municipal Taxation; Property taxes; Special provisions
	Corporation	Act,	207 to 211; 212 to 213;	concerning the water and conservancy taxes
	Section 679-F		214 to 226; 229 to 231;
			232 to 238; 264 to 278;
			282 to 289
			290 to 295; 296 to 318;	Municipal Drains; Disposal of sewage from individual
			319 to 320; 324 to 328;	sources; Water-closets, privies, urinals etc; Inspection
			332 to 336
			373 to 396; 397 to 423;	Public streets; provisions regarding private streets;
			424 to 427; 428 to 435;	Projections and obstructions; naming of streets; street
			436 to 443; 444 to 450;	lighting; dangerous structures, unlawful and other
			451 to 455; 456 to 460;	works; inspection
			461 to 463
			480 to 509			Scavenging and cleaning, Inspection and sanitary
						regulation of premises
			516 to 524			Regulation of Factories, trades, etc
	Source:

Telangana was officially created in February

when the state of Andhra Pradesh was bifurcated. Hyderabad serves as the joint capital until Andhra Pradesh's new capital, Amaravati, is built.

Most officials agreed to be interviewed on the condition of anonymity. For this reason, we have recorded only the place and date of the interview.

For a discussion of rescaling in non-Western contexts, see[START_REF] Park | State Rescaling in Non-Western Contexts[END_REF] Gimm 2013.

The Constitution (Seventh Schedule, List II, item

5) places local government in the "State List" and empowers state governments to constitute municipal bodies and determine their powers.

See Government Order No. 704, Government of Andhra Pradesh, 2005.

See "Report on GHMC staff pattern", News18, November 10, 2011, URL: http://www.news18.com/news/india/report-on-ghmc-staff-pattern-417446.html , last accessed July 4 2018.

See "GHMC sanctions 2,607 new posts", The Hindu, Hyderabad edition, August 15, 2013. See also "TRS plans Delhi civic model of administration for Hyderabad", Deccan Chronicle, May 7, 2014.

See for instance "5 yrs on, short staffed GHMC awaits recruitments", Times of India, Hyderabad edition, January 8, 2016.

Interview with planner, Metropolitan Development Authority, Hyderabad, January 11, 2016.

There are non-contiguous segments of the Nanakramguda IALA that lie outside the municipal boundary.

As of June 2018, one Euro is worth approximately 80 rupees (INR), one US dollar is worth INR 68.

Set at 35% initially, this was increased subsequently to 50% for some of the newer IALAs. In August 2017, a circular noted that the amount would be set uniformly at 35%.

Interview with official at the Finance Department, GHMC Head Office, Hyderabad January 5, 2016.

Only four circles (Khairatabad 1, Khairatabad 2, Kukatpally, and Secunderabad) generated more property taxes than Serilingampally. This information was collected at Circle 11 office, January 5, 2016.

"Controversy-hit APIIC may lose its IALA arm", Times of India, Oct 3, 2010. The report ends by stating "With transfer of powers from IALAs, the GHMC hopes it would get an additional Rs 1 billion revenue from building fee and property tax collections."

Interview with official, GHMC Head Office, Hyderabad January 5, 2016.

'Municipality caught in a piquant situation', The Hindu, February 27, 2007. Available at: https://www.thehindu.com/todays-paper/tp-national/tp-andhrapradesh/Municipality-caught-in-a-piquantsituation/article14726629.ece, last accessed on June 29, 2018.

18 The APIIC (later TSIIC) is not a pure public agency; it is a parastatal entity allowed to earn profits. Such development corporations have become hugely powerful in recent decades as land brokers. See, for instance,[START_REF] Goldman | Speculative Urbanism and the Making of the Next World City[END_REF].

Interview, Hyderabad, October 9,

We thank an anonymous reviewer for pointing out the relevance of Roy's theoretical formulation for our argument here.

A senior state government official situated this provision against the multi-year contest between the GHMC and the TSIIC over the claim to the IALA areas. Interview, Telangana Secretariat, Hyderabad, 17 August 2015.

Meanwhile, GHMC revenue officials claimed that the IALAs were yet to transfer any funds for the year 2015-16 and that transfers in previous years had fallen far short of the demand. Interview, GHMC Head Office, Hyderabad, January 6, 2016.

