E Baccelli

T Zahn

J Schiller
email: schiller@inf.fu-berlin.de

DHT-OLSR

Keywords: network, mobile, ad hoc, routing, IP, DHT, OLSR, MADPastry réseau, ad hoc, mobile, routage, IP, DHT, OLSR, MADPastry

Self-organized networking is foreseen as an important component in the Internet's near-future architecture. An essential challenge concerning the integration of this new component is the accomplishment of scalable and efficient ad hoc routing. This report proposes a new solution in this space, DHT-OLSR, based on OLSR enhanced with dynamic clustering and distributed hash table (DHT) routing. We believe that such a protocol can provide an architecture that may introduce a gradual transition from traditional IP routing towards scalable IP MANET routing.

Introduction

Self-organized networking is foreseen as an important component in the Internet's near-future architecture. An essential challenge concerning the integration of this new component is the accomplishment of scalable and efficient mobile ad hoc IP routing. While current MANET routing protocols perform well in small topologies, they generally fail to provide a functional ad hoc network when the number of nodes involved in the MANET increases. Proactive approaches (such as OLSR [START_REF] Clausen | RFC 3626: Optimized Link State Routing Protocol[END_REF]), as well as reactive approaches (such as AODV [START_REF] Perkins | Ad hoc On-Demand Distance Vector (AODV) Routing[END_REF] or Dymo [START_REF] Chakeres | Dynamic MANET On-demand (DYMO) Routing[END_REF]), require the use of network-wide control signaling that quickly saturates the available bandwidth when nodes participating in the MANET are too numerous and/or too mobile. In order to overcome this problem, specific mechanisms have to be used in conjunction with usual MANET routing. However, additional requirements are to be considered for compatibility with the Internet architecture. In particular, IP routers are basically supposed to either (i) directly forward packets as they are received, or else (ii) drop them if no appropriate route is currently available. This philosophy disqualifies some mechanisms a priori (including reactive routing), and must be taken into account in the design of a solution for scalable mobile ad hoc IP networking. One interesting approach is the cross-fertilization between the fields of mobile ad hoc routing and peer-to-peer networking since both fields are indeed dealing with similar issues, such as decentralized network formation and maintenance. For instance, specific DHT key-based approaches [START_REF] Caesar | Virtual Ring Routing: Network routing inspired by DHTs[END_REF][5] [START_REF] Pucha | Ekta: An Efficient DHT Substrate for Distributed Applications in Mobile Ad Hoc Networks[END_REF] [START_REF] Zahn | MADPastry: A DHT Substrate for Practicably Sized MANETs[END_REF] can provide very efficient routing in large scale MANETs. However, we believe that it is unrealistic to assume that such key-based routing will directly replace traditional IP routing. This paper, thus, introduces and evaluates a hybrid solution, namely DHT-OLSR, based on dynamic OLSR clustering enhanced with distributed hash tables (DHT). This solution uses both the properties of efficient key-based unicast routing to scale as desired, and the properties of OLSR routing to naturally integrate with the Internet infrastructure. Therefore, this protocol provides an architecture that may introduce a gradual transition from traditional IP routing towards scalable IP MANET routing.

INRIA

The remainder of the paper is organized as follows. The next two sections will briefly overview the principles of OLSR routing on one hand, and of MADPastry's key-based routing. The following sections will then describe in detail the functioning of DHT-OLSR, followed by a section providing experimental results. Before concluding this paper, we will briefly revisit related work.

The OLSR Protocol

In this section, we briefly outline OLSR, giving the essential facts about the protocol that are interesting in the context of this paper. For further details on OLSR, or on its performance characteristics, see [START_REF] Clausen | RFC 3626: Optimized Link State Routing Protocol[END_REF]. As a proactive link-state routing protocol, OLSR (Optimized Link State Routing) employs the periodic exchange of control messages in order to accomplish topology discovery and maintenance. This exchange results in a topology map being present in each node in the network, from which a routing table can be constructed. Basically, OLSR employs two types of control messages: HELLO messages and TC (Topology Control) messages. HELLO messages have local scope and are exchanged periodically between neighbor nodes only, essentially tracking the status of links between neighbors. On the other hand, TC messages have larger scope and are emitted periodically to diffuse link-state information throughout the entire network. This operation of diffusing a message to the entire networkalso called flooding -is optimized in OLSR with a mechanism called MPR flooding (MPR stands for Multi-Point Relay, see [START_REF] Qayyum | Multipoint Relaying: An Efficient Technique for Flooding in Mobile Wireless Networks[END_REF] for more details on this OLSR-specific technique). This optimization reduces drastically the cost of performing a flooding operation, through having each node select a minimal set of "relay nodes" (called MPRs), responsible for relaying flooded packets. As shown in Fig. 1, from the local point of view of a node flooding a packeti.e. the center node in the figure -this corresponds to only the minimal number of neighbors (the black nodes) relaying the broadcast, instead of basically all the neighbors.

MADPastry

In this section, we will present a brief overview of MADPastry that provides the DHT functionalities for the DHT-OLSR protocol. MADPastry [START_REF] Zahn | MADPastry: A DHT Substrate for Practicably Sized MANETs[END_REF] is a DHT substrate especially designed for mobile ad hoc networks. It combines AODV ad hoc routing [START_REF] Perkins | Ad hoc On-Demand Distance Vector (AODV) Routing[END_REF] and Pastry overlay routing [START_REF] Rowstron | Pastry: Scalable, distributed object location and routing for largescale peer-to-peer systems[END_REF] at the network layer to provide an efficient and low-overhead primitive for key-based routing in MANETs. For this purpose, each node in a MADPastry network assigns itself a unique virtual ID (for example by hashing its IP address, etc.), which defines its logical position on the virtual overlay ID space [START_REF] Rowstron | Pastry: Scalable, distributed object location and routing for largescale peer-to-peer systems[END_REF]. Additionally, each MADPastry message contains a message key (i.e. an ID from the virtual overlay ID space) in its header. MADPastry then routes the message to the node in the network that is currently responsible for the message key -i.e. to the node whose virtual ID is currently the numerically closest to the message key among all MADPastry nodes in the network. To avoid message broadcasts whenever possible (e.g. for route discovery), MADPastry explicitly considers physical locality in the construction of its routing tables. Clusters. Conventional (Internet-based) DHTs are largely oblivious of the actual physical topology so that two virtual neighbors can be located arbitrarily far from each with respect to the underlying physical network. This can often lead to a large overlay stretch (i.e. the ratio between the length of the physical route traveled during the lookup of a virtual key compared to the direct physical path from the source to the eventual target node) as subsequent overlay hops can literally crisscross the physical network. Due to the volatile nature of physical routes in MANETs, this effect is especially prohibitive in such environments. To exploit physical locality in the construction and maintenance of its overlay, MADPastry uses Random Landmarking [START_REF] Winter | Random Landmarking in Mobile, Topology-Aware Peer-to-Peer Networks[END_REF]. Instead of having fixed landmark nodes -which simply are not available in MANETs -fixed landmark keys are used. These keys divide the virtual overlay ID space into equal sections (e.g. 16 keys with hexadecimal IDs "0800…000", "1800…000", "2800…000", …, "E800…000", "F800…000", etc.). The nodes whose virtual IDs are currently numerically closest to the landmark keys temporarily become landmark nodes and periodically issue beacon messages. Nodes overhear these beacon messages and periodically determine the physically closest temporary landmark node (e.g. in terms of hops). If need be, a node assigns itself a new virtual ID sharing the same prefix with the closest temporary landmark node. It would then (re-)join the network under its new ID. This leads to physically close nodes forming overlay regions, or clusters, with common ID prefixes. In other words, nodes that are close to each other in the virtual overlay ID space are also likely to be close to one another physically. This is demonstrated by Fig. 2 which shows the spatial distribution of virtual ID prefixes in a 250 node MADPastry network. Equal symbols of equal shades represent equal virtual ID prefixes.

INRIA

Routing Tables. MADPastry maintains three different routing tables: a standard AODV routing table for physical routes from a node to specific target nodes, as well as a sparse Pastry routing table and a standard Pastry leaf set for indirect routing. The Pastry routing table only needs to contains as many entries as are necessary to keep a "finger" entry into each MADPastry cluster (i.e. one entry for each distinct cluster's virtual ID prefix).

Routing Table Maintenance.

To avoid the prohibitive overhead induced by routing table maintenance, the only proactive routing table maintenance that a MADPastry node performs is the periodic pinging of its "left" (i.e. the node who has the largest virtual ID smaller than the node's own) and "right" (i.e. the node who has the smallest virtual ID larger than the node's own) leaf as this is necessary to guarantee overlay routing convergence. All other routing entries are gained or updated implicitly by overhearing data packets. Routing. MADPastry routes packets based on a key. When a node wants to send a packet to a specific key, it consults its Pastry routing and/or leaf set to determine the closest prefix match, as stipulated by standard Pastry. Next, it consults its AODV routing table for the physical route (or, rather, the next physical hop on the route) to execute this overlay hop. Intermediate nodes on the physical path of an overlay hop consult their AODV table for the corresponding next physical hop. When a packet thus reaches the destination of an overlay hop, that node again consults its Pastry routing table and/or leaf set to determine the next overlay hop. This process continues until the packet reaches the eventual target node that is responsible for the packet key -i.e. whose virtual ID is the numerically closest to the packet key.

