Pellegrini Elisabeth
email: elisabeth.pellegrini@univ-rennes1.fr

Diotel Nicolas

Vaillant-Capitaine Colette

Maria Rita

Gueguen Marie-Madeleine

Nasri Ahmed

Cano Nicolau

Kah Olivier

Dr Elisabeth Pellegrini

STEROID MODULATION OF NEUROGENESIS: FOCUS ON RADIAL GLIAL CELLS IN ZEBRAFISH

Keywords:

Estrogens are known as steroid hormones affecting the brain in many different ways and a wealth of data now document effects on neurogenesis. Estrogens are provided by the periphery but can also be locally produced within the brain itself due to local aromatization of circulating androgens. Adult neurogenesis is described in all vertebrate species examined so far, but comparative investigations have brought to light differences between vertebrate groups. In teleost fishes, the neurogenic activity is spectacular and adult stem cells maintain their mitogenic activity in many proliferative areas within the brain. Fish are also quite unique because brain aromatase expression is limited to radial glia cells, the progenitor cells of adult fish brain. The zebrafish has emerged as an interesting vertebrate model to elucidate the cellular and molecular mechanisms of adult neurogenesis, and notably its modulation by steroids. The main objective of this review is to summarize data related to the functional link between estrogens production in the brain and neurogenesis in fish. First, we will demonstrate that the brain of zebrafish is an endogenous source of steroids and is directly targeted by local and/or peripheral steroids. Then, we will present data demonstrating the progenitor nature of radial glial cells in the brain of adult fish. Next, we will emphasize the role of estrogens in constitutive neurogenesis and its potential contribution to the regenerative neurogenesis.

Finally, the negative impacts on neurogenesis of synthetic hormones used in contraceptive pills production and released in the aquatic environment will be discussed.

Introduction

Despite the early establishment of the basic architecture of neural circuits, the adult brains of all vertebrates studied so far retain the capacity of remodeling in order to adapt their neuronal networks to environmental demands or to damages [1,2]. For the past twenty years, the dogma according to which the number of neurons is defined at birth without new formation and replacement in adulthood has been challenged by a series of research highlighting the capacity of the adult brain to generate new cells. The pioneering work of Altman and Das in 1960s reported the production of new neurons in a very limited number of brain areas in rodents [3]. This new concept of adult neurogenesis, initially rejected, was reinforced two decades later by the work of Nottebohm who has demonstrated that neurons were generated in the forebrain of adult birds and incorporated in the vocal control center, allowing the annual learning of new song [4]. Since the 1990s, with the introduction of new methods for labeling dividing cells, the existence of proliferative activity in the adult brain of mammals was indeed evidenced in confined regions such as the subventricular zone of the lateral ventricles and the dentate gyrus of the hippocampus [5][6][7] and findings strongly suggest that adult neurogenesis also takes place in the hypothalamus [8][9][10]. With the development of the thymidine analog 5-bromo2'-deoxyuridine (BrdU) incorporation technique as a tool to label newborn neurons, it clearly appeared that adult neurogenesis is not limited to mammals and birds but is a feature conserved across vertebrate evolution. The data generated with that simple and fast technique showed unambiguously that adult neurogenesis occurs in reptiles [11], amphibians [12,13], fishes [14][15][16][17] and mammals notably in humans [18][19][20]. Currently, the adult neurogenesis concept is well accepted and defined as a complex and multistep process by which functional neurons are generated from resident neural stem/progenitor cells. In fact, neurogenesis encompasses the birth, the maturation and the migration of new neurons that integrate into existing neuronal networks [21,22]. Although this phenomenon is common, comparative investigations have brought to light major differences between vertebrate groups in terms of neurogenic niches in the brain [23]. While the generation of new neurons is obvious in two main regions in mammals, the neurogenic potential in adult teleost fish is spectacular in many proliferative areas. This continuous production of new neurons in adulthood is notably supported by the persistence and abundance of radial glial cells (RGCs) [17,24], known in mammals to serve as neural "stem" cells during embryonic neurogenesis [25,26]. Fish are also distinguished by their remarkable potential to regenerate their CNS from mechanical and chemical injuries by replacing damaged neurons such as shown in the cerebellum, the telencephalon and olfactory bulbs, the retina [27][28][29][30][31][32]. Indeed, a massive and transient increase in cell proliferation is observed in response to injuries applied to the brain and the spinal cord and newly generated neurons repopulate the wounded site allowing a complete regeneration of nervous tissue while the regenerative capacity of the adult mammalian brain is limited and the long-term survival of newborn cells is generally impaired [33]. The great neurogenic activity associated with the extraordinary repairing properties of the adult brain have made teleost fish valuable models to study and decipher mechanisms underlying adult neurogenesis in a constitutive or a regenerative context.