See also https://www.youtube.com/watch?v=0BCW8RFbqrA

Acknowledgements

Preliminary drafts of this paper were presented at various conferences: at the TISS and the IGIDR in Mumbai, the IIHM in Bengaluru, the CEIAS-EHESS in Paris and the 2017 AAG conference in Boston in the panel "Uncertainty in the city: Issues of planning, governance and citizenship". The authors thank the organizers for those opportunities and the discussants for their useful comments. We acknowledge generous support from the Centre for Social Sciences and Humanities in New Delhi and the CNRS SMI programme. The authors


Mingyang Guo

Xin Ye

Junyu He

Maykel L González-Martínez

Romain Véxiau

Dajun Goulven Quéméner

Wang

Romain Vexiau

Goulven Quéméner

Dajun Wang
email: djwang@cuhk.edu.hk

Dipolar Collisions of Ultracold Ground-State Bosonic Molecules

come   L'archive ouverte pluridisciplinaire

I. INTRODUCTION

Recent years have witnessed many breakthroughs in quantum simulation of strongly correlated many-body problems with dilute gases of ultracold particles [START_REF] Bloch | Many-body physics with ultracold gases[END_REF][START_REF] Gross | Quantum simulations with ultracold atoms in optical lattices[END_REF]. While the majority of the current investigations are still carried out with atoms interacting via the short-range contact potential, there is a great interest in extending them to ultracold particles with long-range dipolar interactions. Popular systems for realizing dipolar interactions include special atomic species with large magnetic moments which can interact via magnetic dipole-dipole interactions [START_REF] Griesmaier | Bose-einstein condensation of chromium[END_REF][START_REF] Lu | Strongly dipolar bose-einstein con-densate of dysprosium[END_REF][START_REF] Aikawa | Bose-einstein condensation of erbium[END_REF], highly excited Rydberg atoms with gigantic electric dipole moments which can interact via strong electric dipole-dipole interactions [START_REF] Lukin | Dipole blockade and quantum information processing in mesoscopic atomic ensembles[END_REF][START_REF] Saffman | Quantum information with rydberg atoms[END_REF][START_REF] Löw | An experimental and theoretical guide to strongly interacting rydberg gases[END_REF], and ultracold polar molecules (UPMs) which have permanent electric dipole moments (pEDMs) µ 0 typically on the order of one atomic unit [START_REF] Lincoln D Carr | Cold and ultracold molecules: science, technology and applications[END_REF][START_REF] John L Bohn | Cold molecules: Progress in quantum engineering of chemistry and quantum matter[END_REF].

While the dipole-dipole interaction between polar molecules is not as strong as that between Rydberg atoms, it is still much stronger than that between magnetic atoms. On the other hand, the lifetime of groundstate polar molecules is much longer than that of Rydberg atoms. Thus, UPMs hold great promises of broad applications in quantum simulation and quantum information [START_REF] Lincoln D Carr | Cold and ultracold molecules: science, technology and applications[END_REF][START_REF] Trefzger | Ultracold dipolar gases in optical lattices[END_REF][START_REF] Ma Baranov | Condensed matter theory of dipolar quantum gases[END_REF] and great experimental efforts have been devoted to bringing them into the quantum degenerate regime [START_REF] Ni | A high phase-space-density gas of polar molecules[END_REF][START_REF] Takekoshi | Ultracold dense samples of dipolar rbcs molecules in the rovibrational and hyperfine ground state[END_REF][START_REF] Peter K Molony | Creation of ultracold 87 rb 133 cs molecules in the rovibrational ground state[END_REF][START_REF] Woo | Ultracold dipolar gas of fermionic na 23 k 40 molecules in their absolute ground state[END_REF][START_REF] Guo | Creation of an ultracold gas of ground-state dipolar na 23 rb 87 molecules[END_REF]. However, collisions between UPMs have proven to be much more complicated than those between ultracold atoms. In 2010, investigations carried out with fermionic 40 K 87 Rb molecules already observed rapid loss of molecules due to ultracold chemical reactions [START_REF] Ospelkaus | Quantum-state controlled chemical reactions of ultracold potassium-rubidium molecules[END_REF].

Very recently, by controlling the chemical reactivity of bosonic 23 Na 87 Rb molecules via vibrational excitation, a direct comparison has shown that the loss is similar with and without the two-body chemical reactions [START_REF] Ye | Collisions of ultracold 23na87rb molecules with controlled chemical reactivities[END_REF].

The presence of the pEDM, the most important asset of UPMs, is also one of the main causes of the complicated collisions between them. This is already the case without the external electric fields when the induced electric dipole moment µ in the laboratory frame is zero, since the pEDM determines dominantly the long-range dispersion coefficient C 6 via the purely rotational transition contribution which is proportional to µ 4 0 /B v (with B v the rotational constant) [START_REF] Ps Żuchowski | van der waals coefficients for systems with ultracold polar alkali-metal molecules[END_REF][START_REF] Lepers | Long-range interactions between polar alkali-metal diatoms in external electric fields[END_REF][START_REF] Vexiau | Long-range interactions between polar bialkali ground-state molecules in arbitrary vibrational levels[END_REF]. A substantial pEDM µ 0 will lead to a rather large C 6 . Together with the heavy mass of typical alkali dimers, this results in a very dense four-atom density of states (DOS) near the two-body collision threshold which favors a near unity probability of the two-molecule complex formation manifesting as loss of molecules, even in the absence of chemical reaction channels [START_REF] Ye | Collisions of ultracold 23na87rb molecules with controlled chemical reactivities[END_REF][START_REF] Michael Mayle | Scattering of ultracold molecules in the highly resonant regime[END_REF].