The DHT-OLSR Protocol

In this section, we introduce a novel ad hoc routing protocol called DHT-OLSR. The principle of this protocol is that each node runs OLSR locally within the cluster of nodes that are currently within a certain scope (i.e. a given number of hops). When a node needs to forward a packet towards a destination that is not currently listed in the routing table maintained by OLSR, the node uses a DHT-based Unicast to immediately forward the packet towards those more remote destinations. For this purpose, each node running DHT-OLSR maintains a regular OLSR routing table. Being a proactive routing protocol -i.e. each node tries to maintain a valid route to every other node currently in the network at all times -OLSR can provide very efficient and low-delay routing

RR n° 6194

for MANETs. As routes to all potential destinations will usually be known to a node, nodes forward data packets without buffering them. Since nodes in MANETs will likely have quite limited resources, this elimination of the need to queue packets while waiting for route discoveries will often be desirable in MANETs. On the other hand, the apparent downside to this approach is that it will incur an ever larger amount of maintenance traffic as the network size increases. In order to confine this OLSR maintenance traffic in larger networks, DHT-OLSR nodes restrict their OLSR routes to a local scope. This is achieved by simply limiting the TTL of TC messages. For example, nodes might set the TTL of the TC messages that they issue to 2 hops, which effectively places each node at the center of its own OLSR cell with a diameter of 4 hops. Hence, whenever a node receives (or originates) a data packet, it first tries to lookup the route in its OLSR routing table. If a valid route is found, the data packet is forwarded to the next hopas stated in the corresponding routing table entry -on the path towards the destination. However, in case no route could be found in the OLSR routing table, the data packet will be forwarded using DHT-style key based routing. Fig. 3 visualizes the general concept of the DHT-OLSR routing protocol. It depicts node 17 (whose virtual MADPastry ID is 75A1FF) at the center of its local scope (2 hop radius) OLSR cell. In this example, the grey-shaded area around node 17 shows the 2-hop radius in which node 17's TC messages are propagated (with the dotted circle representing the radio range of node 17). Assuming equal radio ranges, the OLSR routing table of node 17 will contain routes to all nodes within this 2-hop radius (as node 17 trivially lies within the respective OLSR cells of its 1-and 2-hop neighbors), as is depicted by the dark-shaded nodes. Note that node 17's routing table might also contain routes to some (but not necessarily all) of its neighbors three hops away (again depicted in dark grey) as they might be included in the TC messages received from 2-hop neighbors. As seen, in order to restrict the overhead of OLSR maintenance traffic, DHT-OLSR nodes only run a local scope instance of OLSR. Therefore, whenever a node wants to forward a data packet to a destination for which it cannot find a valid route in its OLSR routing table, the node engages in DHT-based Unicasting. For this purpose, each DHT-OLSR node also runs an instance of MADPastry with its low maintenance overhead to communicate with more remote nodes in the network. However, deviating from the original MADPastry, DHT-OLSR nodes will always drop data packets rather than engage in an AODV route discovery when the route for the current overlay hop is not known. Being a DHT, however, MADPastry provides key-based routing -i.e. packets are no longer routed based on an IP destination address but rather based on a virtual ID (key) from the MADPastry ID space. The question now arises how DHT key-based routing can be used to deliver a packet to its given IP destination address. To resolve IP destination addresses, DHT-OLSR uses a unicast scheme based on the approach presented in [START_REF] Zahn | DHT-based Unicast for Mobile Ad Hoc Networks[END_REF].

INRIA

In order for nodes to be able to resolve node addresses to their corresponding current virtual IDs, each DHT-OLSR periodically advertises its current virtual ID to the network. For this purpose, a node x hashes its IP address into the virtual overlay ID space to obtain its advertisement key. Using this key, the node will then simply send an advertisement packet containing its current virtual ID towards the node currently responsible for this advertisement key. That node will, upon reception of the advertisement packet, store node x's address along with its current virtual ID. Node address resolution, now, works in an analogous fashion. Whenever a node y wants to send a data packet to a give destination using the DHT unicast, it needs to resolve the destination node address in order to obtain its current virtual ID. If node y does not know the destination's current virtual ID, it will simply hash the destination node address and acquire the same advertisement key that the destination used to advertise its current virtual ID. Next, node y will send the data packet towards that advertisement key -which by definition (assuming consistent DHT routing) -will be delivered to the node that has previously received the destination node's advertisement. That node will then forward the data packet using the key provided in the advertisement and the data packet will be delivered to the given destination node -as that node will trivially be responsible for its own virtual ID. Fig. 4 depicts an example of DHT-OLSR's virtual address advertising. Node 17 intends to advertise its current virtual ID 75A1FF. For this purpose it simply hashes its IP address, which yields the following advertisement key: hash(17) B7E97D. Using MADPastry, node 17 will then send an advertisement packet containing its current virtual ID towards the node currently responsible for its advertisement key. In the first overlay hop, MADPastry routing delivers the packet to node 4 with virtual ID B207D1. In the next overlay hop, node 4 forwards the packet on to node 35 (virtual ID B7E1C1) who, then, forwards the packet to node 79 whose virtual ID B7E9A0 is numerically closest to node 17's advertisement key (B7E97D) among all other nodes' virtual IDs. Thus, node 79 is responsible for the packet and stores the tuple {17, 75A1FF} in its cache. Fig. 5 visualizes how DHT-OLSR nodes use DHT unicasts to forward data packet to remote nodes. In this example, node 51 wants to send a data packet to node 17. After discovering that there is no valid route to destination 17 in its OLSR routing table, node 51 engages in a DHT unicast to deliver the data packet. Since node 51 does not know node 17's current virtual ID, it hashes the destination address into the MADPastry virtual ID space and, by definition, acquires the same advertisement key as node 17 did for its advertisement in the example above: hash(17) B7E97D. Next, node 51 forwards the data packet towards that key. Assuming consistent DHT routing, this will deliver the packet to the same node that has previously received node 17's advertisement: in the first overlay hop, the packet is routed to node 42 with virtual ID B7E705, who then forwards the packet on to node 79 (virtual ID B7E9A0). Obviously, node

RR n° 6194

79 can now resolve node 17's address and then sends the packet towards node 17's current virtual ID. As node 17 is trivially responsible for its own virtual ID, the data packet will, thus, be delivered over node 92 (virtual ID 7FF05C) to the original destination (node 17). By using the hybrid mechanisms described in this section, a particular feature of DHT-OLSR is that it drastically reduces the impact of remote control traffic on the bandwidth available locally. Since MADPastry organizes the nodes into virtual clusters of physically close nodes, control traffic generated by MADPastry will generally not affect nodes in other clusters. Therefore, a node will mostly only have to bear the OLSR control traffic limited to the given hop radius and the leaf set control traffic from its local MADPastry cluster.

Evaluation of the DHT-OLSR Protocol

In order to evaluate the general feasibility of our approach, we have implemented DHT-OLSR in the network simulator ns-2. In order to put the performance of DHT-OLSR into perspective, its results were compared to that of a conventional proactive -OLSR -and reactive routing protocol -AODV (we are using the AODV-UU implementation 0.9.1 for ns-2.). For all simulations conducted, all nodes were moving around according to the Random Waypoint model at a constant velocity of 1.4 m/s (quick walking pace) with 0s pause time (constant node mobility).

Nodes were communicating with each other in an ad hoc mode using the 802.11 communication standard with a transmission range of 250m. We evaluated different network sizes of 50, 100, 150, 200, and 250 nodes while keeping the node density fixed at 100 nodes per square kilometer.

We have analyzed the following two metrics: Packet Delivery Ratio (PDR). This figure represents the percentage of data packets that are successfully delivered to their respective destinations. Total Amount of Traffic. Since many different packet types (e.g. AODV route requests, MADPastry packets, OLSR control packets, etc.) of various packet lengths are transmitted during a simulation run, we are not evaluating the total packet count. Instead, we are considering the total network traffic (in kilo bytes) that is created during the simulated hour. Whenever a node forwards a packet, this figure is increased by the packet size. This figure includes all routing and application level packet types (data packets, control packets, etc.).

To evaluate the performance of the different routing protocols, we chose a very simple traffic pattern. In our simulations, each node sends a data packet to a randomly picked destination every 10 seconds. Each run simulated the course of one hour. Fig. 6 shows the PDR achieved by the respective routing protocols for various network sizes. As can be seen, DHT-OLSR's PDR decreases only slightly with an increasing network size and INRIA remains at or above 90% in all scenarios considered. Both the conventional reactive and the proactive routing protocol, however, do not scale well to large network sizes and see their respective PDRs fall drastically as the number of nodes in the network increases. The reason for this that DHT-OLSR mostly uses local routes (also for MADPastry overlay routing, see [START_REF] Zahn | DHT-based Unicast for Mobile Ad Hoc Networks[END_REF]) that are updated through local control traffic (as explained in the previous section) whereas both AODV's and OLSR's control traffic affects the entire network, which consumes more and more bandwidth as the network size increases. This effect also becomes clear in Fig. 7 which shows that DHT-OLSR also produces significantly less overall traffic than the two reference protocols do. Again, this is due to the fact that DHT-OLSR nodes generally are only affected by local control traffic whereas both OLSR's and AODV's control packets are broadcast.

Related Work

There have been a number of hybrid ad hoc routing protocols proposed such as ZRP [START_REF] Haas | The Zone Routing Protocol (ZRP) for Ad Hoc Networks[END_REF]. These protocols are based on various combinations of proactive (for local scope routing) and reactive routing (for more remote destinations). A whole plethora of protocols have been proposed with OLSR [START_REF] Clausen | RFC 3626: Optimized Link State Routing Protocol[END_REF] being a typical proactive protocol and AODV [START_REF] Perkins | Ad hoc On-Demand Distance Vector (AODV) Routing[END_REF] a very popular reactive one. However, it is clearly beyond the scope of this paper to exhaustively review all of those. In this paper, we will restrict ourselves to the protocols that are considered for standardization in the IETF: one proactive approach and one reactive approach that are not designed to scale to large MANET topologies. Hence, neither hybrid combination of those approaches considered by the IETF can be expected to scale. For key-based routing in MANETs, a few approaches have been proposed recently, including Ekta [START_REF] Pucha | Ekta: An Efficient DHT Substrate for Distributed Applications in Mobile Ad Hoc Networks[END_REF], SSR [START_REF] Fuhrmann | Scalable Routing for Networked Sensors and Actuators[END_REF], VRR [START_REF] Caesar | Virtual Ring Routing: Network routing inspired by DHTs[END_REF], and MADPastry [START_REF] Zahn | MADPastry: A DHT Substrate for Practicably Sized MANETs[END_REF]. We have chosen the latter for its convenient property of explicitly considering physical locality in the construction of its routing tables.

Conclusion

In this paper, we have introduced a scalable ad hoc IP routing protocol, fit for large and mobile MANET topologies, based on a hybrid scheme mixing ideas coming from both the mobile ad hoc routing field, and the peer-to-peer networking field. Simulations so far show that DHT-OLSR outperforms the protocols standardized by the IETF in a variety of large MANET topologies. Future work on DHT-OLSR will include further evaluations of the protocol, both through simulations and real physical testbed implementations. Here, the performance of DHT-OLSR should RR n° 6194 also be compared against more ad hoc routing protocols such as the hybrid ZRP [START_REF] Haas | The Zone Routing Protocol (ZRP) for Ad Hoc Networks[END_REF] or Fisheye OLSR [START_REF] Adjih | Fish Eye OLSR Scaling Properties[END_REF]. Potential enhancements to DHT-OLSR are envisioned such as mechanisms to dynamically adjust OLSR parameters or to adapt the number of MADPastry clusters. DHT-OLSR uses efficient key-based unicast routing to scale to very large MANET topologies along with OLSR routing to naturally integrate with the Internet infrastructure. Therefore, this protocol provides an architecture that may introduce a gradual transition from traditional IP routing towards scalable IP MANET routing.