In mammals, a wealth of factors, notably neurotransmitters, growth factors and hormones, have been shown to modulate adult neurogenesis [34][35][36][37][38]. With respect to hormones, estradiol, is recognized as a major modulator of adult vertebrate neuronal plasticity [39,40] and neurogenesis under physiological conditions and many data also demonstrated its neuroprotective actions in damaged brains [35,[41][42][43][44][45][46][47].

Estradiol may also play significant roles in teleost neurogenesis as the brain of fish is well known for harboring a high expression of aromatase, the only enzyme that catalyses the final step of estrogen biosynthesis. Aromatase is expressed in the brain of all vertebrates, but in teleost fish, the enzymatic activity is much higher than in mammal and bird. In addition, the three estrogen receptors are described in many brain areas of teleost fish [48][49][50].

In the last few years and for the above-mentioned reasons, the zebrafish has emerged as an interesting vertebrate model to elucidate the cellular and molecular mechanisms of adult neurogenesis, and notably its modulation by steroids, in normal and in reparative conditions.

The main scope of this review is to summarize recently released information on the functional link between estrogens production in the brain and neurogenesis in fish with a particular focus on the zebrafish model. First, we will document the capacity of adult fish brain to produce steroids. We will present data demonstrating that RGCs could be an endogenous source of steroids and are directly targeted by local and/or peripheral steroids. We will next emphasize the role of estrogens in constitutive neurogenesis and its potential contribution to the regenerative neurogenesis. Finally, we will provide findings that point out the deleterious impacts on neurogenesis of synthetic hormones used in contraceptive pills production and released in the aquatic environment.

The brain of adult zebrafish: a source of neurosteroids?

De novo neurosteroids synthesis

While neurosteroids synthesis is widely documented in mammals, only few studies focused on de novo steroid synthesis in the brain of teleost fish [51-55] Such a feature raises the question of the origin, local and/or peripheral, of C19 androgens available for brain aromatization. Our laboratory recently demonstrated that the brain of adult zebrafish was able to de novo synthesize a wide variety of radiolabeled neurosteroids from [³H]-pregnenolone. Among these locally-produced steroids, there are notably dehydroepiandrosterone (DHEA), androgens (i.e.: testosterone), estrogens (i.e.: estrone and 17 estradiol), progesterone and derivatives [51,55]. Such results clearly evidence that 17 -hsd, 3 and 3 -hsd, cyp17, 5reductase and cyp19a1b (AroB) are expressed and biologically active in the brain of adult zebrafish. As no specific well-characterized antibodies are available, apart from AroB, and in order to determine the sites of production of neurosteroids in the zebrafish brain, in situ hybridization was performed for the main steroidogenic enzymes leading to estrogen synthesis (cyp11a1 -P450 SCC -, 3 -hsd, cyp17 and cyp19a1b). These experiments show that these steroidogenic enzymes are widely expressed in the whole brain, notably in the telencephalon, the preoptic area, the hypothalamus, the mesencephalon and the cerebellum.