In electric fields, a non-zero µ in the laboratory frame allows two UPMs to interact via the direct dipole-dipole interaction µ 2 (1 -3cos 2 θ)/(4π 0 R 3 ), with θ the relative orientation between the molecules and R the intermolecular distance. The anisotropic nature of the dipoledipole interaction can induce couplings between the relative motional angular momenta (partial waves L) and bring significant modifications to the long-range interaction potential and thus the collisions. Such dipolar effects between collisions of UPMs were first and so far only observed with relatively small µ in 40 K 87 Rb molecules which are identical fermions and chemically reactive [START_REF] Ni | Dipolar collisions of polar molecules in the quantum regime[END_REF].

In this work, we report our investigation of dipolar collisions in an ultracold sample of bosonic, chemically stable [START_REF] Piotr | Reactions of ultracold alkali-metal dimers[END_REF] ground-state 23 Na 87 Rb molecules with µ up to 0.7 D. For the largest µ, the characteristic length of the dipolar interaction l D = mµ 2 /4πε 0 2 reaches 0.75 µm, which is already comparable to the inter-molecular dis-tance of 1.2 µm in our highest density samples. The characteristic energy scale ε D = µ 2 /4πε 0 l 3 D ∝ 1/mµ 4 [27] decreases to 7 nK, which is much smaller than our sample temperature T . Here, m is the molecular mass and is Planck constant divided by 2π. Thus with µ increasing from 0 to 0.7 D, the collisions enter gradually the strongly dipolar regime in which the collisions are significantly different from the universal Wigner threshold regime, even though T is only 100's nK. Experimentally, following the increase of the dipolar interaction, we observed this transition as pronounced enhancement of molecular losses with step-wise features as the result of the increasingly stronger modification to the effective interaction potentials of higher and higher partial waves.

II. EXPERIMENT A. Ground-state molecule preparation and polarization

The optically trapped 23 Na 87 Rb samples were created by transferring weakly-bound Feshbach molecules [START_REF] Wang | Formation of ultracold narb feshbach molecules[END_REF] to the absolute ground state (the |v = 0, J = 0, M F = 3 level of the X 1 Σ + electronic state, with v, J and M F the vibrational, rotational, and total hyperfine quantum numbers) via the stimulated Raman adiabatic passage [START_REF] Guo | Creation of an ultracold gas of ground-state dipolar na 23 rb 87 molecules[END_REF]. The Feshbach molecules were created by magnetoassociation of Na and Rb atoms both in their |F = 1, m F = 1 hyperfine Zeeman level with the Feshbach resonance at 347.64 G [START_REF] Wang | Formation of ultracold narb feshbach molecules[END_REF][START_REF] Wang | Observation of feshbach resonances between ultracold na and rb atoms[END_REF]. Here F and m F are the quantum numbers of the atomic hyperfine level and its projection, respectively. For the population transfer, the |v = 55, J = 1 level of the A 1 Σ + /b 3 Π mixed state was used as the intermediate level [START_REF] Guo | Creation of an ultracold gas of ground-state dipolar na 23 rb 87 molecules[END_REF][START_REF] Guo | High-resolution molecular spectroscopy for producing ultracold absolute-ground-state 23 Na 87 Rb molecules[END_REF]. With a typical transfer efficiency of 93%, up to 1.5 × 10 4 optically trapped ground-state molecules could be created with near 100% quantum state purity [START_REF] Guo | Creation of an ultracold gas of ground-state dipolar na 23 rb 87 molecules[END_REF]. We note that our transfer efficiency is already among the highest for similar experiments [START_REF] Ni | A high phase-space-density gas of polar molecules[END_REF][START_REF] Takekoshi | Ultracold dense samples of dipolar rbcs molecules in the rovibrational and hyperfine ground state[END_REF][START_REF] Peter K Molony | Creation of ultracold 87 rb 133 cs molecules in the rovibrational ground state[END_REF][START_REF] Woo | Ultracold dipolar gas of fermionic na 23 k 40 molecules in their absolute ground state[END_REF][START_REF] Guo | Creation of an ultracold gas of ground-state dipolar na 23 rb 87 molecules[END_REF] and we have also verified previously that the small amount of imperfection has negligible effects on the collisions [START_REF] Ye | Collisions of ultracold 23na87rb molecules with controlled chemical reactivities[END_REF]. The cigar shaped optical trap was formed by crossing two 1064.4 nm laser beams at an angle of 20 • . The measured trap oscillation frequencies of the ground-state molecules were (ω x , ω y , ω z ) = 2π×(217(3),208(3),38(2)) Hz. With the largest sample, the calculated initial peak densities could reach 6 × 10 11 cm -3 .