Fig. 1 .

 1 Fig. 1. Multipoint Relays of a node. A node (center) floods a message that is forwarded only by the neighbors it has selected as its MPRs (the black nodes). The range of the neighborhood of the node is depicted by the circle.

Fig. 2 .

 2 Fig. 2. Spatial distribution of virtual ID prefixes.

Fig. 3 .

 3 Fig. 3. Visualization of DHT-OLSR's routing concept.

Fig. 4 .

 4 Fig. 4. DHT-OLSR virtual ID advertising. Equal symbols of equal shade represent equal virtual ID prefixes.

Fig. 5 .

 5 Fig. 5. DHT OLSR virtual ID resolution and data forwarding. Equal symbols of equal shade represent equal virtual ID prefixes.

Fig. 6 .Fig. 7 .

 67 Fig. 6. Packet delivery ratios vs. number of nodes.

RR n° 6194


N H Ngo

H Lin

J T Hodges

H Tran
email: htran@lmd.jussieu.fr

Spectral shapes of rovibrational lines of CO broadened by He, Ar, Kr and SF 6 : A test case of the Hartmann-Tran profile

Keywords: CO, line shape, Hartmann-Tran profile, cavity ring-down spectroscopy

High signal-to-noise ratio spectra of the (3-0) band P(1) and P(17) lines of CO broadened by He, Ar, Kr and SF 6 were measured with a frequency-stabilized cavity ring-down spectroscopy system. For each collision-partner and both lines, multiple spectra were measured over pressures spanning nearly three decades up to 130 kPa. These data were analyzed with a multispectrum fitting procedure. Line shapes were modeled using the Hartmann-Tran (HT) profile with first-order line mixing as well as several other simplified profiles. The results show that for all considered collision partners (with the exception of SF 6 ), the HT profile captures the measured line shapes with maximum absolute residuals that are within 0.1% of the peak absorption. In the case of SF 6 , which is the heaviest perturber investigated here, the maximum residuals for the HT profile are twice as large as for the other collision partners.

Introduction

Carbon monoxide (CO) is one of the most abundant trace gases in the atmosphere of the Earth. It is also present in planetary and stellar atmospheres as well as in the interstellar medium. As indicated by the large number of papers devoted to its spectroscopy (see [START_REF] Wójtewicz | Low pressure line-shape study of self-broadened CO transitions in the (3←0) band[END_REF] and references therein), CO is one of the most frequently measured diatomic molecules using spectroscopic techniques. In addition to line position and intensity measurements, line shapes of CO transitions in the rotational, fundamental as well as overtone bands also have been the subject of several studies. Also, because CO is a simple diatomic molecule, it is a useful system for evaluating theoretical profiles and for testing intermolecular potential parameters. Many papers [START_REF] Bouanich | Pressure broadening of CO and OCS spectral lines[END_REF][START_REF] Duggan | Testing the validity of the optical diffusion coefficient: Line-shape measurements of CO perturbed by N 2[END_REF][START_REF] Duggan | Line-shape analysis of speeddependent collisional width inhomogeneities in CO broadened by Xe, N 2 , and He[END_REF][START_REF] Henry | Confinement narrowing and absorber speed dependent broadening effects on CO lines in the fundamental band perturbed by Xe, Ar, Ne, He and N 2[END_REF][6][START_REF] Berman | Spectral profiles for atmospheric absorption by isolated lines: A comparison of model spectra with P-and R-branch lines of CO in N 2 and Ar[END_REF][START_REF] Henry | Collision narrowing and speed dependent effect on broadening in vibration rotation line profiles perturbed by different buffer gases up to one atmosphere -difficulties in these analyses coming from the quality of the tunable diode laser emission[END_REF][START_REF] Priem | Lineshape study of the J = 3 ← 2 rotational transition of CO perturbed by N 2 and O 2[END_REF][START_REF] Predoi-Cross | Broadening, shifting, and line asymmetries in the 2←0 band of CO and CO-N 2 : Experimental results and theoretical calculations[END_REF][START_REF] Predoi-Cross | Temperature dependence of self-and N 2 -broadeningand pressure-induced shifts in the 3 ← 0 band of CO[END_REF][START_REF] Sung | Intensities, collision-broadened half-widths, and collision-induced line shifts in the second overtone band of 12 C 16 O[END_REF][START_REF] Colmont | Lineshape analysis of the J=3 ← 2 and J=5 ← 4 rotational transitions of room temperature CO broadened by N 2 , O 2 , CO 2 and noble gases[END_REF][START_REF] Devi | Spectral line parameters including temperature dependences of self-and air-broadening in the 2←0 band of CO at 2.3m[END_REF] have been devoted to studies of N 2 , O 2 and air broadening of CO lines for atmospheric remote sensing applications. The He-broadening of CO transitions was also extensively studied [START_REF] Duggan | Line-shape analysis of speeddependent collisional width inhomogeneities in CO broadened by Xe, N 2 , and He[END_REF][START_REF] Henry | Confinement narrowing and absorber speed dependent broadening effects on CO lines in the fundamental band perturbed by Xe, Ar, Ne, He and N 2[END_REF][START_REF] Henry | Collision narrowing and speed dependent effect on broadening in vibration rotation line profiles perturbed by different buffer gases up to one atmosphere -difficulties in these analyses coming from the quality of the tunable diode laser emission[END_REF][START_REF] Colmont | Lineshape analysis of the J=3 ← 2 and J=5 ← 4 rotational transitions of room temperature CO broadened by N 2 , O 2 , CO 2 and noble gases[END_REF][START_REF] Predoi-Cross | Theoretical and revisited experimentally retrieved He-broadened line parameters of carbon monoxide in the fundamental band[END_REF][START_REF] Bouanich J-P | Determination experimentale des largeurs et des deplacements des raies de la bande 0→2 de CO perturbe par les gaz rares (He, Ne[END_REF][START_REF] Boissoles | IOS and ECS line coupling calculation for the CO-He system: Influence on the vibration-rotation band shapes[END_REF][START_REF] Green | Accurate collision-induced line-coupling parameters for the fundamental band of CO in He: Close coupling and coupled states scattering calculations[END_REF][START_REF] Duggan | Testing Lineshape Models: Measurements forv= 1-0 CO Broadened by He and Ar[END_REF][START_REF] Luo | Shifting and broadening in the fundamental band of CO highly diluted in He and Ar: A comparison with theory[END_REF][START_REF] Mantz | Stabilized Tunable Diode Laser Measurements of the P(2) Line in the 13 CO Fundamental Band Broadened by Helium at Temperatures between 11[END_REF][START_REF] Henry | Confinement Narrowing of the R(0) Line in the 13 CO Fundamental Band Broadened by Helium from Room Temperature down to 40 K[END_REF][START_REF] Valentin | Line profile study down to 80 K of R(7) in the 13 CO (1-0) band perturbed by Ar and 13 CO collisional cooling with He at 6.9 K[END_REF][START_REF] Mantz | A multispectrum analysis of widths and shifts in the 2010-2260 cm -1 region of 12 C 16 O broadened by Helium at temperatures between 80 and 297 K[END_REF][START_REF] Thibault | Broadening of the R(0) and P(2) lines in the 13 CO fundamental by helium atoms from 300 K down to 12 K: Measurements and comparison with close-coupling calculations[END_REF] because this case is relevant to determining the composition of interstellar molecular clouds and the atmospheres of the outer planets. Also, many other rare gases have been considered as collision partners to investigate how CO line shapes depend on the perturber-to-absorber mass ratio [START_REF] Duggan | Line-shape analysis of speeddependent collisional width inhomogeneities in CO broadened by Xe, N 2 , and He[END_REF][START_REF] Henry | Confinement narrowing and absorber speed dependent broadening effects on CO lines in the fundamental band perturbed by Xe, Ar, Ne, He and N 2[END_REF][START_REF] Berman | Spectral profiles for atmospheric absorption by isolated lines: A comparison of model spectra with P-and R-branch lines of CO in N 2 and Ar[END_REF][START_REF] Colmont | Lineshape analysis of the J=3 ← 2 and J=5 ← 4 rotational transitions of room temperature CO broadened by N 2 , O 2 , CO 2 and noble gases[END_REF][START_REF] Bouanich J-P | Determination experimentale des largeurs et des deplacements des raies de la bande 0→2 de CO perturbe par les gaz rares (He, Ne[END_REF][START_REF] Duggan | Testing Lineshape Models: Measurements forv= 1-0 CO Broadened by He and Ar[END_REF][START_REF] Luo | Shifting and broadening in the fundamental band of CO highly diluted in He and Ar: A comparison with theory[END_REF][START_REF] Valentin | Line profile study down to 80 K of R(7) in the 13 CO (1-0) band perturbed by Ar and 13 CO collisional cooling with He at 6.9 K[END_REF][START_REF] Sinclair | Line Broadening in the Fundamental Band of CO in CO-He and CO-Ar Mixtures[END_REF][START_REF] Thibault | Raman and infrared linewidths of CO in Ar[END_REF][START_REF] Wehr | Spectral line shape of the P(2) transition in CO-Ar: Uncorrelated ab initio calculation[END_REF][START_REF] Mantz | Argon broadening of the 13 CO R(0) and R(7) transitions in the fundamental band at temperatures between 80 and 297 K: Comparison between experiment and theory[END_REF][START_REF] Yamada | The line broadening and shift effects on the CO J = 5-4 transition at 576 GHz induced by collisions with rare gases[END_REF][START_REF] Wehr | Dicke-narrowed spectral line shapes of CO in Ar: Experimental results and a revised interpretation[END_REF][START_REF] Wehr | Collisional line shifting and broadening in the fundamental P-branch of CO in Ar between 214 and 324 K[END_REF][START_REF] Bouanich | Pressure-Induced Lineshifts in the 2 ← 0 Band of CO Self-Perturbed and Perturbed by He, Kr, O 2 , and N 2[END_REF][START_REF] Markov | Line broadening and shifting studies of the J = 5 ← 4 transition of carbon monoxide perturbed by CO, N 2 , and O 2[END_REF][START_REF] Markov | Broadening and shifting studies of J=54 carbon monoxide line perturbed by Ne, Ar, and Kr[END_REF][START_REF] Predoi-Cross | Xenon-broadened CO line shpaes in the fundamental band at 349 K[END_REF]. All of these studies indicate that measured CO line shapes deviate from the often-used Voigt profile. Given that deviations between theory and experiment can reach a few percent of the peak absorption, increasingly demanding applications such as remote sensing of the Earth's atmosphere require improved models that account for higher-order effects influencing the line shape. These effects include: collisional-induced velocity changes (Dicke narrowing effect [START_REF] Dicke | The Effect of Collisions upon the Doppler Width of Spectral Lines[END_REF]), speed dependence of the collisional width and shift, correlation between velocity-and internal-state-changing collisions and collisional interference between lines (line mixing). Depending on the specific molecular system, line and pressure range under consideration, all or some of these effects may be important. For isolated lines (no line mixing), various non-Voigt models have been used to represent the measured spectra. These include the Galatry (soft-collision model) [START_REF] Galatry | Simultaneous effect of doppler and foreign gas broadening on spectral lines[END_REF] and Rautian (or Nelkin-Ghatak, hard-collision model [START_REF] Nelkin | Simple binary collision model for Van Hove's Gs(r,t)+[END_REF][START_REF] Rautian | The effect of collisions on the Doppler broadening of spectral lines[END_REF]) profiles for the Dicke narrowing, the speed dependent Voigt profile [START_REF] Berman | Collisional Width and Shift[END_REF] for the speed dependence effect, and finally the speed dependent hard-or soft-collision model which accounts for speed dependence and Dicke narrowing. The choice of line profile used in the data reduction can have a large influence on retrieved parameters. For example, the fitted line broadening parameter can be sensitive to the choice of line profile used in the model.