Moreover, they exhibit an overall similar pattern suggesting a potential co-expression, at least in some regions such as the hypothalamus. Thus, by performing cyp11a1, 3 -hsd and cyp17 ISH followed by AroB immunohistochemistry, some steroidogenic enzymes transcripts were detected in AroB-radial glial cells, raising the question of the steroidogenic capacity of RGCs in zebrafish. In addition, the distribution of these main steroidogenic enzymes (apart from AroB) also strongly argues in favor of a neuronal expression. This is notably reinforced by the fact that 3 HSD-like immunoreactivity was observed in neurons throughout the adult zebrafish brain [52]. Last but not least, steroidogenic enzymes expression in microglia and oligodendrocytes is not excluded, but it would require further investigations. Together, all these results show that the brain of adult zebrafish is a true steroidogenic organ, RGCs being a source of neurosteroids [51,55,56], and raise the question of the targets of such steroids in the brain as well as their functions.

Aromatase and radial glial cells

Cytochrome P450 aromatase (aromatase), the rate-limiting enzyme that transform C19 androgens into estrogen, is described in the gonads and the brain of all vertebrates species studied so far, with a broader distribution in mammals [57]. Strikingly, when compared to other vertebrates and especially to mammals, the brain of adult fish exhibits an exceptionally high aromatase activity in anterior regions such as olfactory bulbs, telencephalon, preoptic area and hypothalamus [48,58,59]. The cyp19a1 genes, which encode aromatase, are highly conserved throughout vertebrate lineages but their expressions are driven by different regulatory mechanisms. In the mammalian genome a single cyp19a1 gene has been characterized (except in the pig) and its expression is driven by the use of distinct tissuespecific promoters and alternative splicing [60,61]. As a result of teleost specific whole genome duplication [62], two cyp19a1 genes, cyp19a1a and cyp19a1b, have been identified in most fish, except in the Japanese and European eel [63,64]. As evidenced in a growing number of teleost species, including the zebrafish, those two genes encode different enzyme isoforms, aromatase A (AroA, produced by the cyp19a1a gene), which is mostly described in the gonads and aromatase B (AroB, the product of the cyp19a1b gene), which is strongly expressed in the brain [65][66][67][68][69]. Pioneering investigations on the localization of AroB have been first undertaken in the brain of goldfish by the group of Callard [70]. In this study, very few aromatase-positive cells were detected and displayed a neuronal phenotype. The small number of labeled cells and the fact that this antibody was raised against human aromatase now suggest that these results were artifactual. Since Forlano et al. work until the most recent publications in fish [71], the development of homologous and specific molecular tools such as cyp19a1b riboprobes and AroB antibodies has revealed in many teleost species a high number of AroB-expressing cells in ventricular position in the forebrain and midbrain, consistent with the strong aromatase enzymatic activity [64,68,[71][72][73]. In zebrafish, cyp19a1b messengers are strongly expressed along the ventricles in the olfactory bulbs, telencephalon, preoptic area, hypothalamus, thalamus and optic tectum [74]. Of particular interest is the fact that cyp19a1b mRNAs are also detected away from the ventricular cavities, suggesting their transport far from the cell bodies in the cytoplasmic extensions [51,74]. Using specific zebrafish AroB-antibodies developed in our laboratory, a strong immunohistochemical labeling is visualized in cells bordering the ventricles, perfectly matching with the distribution of AroB mRNA [17,74,75]. The radial glial nature of AroB-expressing cells is clearly evidenced by their typical morphology (Figure 1A-1B), namely small cells body close to the ventricular cavities and long radial cytoplasmic processes underlining the surface of the brain [17,75]. In addition to their specific morphology, the radial glial identity is demonstrated by the fact that AroB staining is never colocalized with neuronal markers such as Hu or acetylated-tubulin [17]. Moreover, convincing double-immunolabeling with AroB antibodies and radial glial cells markers such as GFAP, BLBP and S100 [17,76,77] reinforced the fact that AroB expression is restricted to RGCs. The radial identity of cells expressing aromatase has been attested in fish and now, it appears clearly that in these species, RGCs are the primary source of aromatase in the brain [64,71,72,78] while in mammals and birds, aromatase expression is confined to neurons under normal physiological conditions [79,80].

Data recently obtained in our laboratory demonstrated that in amphibian, aromatase expression is restricted to neurons during development as in adulthood [81]. In adult zebrafish, we did not observed sexual dimorphism in the expression of AroB (transcripts and protein) while in medaka, females exhibit a stronger periventricular expression in several regions, in particular the optic tectum [73].