Since the pEDM is along the molecular axis, it has to be oriented in the laboratory frame to induce the direct dipole-dipole interaction. To this end, we applied a DC electric field along the vertical direction and parallel to the external magnetic field of 335.2 G with two parallel Indium-Tin-Oxide glass electrodes placed outside the glass vacuum chamber [START_REF] Guo | Creation of an ultracold gas of ground-state dipolar na 23 rb 87 molecules[END_REF]. To prevent the problem of residual electric field from charge accumulation [START_REF] Steven A Moses | New frontiers for quantum gases of polar molecules[END_REF], we limited the electric field to below 1 kV/cm. Thanks to the large pEDM for 23 Na 87 Rb and the relatively small rotational constant B v , µ up to 0.7 D can already be induced with this moderate electric field.

B. Loss rate constant measurement

To investigate the dipolar effect in collisions, we measured the remaining number and the temperature of the ground-state molecule as a function of holding time for different µ. As illustrated in the inset of Fig. 1, following the increase of µ, the loss of molecules accelerates substantially. Accompanying the number loss, the sample temperatures also increase rapidly. In our previous work with samples of the same temperature range but without the electric field [START_REF] Ye | Collisions of ultracold 23na87rb molecules with controlled chemical reactivities[END_REF], we have observed that the collision is outside the Wigner regime and the loss rate constant β is temperature dependent. For the current work, to avoid this complication in the data analysis, we limited the measurement time to less than 20 ms so that the temperature increase is less than 30% thus β can be treated approximately as a constant during the course of a single measurement.

We extracted β for each µ by fitting the evolution of the molecule number N and temperature T simultaneously with the two-body loss model [START_REF] Ye | Collisions of ultracold 23na87rb molecules with controlled chemical reactivities[END_REF][START_REF] Söding | Giant spin relaxation of an ultracold cesium gas[END_REF]

dN dt = -βA N 2 T 3/2 dT dt = 1 4 + h 0 βA N T 1/2 . (1)
Here, A = (mω 2 /4πk B ) 3/2 is a constant, with ω = (ω x ω y ω z ) 1/3 the mean trap frequency. In the temperature evolution, the 1/4 term is due to the potential energy. This can be understood from the fact that inelastic collision rates are faster near the center of the sample where the density is the highest but the potential energy is the lowest [START_REF] Söding | Giant spin relaxation of an ultracold cesium gas[END_REF]. As a result, molecules removed from the trap have lower energies than the average. In addition, since the collision is outside the Wigner regime and β depends on the collision energy [START_REF] Ye | Collisions of ultracold 23na87rb molecules with controlled chemical reactivities[END_REF], following Ref. [START_REF] Söding | Giant spin relaxation of an ultracold cesium gas[END_REF], we also added the h 0 term to account for the kinetic energy contribution. For instance, the s-wave inelastic collision is faster at lower collision energies; thus, the collision prefers to remove molecules with smaller kinetic energies. We emphasize that in the Wigner regime, when β is a constant, the h 0 term is not needed. As can be seen from the results in Fig. 1, within the accessible µ, β increases in a step-wise manner. While β changes little for µ from 0 D to ≈0.2 D, it rises rapidly as µ increases further. This is followed by a plateau from µ ≈ 0.4 D to 0.55 D. For µ > 0.55 D, β starts to increase again.

III. ANALYSIS A. Qualitative understanding with the effective molecule-molecule interaction potentials

To understand our observations, we look at the effective potential [START_REF] Quéméner | Universalities in ultracold reactions of alkali-metal polar molecules[END_REF][START_REF] Quéméner | Strong dependence of ultracold chemical rates on electric dipole moments[END_REF]

LM L | V (R) |L M L = 2 L(L + 1) mR 2 - C 6 R 6 δ L,L δ M L ,M L - C 3 (L, L ; M L ) R 3 δ M L ,M L , (2)
in which the dipole-dipole interaction coefficient C 3 in Eq. 2 can be written in the partial wave basis as