For CO, a number of line profiles have been used to model the measured spectra, although only some studies devoted to the line shape issue of this molecule are recalled here. In Ref. [START_REF] Duggan | Testing the validity of the optical diffusion coefficient: Line-shape measurements of CO perturbed by N 2[END_REF], Duggan et al. used a combination of the soft-collision model for the translational degrees of freedom and a simple exponential decay for the optical coherence to fit measured spectra of CO lines in N 2 . They showed that the fitted narrowing parameter (also called the optical frequency of velocity-changing collisions) is not linear with pressure and the corresponding optical diffusion constant could be up to several times smaller than that deduced from mass diffusion. When fixing the narrowing coefficient to that calculated from the mass diffusion constant, they observed that the time correlation function for the evolution of the optical coherence could not be described by a simple exponential decay. In Ref. [START_REF] Duggan | Line-shape analysis of speeddependent collisional width inhomogeneities in CO broadened by Xe, N 2 , and He[END_REF], this deviation was attributed to the speed dependence of the line broadening.

Consequently, a combination of soft-collision and speed dependence models [START_REF] Ward | Correlation Effects in the Theory of Classical Theory[END_REF] was fit to measured spectra of CO broadened by He, N 2 and Xe. In a similar fashion, a model given by the convolution of hard-collision and speed dependence [START_REF] Ward | Correlation Effects in the Theory of Classical Theory[END_REF] profiles was also fit to measured spectra of CO with various collision-partners [START_REF] Henry | Confinement narrowing and absorber speed dependent broadening effects on CO lines in the fundamental band perturbed by Xe, Ar, Ne, He and N 2[END_REF][START_REF] Berman | Spectral profiles for atmospheric absorption by isolated lines: A comparison of model spectra with P-and R-branch lines of CO in N 2 and Ar[END_REF]. The speed dependent Galatry profile proposed in [START_REF] Ciuryło | Speed-dependent pressure broadening and shift in the soft collision approximation[END_REF] was used to model measured spectra of CO in He and Ar [START_REF] Duggan | Testing Lineshape Models: Measurements forv= 1-0 CO Broadened by He and Ar[END_REF]. The authors claimed that this model is not sufficient for CO in Ar. Rather, one may need to account for the correlation between velocity-changing and dephasing collisions. Finally, in Refs. [START_REF] Wehr | Dicke-narrowed spectral line shapes of CO in Ar: Experimental results and a revised interpretation[END_REF][START_REF] Wehr | Collisional line shifting and broadening in the fundamental P-branch of CO in Ar between 214 and 324 K[END_REF] the speed dependent billiard-ball model was compared to measured spectra of CO in Ar. This analysis requires accurate calculations for the speed dependent width and shift and assumes a hard-sphere model for velocitychanging collisions. Although leading to very good agreement with measured spectra [START_REF] Wehr | Collisional line shifting and broadening in the fundamental P-branch of CO in Ar between 214 and 324 K[END_REF], this model is too computationally intensive and unsuitable for applications such as radiative transfer calculations.

The IUPAC recently recommended the use of the Hartmann-Tran profile (HTp) for high resolution spectroscopy [START_REF] Ngo | An isolated line-shape model to go beyond the Voigt profile in spectroscopic databases and radiative transfer codes[END_REF][START_REF] Tennyson | Recommended isolated-line profile for representing high-resolution spectroscopic transitions (IUPAC technical report)[END_REF] as a reference line profile for data analysis. This profile is a version of the correlated speed-dependent Rautian profile of Pine [START_REF] Pine | Asymmetries and correlations in speed-dependent Dicke-narrowed line shapes of argon-broadened HF[END_REF] with the speed-dependence of collisional width and shift given in the quadratic form proposed by Rohart et al. [START_REF] Priem | Lineshape study of the J = 3 ← 2 rotational transition of CO perturbed by N 2 and O 2[END_REF][START_REF] Rohart | Speed dependence of rotational relaxation induced by foreign gas collisions: Studies on CH 3 F by millimeter wave coherent transients[END_REF]. The HTp profile takes into account Dicke narrowing, speed dependence effects and correlation between velocity-changing and internal-state-changing collisions. In addition, collisional interferences between lines can be easily introduced by invoking the first-order approximation of Rosenkranz [START_REF] Ngo | An isolated line-shape model to go beyond the Voigt profile in spectroscopic databases and radiative transfer codes[END_REF][START_REF] Ciuryło | Speed-dependent line mixing profiles[END_REF][START_REF] Rosenkranz | Shape of the 5 mm oxygen band in the atmosphere[END_REF]. Importantly, this profile can be computed nearly as rapidly as the Voigt profile. Several tests with some molecular systems showed that this profile can describe the measured line shape with a precision of about ±0.1% of the peak absorption (see [START_REF] Tennyson | Recommended isolated-line profile for representing high-resolution spectroscopic transitions (IUPAC technical report)[END_REF] and references therein). Because of the large number of parameters (i.e. at a given temperature, one needs four parameters for the line width, shift and their speed dependences, one parameter to represent the Dicke narrowing, and one parameter for the velocity and internal-state changing collision correlation), and because of numerical correlations between some of these parameters, high signal-to-noise spectra recorded over a wide pressure range are required for precise parameter retrieval [START_REF] Ngo | An isolated line-shape model to go beyond the Voigt profile in spectroscopic databases and radiative transfer codes[END_REF][START_REF] Tennyson | Recommended isolated-line profile for representing high-resolution spectroscopic transitions (IUPAC technical report)[END_REF].

To the best of our knowledge, no validation of the HT profile under such conditions has been performed for CO with various collision partners.

In this work, we quantify how well the HT profile models foreign-broadened CO line shapes. Room temperature data were acquired for broadening by gases of different mass (He, Ar, Kr, SF 6 ) taken over a pressure range spanning three decades. High signal-to-noise spectra of the P(1) and P(17) lines in the (3-0) vibrational band of 12 C 16 O mixed with each of these collision-partners were measured with a frequencystabilized cavity ring-down spectroscopy (FS-CRDS) apparatus, developed at the National Institute of Standard and Technology (NIST) in Gaithersburg. These spectra were analyzed using multispectrum fitting of the line shape model to the measured spectra, whereby the model parameters were adjusted simultaneously for all pressure conditions.

In the remainder of this article, we describe the FS-CRDS measurements and the analysis procedure (Sec.2). The fitting results and the obtained line parameters are reported and discussed in Sections 3 and 4 while conclusions and related perspectives are given in Sec. 5.

Experimental details and spectrum analysis

A detailed description of the present system, which is based on the original FS-CRDS spectrometer discussed in Ref. [START_REF] Hodges | Frequency-stabilized single-mode cavity ring-down apparatus for high-resolution absorption spectroscopy[END_REF], can be found in Ref. [START_REF] Lin | Cavity ring-down spectrometer for highfidelity molecular absorption measurements[END_REF]. Only an overview of the experiment will be given here. The central feature of the cavity ring-down spectrometer is an actively lengthstabilized optical resonator within a vacuum chamber. The resonator comprises two high-finesse, double-coated (F =/(1-R) = 108,000 near  = 1570 nm where R is the intensity reflectivity, and F=60 near  = 633 nm) spherical mirrors separated by L=139 cm. The optical resonator length is stabilized in a closed-loop-servo configuration by maximizing the transmission of an I 2 -stabilized HeNe reference laser which has a long term stability of ±10 kHz. Actuation of the cavity length is achieved by displacing one of the resonator mirrors with a piezoelectric device. The probe laser beam is emitted by a single-frequency (< 500 kHz short-term bandwidth) continuous-wave external cavity diode laser which is amplified to 30 mW of power by a booster-optical amplifier (BOA) and mode-matched into the ring-down cavity. At each frequency step, the probe laser frequency was actively locked to a cavity TEM 00 mode, with the starting frequency of each scan measured to within 100 kHz by comparison to a Cs-clock-referenced optical frequency comb (OFC) as described in Ref. [START_REF] Lin | Cavity ring-down spectrometer for highfidelity molecular absorption measurements[END_REF].

Ring-down events were initiated by using the BOA as an optical switch to extinguish the probe laser beam. 320 decay signals per frequency step were measured with an InGaAs detector/photoreceiver and digitized with a 16-bit board at a sampling rate of 10 Msamples s -1 . In order to determine the cavity decay time , the signals were modeled using the three-parameter function / ()

t b s t Ae y   
where A is the signal amplitude at time t=0 and y b is the baseline offset. This exponential model was fit to each ring-down decay signal by varying all three parameters, yielding a distribution of measured time constants at each frequency step characterized in terms of a mean value  and standard deviation   . We obtained acquisition rates of 150 Hz at each frequency step, and fractional uncertainties /   = 0.04 % resulting in an empty-cavity noise- equivalent absorption coefficient (NEA) of 7×10 -12 cm -1 Hz -1/2 and minimum detectable absorption of 5×10 -12 cm -1 .