Radial glial cells in zebrafish: a target of steroids?

First of all, estrogens can act through three zebrafish nuclear estrogen receptors encoded by esr1 (ER ), esr2a (ER 2) and esr2b (ER 1) genes. These receptors are widely expressed in the brain of zebrafish, in both larvae and adults [50,51,74,75,82]. In adults, esr1, esr2a and esr2b are mainly expressed in the subpallium, the anterior and posterior part of the preoptic area, in the anterior, mediobasal and caudal hypothalamus. Interestingly, they exhibit an overall similar pattern with some specific differences suggesting respective roles of these receptors in the estrogenic modulation of cell signaling and physiology. In fact, in the zebrafish brain, esr were originally described to be expressed in neurons and also along the ventricular layer [74,75]. In vivo and in vitro results also showed that cyp19a1b expression is driven by ERs through an estrogen responsive element (ERE) on the cyp19a1b promoter [75,82]. Together, these data strongly argue for esr expression in AroB positive RGCs, and recent experiments tend to confirm a weak esr2b expression in AroB-positive RGCs [83]. Estrogens could also exert their effect through the binding with a membrane estrogen receptor called GPR30 or Gper. This membrane receptor corresponds to a G-protein-coupled receptor. Few years ago, gper expression was reported in parenchymal cells and also in cells lining the ventricles of adult zebrafish, suggesting its expression in RGCs [84]. Estradiol treatments on acute brain slices of cyp19a1b-GFP transgenic zebrafish line results in a rapid modulation of RGCs and parenchymal cells activities, revealed by calcium imaging [85]. Consequently, it appears that estrogens could target directly or indirectly a wide variety of cell-type and notably RGCs, and probably modify their functions.

In addition, in zebrafish and probably in other species, progesterone and progesterone derivatives may also act directly on RGC. In zebrafish, there is a unique nuclear progesterone receptor (Pgr), that actively binds progesterone (P), 17-hydroxy-P, dihydro-P, and 4-pregnen-17,20 -diol-3-one [86,87], or membrane progestin receptors mPR , and [88]. In the brain of zebrafish, Pgr is expressed in neurons and RGCs, these latter exhibiting a significantly stronger Pgr staining, suggesting that RGCs could be preferential targets for progestagens [89]. We also evidenced that 17 -estradiol up-regulates Pgr expression in the brain of both larvae and adult fish [89]. Similarly, inhibition of estrogen synthesis by an aromatase inhibitor (ATD) results in a significant reduction of pgr expression in the brain of adult zebrafish [89].

Such an estrogenic regulation of pgr expression is further reinforced by a recent transcriptomic analysis showing that pgr is an estrogen target gene in zebrafish [90].

Concerning membrane progestin receptors, their roles and expression are poorly documented in the central nervous system [88]. However, taken together these data highlight the fact that progestagens could also impact cell functions of RGCs as well as neurons.

Finally, in zebrafish, androgens such as testosterone (T), 5 -dihydro-T, 11-keto-T and androstenedione can exert their effects through androgen receptor (AR) [91]. In the brain of adult zebrafish, ar transcripts appeared to be expressed in parenchymal cells [92]. In addition, ar expressing-cells were also observed in cells lining the ventricles of the preoptic area, the hypothalamus and also of the periglomerular gray zone of the optic tectum [92], suggesting expression in RGCs. Further investigations combining ISH and RGCs markers immunohistochemistry would be required for testing this assumption.

Consequently, the brain of adult zebrafish appears to be both a source and a target of steroids. Peculiarly, RGCs express a wide variety of steroidogenic enzymes and are also targeted by estrogens, progestagens and probably androgens. Thus, steroids could impact on the RGCs behavior and neurogenic vs. gliogenic activity and cell-cycle kinetics.

Aromatase-expressing radial glial cells are progenitor cells in adult zebrafish.