C 3 (L, L ; M L ) = µ 2 4πε 0 2 (-1) M L √ 2L + 1 √ 2L + 1 × L 2 L 0 0 0 L 2 L -M L 0 M L . (3)
Here the brackets represent the 3j-symbol which for identical bosons are non-zero only between the same M L components of even partial waves. This non-diagonal, dipolar interaction term in the effective potential mixes the same M L components of different even partial waves [START_REF] Quéméner | Universalities in ultracold reactions of alkali-metal polar molecules[END_REF][START_REF] Quéméner | Strong dependence of ultracold chemical rates on electric dipole moments[END_REF], e.g. between the M L = 0 components of the s-(L = 0) and d-waves (L = 2), etc. In addition, there are also the diagonal, centrifugal term which vanishes for s-wave and the diagonal, isotropic van der Waals term characterized by the C 6 coefficient. Here, the C 6 coefficient includes a van der Waals term coming from the electronic structure, C el 6 = 9018 a.u. [START_REF] Vexiau | Long-range interactions between polar bialkali ground-state molecules in arbitrary vibrational levels[END_REF] and another one coming from the rotational structure, C rot 6 = µ 4 0 /(192π 3 2 0 B v ) = 1.3184 × 10 6 a.u., calculated from the experimental values of µ 0 = 3.2(1) D [START_REF] Guo | Creation of an ultracold gas of ground-state dipolar na 23 rb 87 molecules[END_REF] and the rotational constant B v = 2.0896628(4) GHz [START_REF] Guo | High-resolution internal state control of ultracold 23 Na 87 Rb molecules[END_REF]. The total C 6 , which is apparently dominated by the very large C rot 6 , amounts to 1.327 × 10 6 a.u. Since our molecules are identical bosons prepared in a single internal state, the scattering between them can only proceed via even partial waves.

At zero electric fields, the dipolar C 3 term vanishes and the effective potentials for s-and d-waves are depicted by the dashed curves in Fig. 2(a) and (b), respectively. Due to the large total C 6 , the barrierless swave effective potential has a large characteristic length r 6 = (mC 6 / 2 ) 1/4 of 720a 0 and a rather small characteristic energy E 6 = ( 2 /mr 2 6 ) of 3.0 µK [START_REF] Gao | Universal model for exoergic bimolecular reactions and inelastic processes[END_REF], while the d-wave components (|M L | = 0, 1, 2) coincide with each other with a barrier of 17.2 µK located at R ≈ 600a 0 . Since our average sample temperature is T ≈ 400 nK during the measurement, the scattering is dominated by s-wave.

In electric fields, when µ and thus the C 3 term in Eq. 2 are not zero, the effective potentials can be changed dramatically. As an example, Fig. 2 also shows the effective potentials for µ = 0.5 D (solid curves) obtained by diagonalizing Eq. 2 for each R. Strictly speaking, with the coupling between different partial waves induced by the non-zero C 3 term, only M L remains a good quantum number but L is not. However, for convenience, we will still distinguish the potentials with L and keep the s-wave and d-wave notations. Comparing the two s-wave effective potentials in Fig. 2(a), the µ = 0.5 D potential gets more attractive due to the increasing strength of the dipolar interaction. In Fig. 2(b), the d-wave components for µ = 0.5 D are split into three curves corresponding to |M L | = 0, 1, and 2. Both the locations and the heights of the barriers for these three potentials are significantly modified from the µ = 0 D case. Especially, due to the coupling with the g-wave (L = 4), the potential barrier for the |M L | = 1 component of the d-wave is vanishingly small which makes the d-wave scattering along this component favorable.

The modified s-wave potential can be represented by a generalized power law function -C α /R α with the power index α varying from 6 to smaller values with increasing µ [START_REF] Gao | General form of the quantum-defect theory for-1/r α type of potentials with α > 2[END_REF]. Accordingly, the definitions of the characteristic length scale and energy can also be generalized to r α = (mC α / 2 ) 1/(α-2) and E α = ( 2 /mr 2 α ) [START_REF] Gao | General form of the quantum-defect theory for-1/r α type of potentials with α > 2[END_REF]. We have calculated the s-wave potentials for µ from 0 to 0.72 D. The R = 400a 0 to 2000a 0 range of each potential is then modeled with the power law function with α and C α as free parameters. Here, we chose a lower bound smaller than r 6 so that the van der Waals interaction can be fully taken into account.

With α and C α obtained from the fit, r α and E α can then be calculated for each µ. The E α vs. µ curve is shown in Fig. 3(a). For a direct comparison, we replot in Fig. 3(b) the measured loss rate constants for µ < 0.5 D, which we call β s-wave since they can be attributed mainly to s-wave scattering. In the van der Waals dominated region (µ < 0.2 D), E α is nearly a constant and β s-wave also changes little. Near 0.2 D, when the dipolar interaction becomes comparable to the van der Waals interaction and E α starts to drop, β s-wave shows an apparent increase. For µ ≈ 0.44 D, when E α is lowered to be comparable to the sample temperature T , β s-wave reaches its maximum value bound by the unitarity limit 4π /mk, with k the scattering wave number determined by the sample temperature.