Absorption spectra were acquired by step-wise tuning the laser frequency through successive longitudinal modes q of the ring-down cavity which are separated by the cavity free spectral range f  , nominally equal to 109 MHz. In order to account for variations in f  with gas density and composition, the mode spacing was measured for each spectrum using the OFC at the beginning and end of the scan and by counting mode orders. This method yielded an uncertainty of less than 5 kHz in f  for all spectra.

The total loss-per-unit length of a ring-down cavity equals the sum of the base losses associated with the high-reflectivity mirrors  0 =(1-R)/L, the frequency-dependent absorption coefficient of the sample  ab ( q ), and other weak and slowly varying losses such as Rayleigh scattering that can be combined with the mean mirror losses 0

 . Here qf q    
is the frequency detuning relative to the first point of the spectrum. The base losses also exhibit sinusoidal oscillations (etalons) about 0  given by ()

et q  
which are caused by coupled-cavity effects [START_REF] Courtois | Differential cavity ring-down spectroscopy[END_REF]. In the present study, the dominant etalon had a period of 26 GHz with an amplitude 10 -9 cm -1 , which is approximately 0.5% of 0  . This subtle feature in the spectrum baseline is caused by etaloning between the planar and concave surfaces of the 4-mm-thick ring-down cavity mirrors. With the foregoing definitions, measured spectra were modeled by

0 1 ( ) ( ) () et q ab q q c             (1)
in which c is the speed of light. Measurements of the cavity free spectral range, mode-order difference q, and decay rates  -1 , thus provided the x and y axes of the spectra, respectively. Using this approach, the spectrum axes were directly obtained in terms of precise and accurate observations of laser frequency and ring-down decay time.

Absorption spectra were acquired at room temperature on samples comprising binary mixtures of high-purity (99.998 %) CO diluted by the He, Ar, Kr and SF 6 buffer gases. To this end, a small amount of CO (300 Pa -450 Pa) was introduced into the evacuated cavity and back-filled with each buffer gas to a maximum pressure close to atmospheric pressure. This technique resulted in CO molar fractions spanning 0.25 % to 0.4 %. For each binary mixture, spectra of the P(1) and P(17) lines were acquired for 6 to 9 static pressure conditions, beginning at the maximum pressure and stepwise pumping to lower pressures. The resulting measurement conditions ranged from 0.13 kPa to 130 kPa and are given in Table 1. The measured spectra were fit using the HT profile and with simplified models: the speed dependent hard collision model (SDHC [START_REF] Lance | On the Speed-Dependent Hard Collision Lineshape Models: Application to C 2 H 2 Perturbed by Xe[END_REF]), the speed dependent Voigt profile (SDV), the hard-and soft-collision models (HC and SC) and the Voigt profile (V). The quadratic forms [START_REF] Priem | Lineshape study of the J = 3 ← 2 rotational transition of CO perturbed by N 2 and O 2[END_REF][START_REF] Tennyson | Recommended isolated-line profile for representing high-resolution spectroscopic transitions (IUPAC technical report)[END_REF][START_REF] Rohart | Speed dependence of rotational relaxation induced by foreign gas collisions: Studies on CH 3 F by millimeter wave coherent transients[END_REF] for the speed dependences of the line width and shift were used, i.e.: ( )

( ) ( )[( ⁄ ) ⁄ ]
where ̃ √ ⁄ is the most probable speed for an absorbing molecule of mass . Detailed expressions of these profiles can be found in [START_REF] Ngo | An isolated line-shape model to go beyond the Voigt profile in spectroscopic databases and radiative transfer codes[END_REF] and references therein. For the HT profile, the normalized ( ) line shape is a function of eight parameters [START_REF] Ngo | An isolated line-shape model to go beyond the Voigt profile in spectroscopic databases and radiative transfer codes[END_REF],

( ) ( ), (2)
where  0 is the unperturbed position of the line, is the Doppler broadening, is the frequency of velocity-changing collisions (the Dicke narrowing effect, described by the hard-collision limit within the HT profile) and is the correlation parameter which accounts for temporal correlation between velocity-changing and internal-state-changing collisions. The line parameters of the HT profile vary simply with the total pressure : and are constant while , , , and are proportional to . Note that the SDHC model is obtained from Eq. ( 2) when is set to zero. When , we obtain the SDV profile while Eq. ( 2) becomes the HC model when . Finally, the Voigt profile is obtained if all higher-order line shape parameters are zero ( ). In addition, the line mixing (LM) effect has also been taken into account in our fits through the use of the first-order approximation [START_REF] Ngo | An isolated line-shape model to go beyond the Voigt profile in spectroscopic databases and radiative transfer codes[END_REF][START_REF] Rosenkranz | Shape of the 5 mm oxygen band in the atmosphere[END_REF]. With this assumption, the magnitude of the first-order line mixing effect is given by the (pressure dependent) coefficient Y.

For each line and for a given perturber, a set of calculated line profiles was simultaneously fit to multiple spectra (measured at various pressures) by global least-squares adjustment of the fitted parameters, similarly to the multispectrum fitting technique of Ref. [START_REF] Benner | A multispectrum nonlinear least squares fitting technique[END_REF]. The set of shared parameters (i.e. those considered for all pressures) were: with , , , and . For each spectrum, the integrated line intensity and a linear baseline (with etalon) representing the zero absorption level was also retrieved. All fitted spectra shown below were normalized to have a peak absorption of unity (dimensionless) at line center. The Doppler contribution was calculated from the measured temperature and frequency for each transition and then held constant during the fits.

Fit residuals and obtained parameters

CO-He

Figure 1 presents the fit residuals obtained by fitting the two considered lines of CO broadened by He with various line shape models. Note that for the non-Voigt profiles, only the results obtained with line mixing are presented. Spectral fits with these profiles and without line mixing were carried out but are not plotted here. The obtained parameters for each model are reported in Table 2. We can observe that the value of the linemixing parameter (Y/P) is nearly independent of the line shape model used. Comparison of these values and the fit residuals obtained with and without (not shown here) line mixing show that line mixing for the P(1) line is more important than for the P(17) line. As expected, the Voigt profile leads to the worst fit residuals in comparison to the results obtained with the other profiles. Considering only the Dicke narrowing effect, the SC model leads to much better results than does the HC model. This is consistent with theoretical predictions [START_REF] Galatry | Simultaneous effect of doppler and foreign gas broadening on spectral lines[END_REF][START_REF] Hartmann | Collisional effects on molecular spectra[END_REF] which show that the SC model is more suitable than the HC model when the active molecule is much heavier than the perturber. The remaining residuals can be explained by the contribution of the speed dependence effect, which is neglected by the SC and HC models. The speed dependent Voigt profile leads to good fits of the measured spectra, with fit residuals being almost within the experimental noise below 0.1% of the peak absorption. Note that comparison between the various profiles can be also done through the standard deviation of the fits (i.e. rms) as reported in Table 2. As discussed in [START_REF] Duggan | Testing Lineshape Models: Measurements forv= 1-0 CO Broadened by He and Ar[END_REF] for the CO/He system, the characteristic decay time of the optical coherence, given by (with GHz at 100 kPa), is seven-fold smaller than the relaxation time of the velocity, given by ( GHz at 100 kPa). This quantity is the rate of velocity-changing collisions based on the mass diffusion coefficient which is calculated using a simple Lennard-Jones potential with parameters given in [START_REF] Hirschfelder | Molecular Theory of Gases Liquids[END_REF]. In this case, we can safely assume that the correlation between velocity-changing and internal-state-changing collisions is negligible. With this assumption, the HT profile reduces to the SDHC model (by fixing in Eq. ( 2)). The latter is then used to fit the measured spectra of CO in He. As can be observed in Fig. 1, the fit residuals in this case are slightly improved with respect to the SDV profile and completely within the experimental noise. The fitted Dicke narrowing parameter (see Table 2) is close to zero showing that the contribution of this effect should be small for CO in He. Consequently, the measured spectra of CO in He over the considered pressure range can be precisely modeled using the SDV profile.

CO-Ar

The results obtained for CO in Ar are plotted in Figure 2. The observed non-Voigt effects for this system are much more important than for CO in He, as was also discussed in Refs. [START_REF] Colmont | Lineshape analysis of the J=3 ← 2 and J=5 ← 4 rotational transitions of room temperature CO broadened by N 2 , O 2 , CO 2 and noble gases[END_REF][START_REF] Duggan | Testing Lineshape Models: Measurements forv= 1-0 CO Broadened by He and Ar[END_REF]. For the two lines considered here, the HC and SC models give similar fit residuals. The SDV profile leads to better fit residuals than the HC and SC models for the P(1) line whereas for the P(17) line, the opposite situation is observed.

Obviously, both speed dependence and velocity-changing collision effects contribute to the line shape because none of the SDV, HC and SC models result in a perfect fit to the measured spectra. The mass-diffusion-coefficient-derived value kHz/Pa, which characterizes the velocity relaxation, is more comparable to the value of (see Table 2) than for the case of CO in He. Consequently and consistent with the claim in Ref. [START_REF] Duggan | Testing Lineshape Models: Measurements forv= 1-0 CO Broadened by He and Ar[END_REF], we expect that the correlation between velocity-changing and internal-state-changing collisions should contribute to the line shape of CO in Ar. When fitting measured spectra of CO in Ar with the HT profile, we fit all the line shape parameters, including the Dicke narrowing.

Note that, in some studies, because of the limited signal-to-noise ratio and/or a narrow pressure range, the Dicke narrowing parameter is often fixed to in order to decrease the number of floated parameters (e.g. [START_REF] Larcher | Spectral shape parameters of pure CO 2 transitions near 1.6µm by tunable diode laser spectroscopy[END_REF][START_REF] Le | Isolated line shape of methane with various collision partners[END_REF]). This approximation can be safely used for systems for which the relative contribution of the Dicke narrowing effect to the line shape is small. However, in the general case, because of the different approximations made in derivation of the HT profile (quadratic speed dependences of the line width and shift, hard collisions for the velocity changes), the value of beta should not be equal to .

For the P(1) line, the value of retrieved with the HT profile (see Table 2) is close to . The much better fit residuals obtained with the HT profile (better than ±0.1%) with respect to those obtained with the SDHC demonstrates that the correlation between velocity-and internal-statechanging collisions has to be taken into account. These results are consistent with the very recent work of [START_REF] Kowzan | Line positions, pressure broadening and shift coefficients for the second overtone transitions of carbon monoxide in argon[END_REF] which also shows that the HTp leads to better fit of spectra of CO in Ar than the SDHC. For the P( 17) line, the HT and SDHC profiles lead to similar fit residuals and line shape parameters.