As mentioned above, in all teleost fish studied so far, AroB expression is strictly localized in RGCs. The zebrafish is certainly the best-documented species regarding AroB expression in RGCs as shown by studies based on in situ hybridization, immunohistochemistry and transgenic zebrafish expressing GFP under the promoter of cyp19a1b gene [17,74,75,77]. In mammals, RGCs appear at the onset of neurogenesis. They were first described as cells providing guidance for newborn cells, but their role has been extended and it is now well established that these cells also divide and contribute to the embryonic neurogenesis in many brain regions [26,[93][94][95][96]. In adulthood, RGCs progenitors mostly disappeared in the brain of mammals, but some persist in restricted neurogenic areas such as the subgranular zone of the dentate gyrus of the hippocampus [96,97]. In order to determine what roles RGCs encompass in teleost fish, we performed BrdU-labeling experiments with adult zebrafish. When zebrafish are sacrificed short time after the onset of BrdU treatment (12 or 24 hours), many dividing cells are observed at the edge of ventricles while no BrdU-staining is observed in the parenchyma [16,17,98]. When male and female were compared, no obvious differences were found in the ventral telencephalon, in the preoptic area and in the ventromedian hypothalamus [17]. However, more recent data showed that the dorsal telencephalon and the thalamus exhibited higher level of proliferating cells in females while in the dorsal part of the hypothalamus the quantity of cycling cells is higher in males [99]. Our data clearly shown for the first time that some of the dividing cells along the ventricles correspond to AroB-RGCs, which demonstrate that in fish as in mammals, RGCs are capable to generate new cells and display progenitor properties (Figure 1C-1E) [17,100].

At longer survival times (5 to 45 days), Brdu-positive cells are seen at the ventricular surface, but many are also described away from the ventricle (Figure 1F) and interestingly in close contact with AroB-positive radial extensions, indicating that new-generated cells migrate laterally deeper in the parenchyma by using RGCs processes as a guidance support [17].

While some newborn cells move away from their birthplace, others in the subventricular layer appear to retain mitotic activity as evidenced by double BrdU/PCNA (a marker of

Estrogens effects on constitutive and reparative neurogenesis in the adult zebrafish.

Estrogens are recognized as major factors orchestrating the establishment of brain circuitry during development. Powerful effects on brain plasticity are also described in adulthood in basal condition and data in mammals have shown that estradiol contributes to neurogenic activity and modulates processes such as proliferation, migration and apoptosis of new-generated cells [35,43,[102][103][104][105]. Several studies have pointed to a role of estradiol in brain repair processes following injury. The neuroprotective effects of estradiol would be to stimulate neurogenesis and to reduce apoptosis pathways [106][107][108][109]. The massive induction of aromatase mRNA and protein at the lesion site corroborates the role of estradiol in neuroprotection. Interestingly, while under physiological condition aromatase is mostly restrained to neurons, de novo expression is reported after lesions in reactive astrocytes surrounding the injury site in mammals and in radial glial cells facing the lesion in birds [45,[110][111][112]. The data from mammals and birds regarding estrogens and adult brain plasticity in physiological and reparative conditions raised the question of the close relationships between the strong and restricted expression of AroB in RGCs progenitors in fish under physiological conditions. By manipulating the level of circulating estradiol, we investigated whether the sustained neurogenesis of adult zebrafih brain is closely related to the production of estradiol in RGCs. In a first set of experiments, adult zebrafish have been exposed with the aromatase inhibitor ATD (1,4,6-Androstatrien-3,17-dione . As expected, the treatment with ADT (10 - 6 M) strongly reduced cyp19a1b expression and completely blocked its brain enzymatic activity. The proliferative activity was then checked with PCNA immunohistochemistry and surprisingly, even if no significant difference could be evidenced, all ATD-treated animals exhibited more PCNA-positive cells than control zebrafish in the anterior part of the brain, notably at the junction between the olfactory bulb and the telencephalon, in the preoptic area and in the mediobasal hypothalamus [32]. As the data obtained in mammals mainly emphasized the stimulatory effects estradiol on neurogenesis, our results were somewhat surprising and thus we used a complementary approach. Male adult zebrafish were treated with ICI 182,780 (10 -7 M), an antagonist of nuclear estrogen receptors, during 48 or 54 hours.