Similarly, as plotted in Fig. 3(d), the d-wave contribution β d-wave for large µ can also be treated separately by subtracting out the unitarity limited s-wave rate constant. In this case, the characteristic energies are the barrier heights E d-wave of the |M L | channels which we extract from the calculated effective potential of d-wave for each µ (Fig. 3(c)). Noticeably, the barrier height of the |M L | = 1 channel decreases with µ most rapidly and thus this channel contributes the most to the scattering. When the barrier height is still above the sample temperature, the loss rate is determined by the tunneling rate and thus small. However, when it finally lowered to a value comparable to the sample temperature at about 0.55 D, β d-wave starts to be significant and increases rapidly.

B. Quantum close-coupled modeling

Based on this understanding, we performed a quantum close-coupled (CC) calculation with L up to 10. Following the highly-resonant scattering picture as a result of the very high four-atom DOS, at the short-range, a unit probability of collision complex formation is used in our model [START_REF] Ye | Collisions of ultracold 23na87rb molecules with controlled chemical reactivities[END_REF][START_REF] Michael Mayle | Scattering of ultracold molecules in the highly resonant regime[END_REF]. Same as ultracold chemical reactions, the loss rate constant is then determined by the long-range interaction [START_REF] Ospelkaus | Quantum-state controlled chemical reactions of ultracold potassium-rubidium molecules[END_REF]. For zero electric field, we have verified previously [START_REF] Ye | Collisions of ultracold 23na87rb molecules with controlled chemical reactivities[END_REF] that the loss of non-reactive samples of 23 Na 87 Rb molecules is consistent with this model.

The CC calculation was performed using a timeindependent quantum formalism, including the internal rotational structure of the NaRb molecule, an external electric field, and a partial wave expansion between them [START_REF] Quéméner | Cold Chemistry: Molecular Scattering and Reactivity Near Absolute Zero[END_REF]. Following the complex formation model, at short-range, a boundary condition is introduced so that when the two molecules meet, they are considered lost with a unit probability (see Ref. [START_REF] Quéméner | Cold Chemistry: Molecular Scattering and Reactivity Near Absolute Zero[END_REF] or [START_REF] Wang | Tuning ultracold collisions of excited rotational dipolar molecules[END_REF] for more details). Asymptotic boundary conditions at long-range lead to the loss rate constant as a function of the applied electric field, and hence the corresponding induced dipole moment, for a given temperature. We imposed a short-range boundary condition at R min = 5a 0 and a long-range boundary condition at R max = 10000a 0 . The loss rate constants are converged within 0.1%.

Since our CC calculation includes the rotational structure, we input only the electronic coefficient C el 6 = 9018 a.u. [START_REF] Vexiau | Long-range interactions between polar bialkali ground-state molecules in arbitrary vibrational levels[END_REF], while the rotational coefficient C rot 6 follows directly from the dipole-dipole interaction in the second order. We also used the aforementioned experimental µ 0 [START_REF] Guo | Creation of an ultracold gas of ground-state dipolar na 23 rb 87 molecules[END_REF] and B v [START_REF] Guo | High-resolution molecular spectroscopy for producing ultracold absolute-ground-state 23 Na 87 Rb molecules[END_REF] values in the calculation. The C rot 6 has a ±12% uncertainty mainly from the uncertainty of the µ 0 measurement. The uncertainty of C el 6 can be safely ignored since it is more than 2 orders of magnitude smaller than C rot 6 [START_REF] Ps Żuchowski | van der waals coefficients for systems with ultracold polar alkali-metal molecules[END_REF][START_REF] Lepers | Long-range interactions between polar alkali-metal diatoms in external electric fields[END_REF][START_REF] Vexiau | Long-range interactions between polar bialkali ground-state molecules in arbitrary vibrational levels[END_REF]. The theoretical CC result without any adjustable parameters is shown as a solid black curve in Fig. 1 and agrees nicely with the measurement. Contributions from all M L components for L up to 10 are included in order to obtain this curve. In addition, the calculated individual contributions from s-wave and d-wave, as shown by the solid black curves in Fig. 3(b) and Fig. 3(d), also agree well with the measured loss rate constants β s-wave and β d-wave , respectively. We note that for the β d-wave calculation, |M L | = 0, 1 and 2 channels are all included, although the contribution from |M L | = 1 is typically sev- eral hundred times more than those from the other two channels.