CO-Kr and CO-SF 6

The results obtained for CO in Kr and in SF 6 are plotted in Figures 3 and4, respectively. These results are quite similar to those of CO in Ar. For these two collision-partners (as for the CO-Ar case) the SDV profile gives better fit residuals than do the hard-and soft-collision models for the P(1) line. However, for the P(17) line the HC and SC models lead to slightly better fits to the data than does the SDV profile (see also the values of the root mean square in Table 2). It is clear that with such a large pressure (or ) range, one needs to account for both the speed dependence and Dicke narrowing to accurately model the observed line shape. The Dicke narrowing parameters deduced from the mass diffusion coefficient are 9.23 and 22.16 kHz/Pa for CO in Kr and SF 6 respectively. These values are comparable to the corresponding values of the line broadening coefficients (see Table 2). Therefore, again, when using the HT profile, we have chosen to fit all the line shape parameters and not to fix the Dicke narrowing parameter to . For the two lines that we considered, the HT profile leads to better fit residuals than does the SDHC model. However, the HT fit residuals are clearly larger than the experimental noise and exhibit relatively large systematic structures, particularly for the P(1) line of CO in SF 6 (up to ±0.2%). As shown in Refs. [START_REF] Vizia | Speed dependence of collision parameters in the H 2 18 O near-IR spectrum: Experimental test of the quadratic approximation[END_REF][START_REF] Lisak | Application of the Hartmann-Tran profile to analysis of H 2 O spectra[END_REF] for heavy perturbers, the speed dependence effect is increasingly important and the quadratic approximation is probably not sufficiently realistic to describe the speed dependence of the line width and shift.

Also, for perturber much heavier than absorber, the hard collision approximation is not adequate for realistic description of velocity changing collision. To determine the influence of these approximations on the spectral shape, comparison between the HTp results with ab initio calculations [START_REF] Hartmann | Abinitio calculations of the spectral shapes of CO 2 isolated lines including non-Voigt effects and comparisons with experiments[END_REF][START_REF] Tran | Spectral shapes of Ar-broadened HCl lines in the fundamental band by classical molecular dynamics simulations and comparison with experiments[END_REF][START_REF] Hartmann | Line broadening of confined CO gas: From molecule-wall to molecule-molecule collisions with pressure[END_REF] would be helpful.

Discussion

For all collision-partners except He, we have shown that the HT profile provides the best fits to the measured spectra by comparison to the other considered profiles. The HT profile can model the measured spectra of CO with these collision-partners over a wide pressure range with a relative precision better than ±0.2% of the peak absorption. This model accounts for the three principal collisional effects that influence the line shape: velocity-changing collisions, the speed dependences of the line width and shift, and correlation between velocity-changing and internalstate-changing collisions. Because of the different physical approximations used to derive the HTP model such as the hard-collision limit for the collision-induced velocity changes, and the quadratic form for the speed dependence, the resulting line shape parameters should be considered as effective quantities that do not exactly reflect the underlying physics. In the following, we will nevertheless discuss the obtained line shape parameters.

In Table 2, it is evident that the fitted line width strongly depends on the model used. The Voigt profile leads to a smaller line width with respect to the more advanced line shape models. For example, the difference between the line width obtained by Voigt and HT profile can be as much as 8 %. Conversely, the pressure shift is nearly independent of the line shape used, because it is primarily determined by the variation of the peak absorption position with pressure. Fitted values of the speed dependence of the line shift are also independent of the line shape model used (i.e. SDV, SDHC and HT) and are relatively small. As expected, for all considered rare gases (with the exception of the SF 6 P(17) line) the ⁄ ratio obtained from the SDV and HT profiles increases with the perturber mass, as also observed previously in [START_REF] Colmont | Lineshape analysis of the J=3 ← 2 and J=5 ← 4 rotational transitions of room temperature CO broadened by N 2 , O 2 , CO 2 and noble gases[END_REF][START_REF] Seleznev | Shape of collisionbroadened lines of carbon monoxide[END_REF]. For the Dicke narrowing parameters, as shown in Table 2, the values obtained with the HT profile increase with the perturber mass. Within the hard-sphere interaction approximation, this can be explained by the increasing value of the corresponding mean hard-sphere diameter with the perturber mass [START_REF] Hirschfelder | Molecular Theory of Gases Liquids[END_REF].

From the values of  2 and  0 obtained by using the (quadratic) speed dependent profiles, the corresponding hypergeometric speed

dependence [i.e.   r r r r (v ) (v ) v / v    
] parameters can be deduced using Eq. ( 11) of [START_REF] Rohart | Lineshapes of the 172 and 602 GHz rotational transitions of HC15N[END_REF]. The values of can then be related to the empirical collisional interaction potential ( ) with . The values of q can thus be determined and considered as an indicator of the implied interaction potential. For CO in He and for the two lines considered here, from the SDV profile results we found that is very close to unity, which corresponds to the case of a hard-sphere interaction ( ). Similar results are obtained with the SDHC model. The broadening mechanism for CO in He is thus probably mainly caused by the repulsive wall of the potential at short range [START_REF] Hirschfelder | Molecular Theory of Gases Liquids[END_REF]. This result is also confirmed by the fact that the broadening coefficient of CO in He is nearly independent of the rotational quantum number (see Table 2). For CO in Ar, the value of , deduced from the ratio ⁄ obtained with the SDV model, is 5.0 and 7.2 for the P(1) and P( 17) lines respectively, while with the HT profile, it is 6.0 and 5.3. This demonstrates that for CO in Ar, the broadening mechanism is mostly driven by the long-range dispersive interaction potential, in opposition to the case of CO in He. For CO in Kr, the value of deduced from the ⁄ ratio obtained with the SDV profile is 6.5 and 7.1 for the P(1) and P(17) lines while it is 9.0 and 5.6, respectively for CO in SF 6 . With the HT profile, the value of is 16.5 and 6.0 for the P(1) and P(17) lines for CO in Kr whereas it tends to infinity ( is very close to 1) and is 4.8 for CO in SF 6 . Except for the result obtained with the HT profile for the P(1) line of CO in Kr and SF 6 , these results show that, the long-range dispersive force seems to play a dominant role in the broadening mechanism for CO in Kr and SF 6 .

Table 2: Fitted parameters with the various models used. and are in units of kHz/Pa while is in units of 10 -5 kPa -1 and is dimensionless. These quantities can be converted to conventional units using the identity, 1 cm -1 atm -1 = 295.872 kHz Pa -1 . We also report the frequency of velocitychanging collisions is based on the mass diffusion coefficient which is calculated assuming simple Lenard-Jones potentials with parameters given in [START_REF] Hirschfelder | Molecular Theory of Gases Liquids[END_REF] for each collision-partner. The reported uncertainty, in the same unit of the last digit of the corresponding parameter, is three times the standard deviation given by the fit.

Conclusions and perspectives

We have shown that the Hartmann-Tran profile, recently recommended by IUPAC [START_REF] Tennyson | Recommended isolated-line profile for representing high-resolution spectroscopic transitions (IUPAC technical report)[END_REF] for high resolution spectroscopy is able to fit measured spectra of CO in various perturbers for large pressure ranges with a precision of better than 0.2 % of the peak absorption. This study confirms the capability of the HT profile to accurately represent observed line shapes for various molecular systems, making the use of this model completely compatible with the precision requirement of current Earth remote sensing experiments.

Because of different approximations used in the model, the fitted line shape parameters do not exactly reflect the underlying physics and should be considered as effective.

Nevertheless, they give good indications of the contribution of the various mechanisms that contribute to the line shape. Ab initio calculations such as molecular dynamic simulations or quantum calculations may bring detailed information on the underlying physics and should be helpful to improving phenomenological models such as the HT profile. Information obtained from ab initio calculations can be used to determine the relative contribution of the various higher-order effects to the line shape and to explain the different behaviors of the P(1) and P(17) lines, for instance. This type of information can also be used to constrain fitted parameters in measured spectra with the HT profile [START_REF] Wcisło | The implementation of non-Voigt line profiles in the HITRAN database: H 2 case study[END_REF]. This approach should help to decrease the numerical correlation between line shape parameters, resulting in parameters that would be more physically-meaningful.

Fig. 1 :

 1 Fig.1: Top panel: Measured absorption spectra of the 3-0 P(1) (left) and P(17) (right) lines of 12 C 16 O broadened by He, obtained from FS-CRDS measurements at room temperature and various total pressures. The spectra are normalized for unity peak absorption with the fitted base losses are removed. Because of the precise agreement between measurements and model, the fitted data points are not shown. Bottom panels: residuals (observedcalculated) obtained from multispectrum fits of the measured spectra with the considered line shape models (see text).

Fig. 2 :

 2 Fig.2: Top panel: absorption spectra of the 3-0 P(1) (left) and P(17) (right) lines of 12 C 16 O broadened by Ar, measured at room temperature and various total pressures. The spectra are normalized for unity peak absorption with the fitted base losses are removed. Bottom panels: residuals obtained from multispectrum fits of the measured spectra with the different considered line shape models.

Fig. 3 :Fig. 4 : 6 Highlights

 346 Fig.3: Same as figure 2 above but for CO in Kr Fig.4: Same as figure 3 but for CO in SF 6

Fig. 1 Fig 2 Fig 3

 123 Fig.1

Table 1 :

 1 Experimental conditions for the measured spectra of the P(1) and P[START_REF] Boissoles | IOS and ECS line coupling calculation for the CO-He system: Influence on the vibration-rotation band shapes[END_REF] lines in the (3-0) band of 12 C 16 O diluted by He, Ar, Kr and SF 6 . The corresponding values are also reported (with , respectively the estimated Lorentz and the calculated Doppler widths). The pressures and molar fractions are nominal values, with the latter estimated from the peak areas and line intensities.

	Perturber Line	Pressure (kPa)		CO molar fraction
	He	P(1)	1.3, 3.3, 6.7, 10, 13, 33, 67, 100, 127	0.088-8.39	2.5×10 -3

P(17) 1.3, 3.3, 6.7, 10, 13, 33, 67, 100, 127 0.085-8.03

Acknowledgement:

This work was supported by the NIST Greenhouse Gas Measurement and Climate Sciences Program.