C. Temperature dependence

For dipolar collisions in the Wigner regime, an approximately universal relation β ∝ µ 4(L+ 1

2 ) [START_REF] Quéméner | Universalities in ultracold reactions of alkali-metal polar molecules[END_REF][START_REF] Quéméner | Strong dependence of ultracold chemical rates on electric dipole moments[END_REF] has been verified experimentally for p-wave scattering in the 40 K 87 Rb system [START_REF] Ni | Dipolar collisions of polar molecules in the quantum regime[END_REF]. This relation, however, is not expected to hold outside the Wigner regime. Indeed, power-law fittings to our data at T = 400 nK give β ∝ µ 1.3(0.6) for the s-wave collision (Fig. 3(a)) and β ∝ µ 5.4(2.1) for the d-wave collision (Fig. 3(b)). Compared with the predicted relations β ∝ µ 2 and β ∝ µ 10 , the d-wave collision with larger µ shows a much larger deviation. In addition, as can be seen in Fig. 4 which shows β vs. µ for three different temperatures, T = 400, 700, and 1400 nK, the dependence of β on µ changes obviously with T and thus cannot be universal.

Several other important features can also be revealed from the measurements at different temperatures shown in Fig. 4. Although near 0 D β are different for different T , they all start to rise at nearly the same induced dipole moment of µ 0.2 D since E α is T independent. However, for higher sample temperatures, the s-wave unitarity limit becomes lower and thus can be reached with smaller µ. Meanwhile, with higher collision energy the d-wave barrier can also be overcome by the colliding molecules at smaller µ. As a result, the boundary between the s-wave and the d-wave regimes becomes harder to distinguish. The CC calculations depicted by the three solid curves in Fig. 4

D. Discussion

The good agreement between the CC calculation and the measurement indicates strongly that the short-range loss probability should be close to unity as we assumed in the model. This is also consistent with the lack of observable resonances for all three temperatures with the current steps of µ. Both our present study with dipolar interactions and our previous one without dipolar interactions [START_REF] Ye | Collisions of ultracold 23na87rb molecules with controlled chemical reactivities[END_REF] are consistent with the model that complex formation with near unity probability is responsible for the loss of non-reactive ultracold 23 Na 87 Rb molecules. We further argue that this most probably is general for all other available non-reactive alkali polar molecules due to the similar four-atom DOS [START_REF] Michael Mayle | Scattering of ultracold molecules in the highly resonant regime[END_REF].

The above analysis comes with a caveat. Limited by the detection method, we cannot observe the complex directly. Furthermore, there must be some loss mechanism for the complex after its formation. Otherwise, it should either collide with another molecule or eventually dissociate back into two separated molecules [START_REF] Michael Mayle | Scattering of ultracold molecules in the highly resonant regime[END_REF]. However, we have not observed any signatures of these possible post-complex-formation dynamics experimentally with or without the dipolar interactions [START_REF] Ye | Collisions of ultracold 23na87rb molecules with controlled chemical reactivities[END_REF]. Unfortunately, loss measurement in bulk samples is a rather cumbersome way to distinguish these possible contributions. It is thus very hard to claim whether it is these post-complex-formation dynamics or other unidentified mechanism are responsible for the loss of complexes. A much better method is to study molecular collisions in the single molecule level. Recently, the capability of forming single molecules in optical tweezers has been demonstrated [START_REF] Liu | Building one molecule from a reservoir of two atoms[END_REF].

IV. CONCLUSION

In this work, we investigated the ultra-low energy dipolar collisions in a previously unexplored regime. We demonstrated how dipolar interactions modify profoundly the scattering between bosonic UPMs. While a strong dipolar interaction is often desirable for many applications, it also leads to collisions with significant contributions from multiple partial waves, typically L = 0, 2, 4 ... for indistinguishable bosons and L = 1, 3, 5 ... for indistinguishable fermions. This results in strongly anisotropic interactions between molecules. We note that for strong enough dipolar interactions, e.g., as we have reached here, this kind of behavior should persist even in the zero-temperature limit. This is in stark contrast to the conventional ultracold collisions dictated by short-range van der Waals interactions which proceed via a unique single partial waves at low enough temperatures, typically L = 0 for indistinguishable bosons and L = 1 for indistinguishable fermions. This strongly dipolar regime achievable with UPMs is also beyond the scope of currently available dipolar quantum degenerate gases with magnetic dipolar interactions [START_REF] Griesmaier | Bose-einstein condensation of chromium[END_REF][START_REF] Lu | Strongly dipolar bose-einstein con-densate of dysprosium[END_REF][START_REF] Aikawa | Bose-einstein condensation of erbium[END_REF] in which ε D is still much larger than the collision energy and thus universal threshold behavior can still be observed [START_REF] Aikawa | Reaching fermi degeneracy via universal dipolar scattering[END_REF].