Gaël Varoquaux

Nassim Zahzam

Walid Chaibi

Jean-François Clément

Olivier I C E Carraz

Jean-Philippe Brantut

Robert A Nyman

Franck Pereira

Dos Santos

Linda Mondin

Michel Rouzé

An Ultra-Cold Atom Source for Long-Baseline Interferometric Inertial Sensors in Reduced Gravity

published or not. The documents may come

Inertial sensors are useful devices in both science and industry. Higher precision sensors could find scientific applications in the areas of general relativity 3 , navigation, surveying and analysis of Earth structures. Matter-wave interferometry was first envisaged to probe inertial forces 4 . Neutron interferometers were used to measure the acceleration due to gravity 5 and the rotation of the Earth 6 at the end of the 1970s. In 1991, atom interference techniques were used in proof-of-principle work to measure rotations 7 and accelerations 8 . Many theoretical and experimental works have been performed to investigate this new kind of inertial sensors [START_REF]Atom Interferometry[END_REF] . Some of the recent works have since shown very promising results leading to a sensitivity comparable to other kinds of sensors, for both rotation [START_REF] Gustavson | [END_REF]11,12 as for acceleration 1,13 . philippe.bouyer@institutopique.frhttp://www.ice-space.fr 1 Atoms in microgravity as probes of the gravito-inertial field 1.1 Using atoms as test masses.

Following pioneering work on atomic clocks 14 , ultra-high precision inertial sensors are expected to be used in micro-gravity for tests of gravitation theories or to provide accurate and exact drag-free motion that is required for deep-space mapping of gravity [START_REF]Study of the Pioneer anomaly[END_REF] . Closer to Earth, they can lead to possible experiments that could test the Einstein equivalence principle 16 : Lorentz invariances, the universalities of a free fall and gravitational redshift, as well as the constancy of gravitational and fine-structure constants or higher order gravitational effects such as the Lense-Thirring effect 17,18 .

Conventional gravity and acceleration probes 17 rely on artifact-based macroscopic test masses to probe the gravito-inertial field. Using atoms as proof masses directly relates measurements to fundamental quantities, without the need for geometrical factors. The test masses are not subject to manufacturing errors and their displacement is referenced to the well-controlled wavelength of a pair of laser beams, providing long term accuracy and precision.

Atom interferometry and precision gravimetry

An atom interferometer measures the phase-shift acquired by atoms through different coherencepreserving paths. Since the phase acquired by an atom during its free propagation is strongly dependent on the gravito-inertial field it experiences 19 , the interferometric read-out of this phaseshift can give access to direct measurements of the metric tensor [START_REF]Clocks and Interferometers: Testing Relativistic Gravity in Space[END_REF] .

In most atom-interferometry experiments, an ensemble of particles is split into two different paths by a coherent beam-splitting process 9 . After a phase accumulation time T , the two paths are recombined by a second beam-splitting process. The probabilities of detecting particles in the two output channels of the beam-splitter are given by quantum interference of the two coherent propagation paths and are sinusoidal functions of the accumulated phase difference. The ultimate precision in the read-out of the phase is limited by the number of detected particles and scales as ∆φ min = 2π/ √ N (quantum projection noise limit [START_REF] Wineland | [END_REF] ). Typically ∆φ min ∼ 2 mrad for 10 7 particles.

To detect inertial forces, an atom-interferometer must have physically separated paths. Therefore, unlike in atomic clocks, the beam-splitting processes must communicate momentum to the atoms. A common scheme uses two-photons Raman transitions to coherently transfer momentum from lasers beams to atoms 22 . Two hyperfine levels of an atom can be coupled via two counter-propagating laser beams. Raman transitions contribute two photon momenta and can be used as mirrors and beam-splitters (see figure 1).

The phase shift at the output of such a light-pulse interferometers arises from three contributions 19 : 1. the difference in the action integral along each path, 2. the difference in the phases imprinted on the atom waves by the beam splitters and mirrors, 3. the term due to the splitting of the wave-packets at the output of the interferometer. Gravito-inertial effects are found in the first term, but can also be hidden in the second term depending on the chosen reference frame, through movement of the Raman beams. When performing the calculation in an inertial frame, terms 1 and 3 nearly cancel out and leave only the term 2, the laser phase difference between mid-points of classical (non-quantum) trajectories. This shows that interferometric process can be pictured 1 as measuring the position of freely falling atoms on an optical ruler made by the two Raman lasers beating together with a wavevector given by the difference of their wavevectors k eff = k 2 -k 1 . This simple picture allows to understand the stringent requirement on the lasers for a high-precision measurement, as their spectral quality determines the quality of the optical ruler.

For a light-pulse interferometer with equal times T between the three pulses, in the case of an accelerated frame with no rotation or gravity gradient, the final phase shift is given by ∆φ

= -→ k eff • -→ a T 2 , (1)
where -→ a is the local acceleration: the atom interferometer acts as a gravimeter. Current stateof-the-art atom-gravimeters 1 have a shot-to-shot accuracy of 10 -7 m • s -2 due to technical noise.

1.3 Micro-gravity, the route to enhanced atom-interferometric sensors Equation 1 shows that the sensitivity of an atom-interferometer increases with interrogation time. The longer the time the atoms spend between the beam splitters, the greater the scaling factor between the accumulated phase shifts and the effect they probe. In order to avoid uncontrolled residual phase-shifts, it is best not to apply fields other than that which is probed during the phase accumulation period. In the case of inertial sensing this implies that atoms must be in free fall between the beam-splitting processes. In Earth-based interferometers, with cold-atom sources, the expansion of the atomic cloud is small, and the interrogation time is limited to a fraction of second by the available fall height, limiting their precision. Atom interferometry in micro-gravity allows for longer free fall and thus increased precision.

2 Atom-interferometric sensors in the Zero-G Airbus

We are conducting atom interferometry experiments for inertial sensing on board an airplane during ballistic flights. Microgravity is obtained via 20 second-long parabolas by steering the plane to cancel drag and follow gravity. Residual acceleration is on the order of 10 -3 g. Even though this tropospheric microgravity facility does not provide the environmental quality of a space-borne mission, either on the ISS or on a dedicated platform, it offers the possibility to perform test and qualification campaigns for future space atomic inertial sensor missions. It also provides the required environment for the first comparison of sensors performances and possibly the first fundamental physics test with atomic sensors in microgravity.

Airborne test of the equivalence principle: an Airbus as an Einstein elevator.

The Einstein equivalence principle states that physics in a freely falling reference frame, in a gravitational field, is locally equivalent to physics without any gravito-inertial fields. An atom interrogated during its free fall in an interferometer on Earth behaves like an atom interrogated in deep-space. But inertial-sensing interferometers have a non-zero physical size and can be subject to tidal effects 23 (e.g. Lense-Thirring). An experiment carried out nearby a massive object is therefore not equivalent to a deep space experiment. On the other hand, there is no difference between an experiment carried in a freely falling airplane and one on a satellite orbiting around the Earth or the Sun.

In the airplane, atoms falling in the interferometer's vacuum chamber experience true free fall as long as they do not hit the chamber walls. The interferometer itself is attached to the airplane and subject to acceleration noise. All movements of the mirrors used for the optical-ruler (the Raman lasers) strongly degrade the performance of the interferometer 24 (see figure 2 (b)). To improve the performance, the interferometer can be left freely flying, released from the airplane, to allow for strong vibration-noise rejection, and increased interrogation time. Since during a few seconds of free fall an object can move by several meters in the airplane (see figure 2 (a)) a rigid construction, called a free flyer, will be required to restrict and damp the displacements of the interferometer. Choosing a free flyer with 1.2 m travel gives a 50% probability of success for a 4 s long free fall for each release of the interferometer. As the airplane is rotating about the axis of its wings during the parabola, the rotation of the interferometer cannot be controlled and will give rise to Sagnac shifts. They can be canceled by doing two measurements with the area enclosed by the interferometer reversed.

Test flight of a prototype micro-gravity interferometer

An atom interferometer is made of: a vacuum chambers with optics; lasers sources for cooling and coherent manipulation of atoms; and a stable oscillator (in our case a hyperfrequency source 24 ) which serves as a frequency reference for the Raman lasers. A lab experiment weighs at least one tonne and requires a highly-controlled environment. We assembled a prototype atomic source suitable for inertial-sensing in a jet airplane from the I.C.E. collaboration components 24 (see figure 3 (a)). We prepare clouds of cold 87 Rb in a Magneto-Optical Trap (MOT) and release them for interrogation during their free fall. Novel integrated fibered source for rubidium laser-cooling. Laser cooling and manipulation of atoms requires frequency-stable, narrow-linewidth laser sources. The laser systems generally used in ultracold atom experiments are neither transportable nor reliable and robust enough for our application. Indeed, free-space optical benches with macroscopic cavities often need regular re-alignment. Moving away from the standard semiconductor-laser based design 14 , we have created laser sources at 780 nm, suitable for atom interferometry with 87 Rb, using frequency-doubled fiber lasers and other telecom components at 1560 nm. These novel laser sources have been described in length elsewhere 25 , we will limit ourselves to outlining the successful design choices in light of the test flight.

To achieve a frequency-agile configuration, we use a master laser locked on a rubidium transition and slave lasers which are frequency-locked to the master laser with an arbitrary frequency difference (see figure 4). The master laser (linewidth of 10 kHz) is a monolithic semiconductor element: a 1560 nm Distributed Feed-Back (DFB) fiber laser, amplified in a 500 mW Erbiumdoped fiber amplifier and frequency doubled in a PPLN waveguide. The resulting 780 nm light is then sent into a saturated-absorption spectroscopy setup for frequency locking to a rubidium transition. An error signal is obtained by modulating the frequency of the master laser for phasesensitive detection. Control of the frequency is achieved via a piezoelectric transducer (acting on the DFB laser) but we also change the temperature of the DFB fiber when the piezoelectric voltage approaches its maximum range.

The slave lasers are 80 mW 1560 nm DFB laser diodes (linewidth of 1.1 MHz). After amplification through an Erbium-doped fiber amplifier they are frequency doubled in free space with two 2 cm bulk PPLN crystals in cascade (similar to 27 ). With a 5W fiber amplifier, we obtain ∼ 0.3 W at 780 nm. The slave lasers are frequency-locked to the master laser by measuring the frequency of a beat-note between the two 1560nm lasers recorded on a fibered fast photodiode. Control of the frequency of the slave lasers is achieved via feedback to their supply current.

The power of the cooling laser can be adjusted by switching off the 1560 nm input laser of the fibered amplifier with an optical switch after saturating it with a laser source at 1556 nm. The 1556 nm light is not frequency doubled by the PPLN crystals and is filtered by the singlemode 780 nm fibers. A very good extinction is obtained, limited by the amplified spontaneous emission of the fibered amplifier that is frequency-doubled. Mechanical shutters are used to completely extinguish the lasers over long timescales (they have a 7 ms dead time), but the use of the saturation diode allows for quicker switching times (∼ 50 µs).