For future investigation on many-body dipolar physics, suppression of the undesired loss is necessary. This may be achieved by dipolar interaction mediated long-range shielding with J = 1 molecules in a specially chosen electric field [START_REF] Wang | Tuning ultracold collisions of excited rotational dipolar molecules[END_REF][START_REF] Alexander V Avdeenkov | Suppression of inelastic collisions of polar σ 1 state molecules in an electrostatic field[END_REF][START_REF] Maykel | Adimensional theory of shielding in ultracold collisions of dipolar rotors[END_REF] which for 23 Na 87 Rb is ∼ 4 kV/cm. Although this field is out of reach for our current setup, it should be experimentally accessible with electrodes inside the vacuum chamber [START_REF] Steven A Moses | New frontiers for quantum gases of polar molecules[END_REF]. Alternatively, we can also prepare molecules in deep 3D optical lattice potentials to isolate them from each other [START_REF] Danzl | An ultracold high-density sample of rovibronic ground-state molecules in an optical lattice[END_REF][START_REF] Chotia | Long-lived dipolar molecules and feshbach molecules in a 3d optical lattice[END_REF]. For a typical lattice constant of 532 nm, the currently achieved dipolar length l D is already enough to explore the strongly-correlated physics with significant non-local interaction effects.

FIG. 1 .

 1 FIG. 1. Two-body loss rate constant β vs. the induced dipole moment µ. The open circles are β obtained from fitting the number loss and heating data simultaneously to Eq. 1 with average sample temperatures of T = 400 nK. The error bars are from the fitting. The solid curve comes from a theoretical close-coupling calculation without adjustable parameters for the same sample temperature. The horizontal bar marks the inelastic s-wave unitarity limits of T = 400 ± 50 nK. Inset: example number loss measurements at different µ with error bars representing one standard deviation of typically three experimental runs.

FIG. 2 .

 2 FIG. 2. Dipolar modification to the inter-molecular interaction. (a) The s-wave adiabatic potentials for µ =0 D (dashed orange curve) and 0.5 D (solid orange curve). (b) The d-wave adiabatic potentials. For µ =0 D (blue dashed curve), the different ML components overlap with each other. The d-wave barrier with a height of 17.2 µK is located at 600a0, with a0 the Bohr radius. For 0.5 D, the anisotropic dipolar interaction breaks the degeneracy which results in three different sets of potentials with |ML| = 0 (solid red curve), 1 (solid cyan curve), and 2 (solid blue curve). The heights and the locations of the barriers are both modified substantially.

FIG. 3 .

 3 FIG. 3. Dipolar collisions for individual partial waves. (a) and (b) are the generalized characteristic energy Eα and loss rate constant βs-wave vs. µ s-wave. The vertical line near 0.22 D marks the position when the dipolar interaction starts to be comparable with the van der Waals interaction, while the vertical line near 0.44 D represents the point when Eα is lowered to ≈ T . The gray horizontal bar in (b) is the inelastic s-wave unitarity limit for T = 400 ± 50 nK. (c) illustrates the d-wave barrier heights E d-wave for different |ML| channels, and (d) shows β d-wave including contributions from all three |ML| channels with the |ML| = 1 channel playing a dominant role. The losses from |ML| = 0 and 2 are typically several hundred times slower than that from |ML| = 1. The vertical bar near 0.55 D marks the position E d-wave ≈ 5T for |ML| = 1.

  capture influences of the temperature very well.

		14	Exp: 400 nK Exp: 700 nK
		12	Exp: 1400 nK CC: 400 nK
	 (10 -10 cm 3 /s)	6 8 10	CC: 700 nK CC: 1400 nK
		4
		0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 2
			 (D)
	FIG. 4. Dipolar collisions at different temperatures. The data
	points in black squares, red circles, and blue triangles are mea-
	sured loss rates with sample temperatures of about 400 nK

(same as in Fig.

1

), 700 nK and 1400 nK, respectively. The same color-coded solid curves are CC calculations with corresponding sample temperatures. The horizontal bars indicate the unitarity s-wave loss rates with temperature ranges of 400±50 nK, 700±50 nK and 1400±100 nK from top to bottom.

V. ACKNOWLEDGMENTS

We thank Bo Gao and Olivier Dulieu for insightful discussions.

This work was supported by the COPOMOL project which is jointly funded by Hong Kong RGC (grant NO. A-CUHK403/13) and French Agence Nationale de la Recherche (grant NO. ANR-13-IS04-0004-01). The Hong Kong team was also supported by the RGC General Research Fund (grant NO. CUHK14301815) and the National Basic Research Program of China (grant NO. 2014CB921403).