In order to laser cool 87 Rb, an additional frequency (called the repumping laser), located fiber Mach-Zehnder modulator to generate two sidebands 7 GHz apart. One sideband is for repumping and the other is off-resonnace, so causes no ill effects.

Laser light is transported to the vacuum chamber using polarization-maintaining optical fibers. A fiber beam-splitter (Schäfter and Kirchhoff) based on miniature polarizing optics divides the laser-cooling fiber in three to provide separate beams for the operation of the MOT.

The laser sources have proved remarkably robust during the test flight, surviving pressure changes of 200 mPa, temperature changes of 15 • C, and remaining frequency-locked in spite of the noisy environment. It is worth noting that an amplifier was damaged during flight operations, its output power dropping by a factor of 10. This failure did not prevent the MOT from functioning. The cause is currently being investigated.

A robust transportable interferometer setup. Keeping with the philosophy of a flexible prototype, the atomic-physics part of the interferometer was built using standard lab equipment mounted on a 600×600 mm optics breadboard (see figure 3 (b)). A rigid frame is bolted through the breadboard, holding the vacuum chamber to protect it and meet flight security requirements.

The core of the apparatus is a stainless-steel ultra-high vacuum chamber in which the laser beams intersect for trapping and manipulating the atoms. The chamber has two 63 mm diameters windows and eight lateral 40 mm ports. The large number of available ports allows us to dedicate separate windows for different beams and for observation. MOT and compensation coils are directly wound onto the chamber. The rubidium atoms are released from commerciallyavailable alkali-metal dispensers directly into the MOT chamber. While operating the interferometer, the dispensers are run continuously and a dilute (< 10 -8 mBar) rubidium vapor fills the chamber. There are two pumps: an ion pump and a getter pump, maintaining the required vacuum even during night power cut. No special care has been taken to ensure that all parts of the system are non-magnetic and the ion pump was not shielded. We relied solely on the compensation coils to cancel out the magnetic fields in the surroundings of the atoms.

The six counter-propagating lasers beams of the MOT are made of three retro-reflected beams each expanded out of a fiber by an producing a 25 mm diameter beam. The couplers are positioned on kinematic mounts (New Focus 9071) held by 38 mm posts bolted on the breadboard. The setup was optimized in our lab in Palaiseau, then carried on a truck 500 km away to Bordeaux and loaded into the airplane with no particular precautions. Every day temperature cycled from 6 • C to 20 • C. We did not notice any misalignment.

The laser source driving the Raman transition is similar to the cooling laser. The second Raman frequency is achieved as with the repumping frequency by intensity-modulating the laser light. The presence of the second sideband adds new paths to the interferometer, but they need not be taken in account as these secondary interferometers are not closed. For the Raman pulse manipulation, MOT coils are switched from quadrupole configuration to dipole configuration to provide a polarizing field raising the degeneracy between Zeeman sub-levels. The intensity of the lasers can be up to 20 times the saturation intensity of rubidium, which allows for short Raman pulses with weak velocity selection to address broad momentum distributions. The pulse is controlled via an acousto-optical modulator after the frequency-doubling stage. Raman transfer was not tested during this first flight.

We load 10 9 atoms of 87 Rb in the MOT in one second. A photodiode monitors the fluorescence, which is proportional to the number of atoms. We release the atoms from the MOT and further cool them through a brief phase of optical molasses during which we can prepare the atoms in the lower hyperfine state by turning off the repumping light. The light pulses for the interferometer (see figure 1) can then be applied. The cooling laser is turned back on to detect the atoms still in the MOT volume in a state selective way. The flight of the atoms in the optical molasses was recorded during the test flight. Our preliminary setup had no magnetic shield and the rotation of the Earth's magnetic field created uncompensated Zeeman shifts. These shifts imbalance the radiation pressure during molasses, limiting the atomic escape velocity (see figure 5).

I.C.E.: the next-generation apparatus

Temperatures achieved through laser-cooling techniques reach a limit of around 1 µK (v rms ∼ 1 cm • s -1 ). Ballistic expansion of laser-cooled atoms thus limits interrogation times to a few seconds 26 . To make full use of micro-gravity (e.g. with a space-borne experiment) further cooling is needed. The limiting factor for atom-interferometric metrology is the size of the atomic cloud after expansion, given by both its initial size and velocity spread. This size is closely related to the phase-space density of the source, which can be seen as an atom-optic equivalent of the luminance of a photonic source. The source of maximum luminance in optics is the laser, and which is widely used in photon-interferometry. In atom-optics such a source is a Bose-Einstein condensate. The intrinsic linewidth of a Bose-Einstein condensate is very narrow, however the momentum-width of a freely falling condensate depends on the trap release process.

Within the I.C.E. project 24 , we are building a next-generation atom interferometer making use of quantum degenerate atomic gases for increased interrogation times during ballistic flights. Degenerate atom sources can be achieved by evaporative cooling, where the depth of a nondissipative trap is lowered to eject higher energy atoms while relying on two-body collisions to thermalize the cloud, thus lowering its temperature. Magnetic traps, where atoms are trapped near a minimum of magnetic field, are most often used to perform this evaporation. However, releasing atoms from a magnetic trap is an ill-controlled process that will affect the sensor performances. On the contrary, optical-dipole traps, where atoms are trapped near a maximum of laser light intensity, can be controlled with much more precision. Ramping down to zero the power of the trapping laser yields a jerk-free release process. In the I.C.E. interferometer, we transfer the atoms from the MOT to an optical-dipole trap made of two intersecting laser beams at 1565 nm. Efficient capture of the atoms is achieved for a trap depth of a few times their kinetic energy. The phase-space volume of a dipole trap is limited by the available laser power. As a MOT is a rather large cloud, it is best to capture it with the spatially largest possible trap while still deep enough to load the atoms. Using a 50 W fiber laser, we can load the atoms using trap diameters up to 350 µm.

To permit a short duty cycle that allows for high precision measurement and high accuracy, the production of the degenerate atomic source must be fast. For the evaporation process to be efficient, the collision rate needs to increase as the number of trapped atoms decreases. However, lowering the power of the trapping laser reduces the depth of the trap, but not its size, and, as the trap depth goes to zero, so does the density of the trapped atoms and the collision rate. We use a mechanical zoom to change the diameter of the trapping laser beam during the evaporation and optimize the collision rate for quick evaporative cooling 28 .

Bose-Einstein condensates are relatively high-density samples, and the interactions between atoms cannot be neglected. These interactions give rise to uncontrolled shifts in interferometers 29,26 . Inertial-sensing atom interferometers have a physical extent, and the wave-packets in the different arms of the interferometers spend most of their time non-overlapping. The collisional shifts occur at the beam-splitters, where each atom interacts with the atoms in the other arm 26 . On the contrary, due to Pauli blocking, ultracold, spin-polarized, degenerate fermions do not interact. They suffer no interaction shifts 29 , but, as their phase-space density cannot exceed unity, they form less bright sources and, when released from tight traps, their increased momentum spectrum could limit interrogation times. However, Pauli blocking in Fermi gases and interactions in Bose gases yield similar orders of magnitude [START_REF]When suddenly releasing interacting Bose gases from a trap[END_REF] for momentum broadening over the range of accessible experimental parameters as long as the interaction is not suppressed via magnetically-tunable Feshbach resonances. Nevertheless, both collisional-shifts and momentum broadening can be strongly reduced by adiabatically opening the trap and reducing the density before the release, or by the use of an external magnetic field to tune the interactions (Feshbach resonances). The I.C.E. interferometer has been designed to operate with fermionic 40 K in addition to bosonic 87 Rb to allow for comparison of the achievable precisions using different species.

Conclusion

We have successfully tested a cold atom source for inertial sensing in aircraft parabolic flights. With the use of a free-flyer, it will allow interrogation of the freely-falling atoms during several seconds, paving the way for high-precision inertial sensors. The interrogation time is then limited be the residual acceleration. The aircraft is a valid frame for fundamental tests of gravitation theories. Our preliminary results show that laboratory experiments can be adapted for this new experimental platform. Unlike orbital platforms, development cycles on ground-based facilities, either on the plane (it took us 3 months to assemble the test prototype), or on drop towers 31 , can be sufficiently short to allow for the rapid technological evolution for future sensors. Indeed high-precision drag-free space-borne applications require further progress on achieving longer interrogation times using ultra-low velocity atoms. Our new-generation degenerate atomic source design minimizes trap-release and interaction energies for these purposes.

1 .

 1 hyperfine levels |e and |g with momentum transfer create a Mach-Zehnder type interferometer: Beam splitter: a π 2 pulse splits the wave packet in a superposition of different momentum states 2. Mirror: a π pulse inverts the two states 3. Output beam splitter: a second π 2 pulse recombines the wave packet

Figure 1 :

 1 Figure 1: Light-pulse interferometer

Figure 2 :

 2 Figure 2: (a) Histograms of the displacements of a free-flying object, in the Airbus frame, for different times of flight. The median value is displayed for each flight time. The displacements depend on atmospheric conditions and vary from flight to flight. These measurements where taken during three flights (90 parabolas), during poor weather conditions. (b) Acceleration noise spectrum measured on the optical breadboard during a parabola.

Figure 3 :

 3 Figure 3: (a) The atom interferometer assembled in the Airbus. The main rack, on the left, houses laser sources and control electronics. The rack on the front right houses the uninterruptable power-supply and high-power electrical components. The rack in the back is the atom-optics part of the experiment. (b) Inside the atom-optics rack: the vacuum chamber and the free-space optics. On the front left, the fiber beam-splitter is clamped on the breadboard.

Figure 4 :

 4 Figure 4: Diagram of our laser system. The master laser is pictured on top, the slave below.

Figure 5 :

 5 Figure 5: Images of molasses at different airplane angles. The tilt in the Earth's magnetic field produces an imbalance in the radiation pressure during the molasses phase, and alters the direction in which the atoms escape.The arrows connect the positions of the initial trapped cloud to the escaping atoms. The escape direction does not directly relate to the pitch angle of the airplane, as its bearing also changes the direction of the magnetic-field.

Acknowledgments

The I.C.E. collaboration is funded by the CNES, as are JPB, RAN and NZ's salaries. Further support comes from the European Union STREP consortium FINAQS. Laboratoire Charles Fabry, ONERA, and LNE-SYRTE are affiliated to IFRAF 32 .