As the regulation of AroB expression is estrogen-dependent [75,113], cyp19a1b gene expression is significantly decreased at the end of ICI 182,780 exposure. In agreement with the results obtained with ATD, the quantification of the number of PCNA-labeled cells revealed a significant increase in the proliferative activity at the olfactory bulbs/telencephalon junction and in the mediobasal hypothalamus at 54 hours but not at 48 hours [32]. On the contrary, the treatment of zebrafish with 17β estradiol (10 -7 M) for 100 hours is associated with a significant decrease in the number of nuclei stained with the PCNA antibody at the junction of the olfactory bulbs and telencephalon, the periventricular pretectal nucleus and the mediobasal hypothalamus, a shorter treatment (48 hours) does not affect proliferation in these regions [32]. Taken together, these data are consistent and indicate that in fish, under our experimental conditions (time of exposure, concentration, region considered), estradiol inhibits rather than stimulates cell proliferation. As newborn cells move laterally along the radial glial cytoplasmic extension, we decided to investigate the impact of estradiol exposure on migration processes. In fish, exposure to 17β estradiol (10 -7 M) inhibits the migration of BrdU-labeled cells (Figure 2A-2B) but the effect is time and region-dependant, ie the migration is inhibited after 14 days of exposure in the ventral hypothalamus while 28 days of treatment are required to observe a significant inhibition at the junction of the olfactory bulbs/the telencephalon [32]. Cell survival was also slightly decreased at the junction between the olfactory bulbs after long-term treatment with estradiol, but these results requires further investigation [32]. Interestingly, the role of estradiol in neurogenesis has been addressed in adult female zebrafish and, as in male, 17β estradiol induces a region-specific decrease in the number of cycling cells especially in telencephalic, hypothalamic and cerebellar areas [114].

In order to highlight the potential role of estradiol in regenerative neurogenesis, we have developed a model of mechanical lesion of the telencephalon. As described in previous papers, a very significant increase in proliferation activity is observed in the injured telencephalon compared to the undamaged telencephalic hemisphere [29,30,32,115,116].

The rise in the number of PCNA-positive cells is first apparent in the parenchyma surrounding the lesion site 24h-48h after the lesion. At this time, parenchymal proliferating cells have been identified as oligodendrocytes and microglial cells [29]. The proliferative activity gradually disappeared in the parenchyma while 5-7 days after injury, more and more PCNA-labeled cells massively concentrated in ventricular layer [29,32]. The nature of cycling cells has been determined with antibodies directed against RGC markers (AroB, BLBP, GFAP, S100β), neural progenitor markers (Sox2, NESTIN) and neuroblasts (PSA-NCAM). At this stage, most of periventricular proliferating cells correspond to RGCs expressing BLPB/GFAP/S100β but, surprisingly, not AroB [29,32,117]. Unexpectedly, cyp19a1b mRNA amount dropped in the damaged telencephalon immediately after the wound and the decrease remained noticeable even 7 days after the lesion when ventricular cells start to proliferate very actively. This inverse relationship is fully consistent with the results pointing out an inhibitory role of estradiol in physiological neurogenesis [32]. Interestingly, while AroB-expressing cells have never been observed in the parenchyma under normal condition, 3 days after the damage, AroB is detected in cells near the lesion site (Figure 2C-2H) [32]. The identity of these de novo AroB-synthesizing cells is not known presently and further investigations are required. In order to go deeper inside the relationship between estradiol and the increase of proliferative activity in this context of reparative neurogenesis, stab wounded zebrafish were treated with estradiol or with ICI during 2 or 7 days. These treatments did not impact the injury-induced proliferation [32]. However, estradiol effects on migration, differentiation and survival of newborn cells have not been studied and cannot therefore be excluded.

Altogether, those results support the existence of a negative control exerted by estradiol on neurogenesis processes that takes place in the adult brain of zebrafish. As described above, under physiological conditions, estradiol exerts differential effects on proliferation, migration and survival of new-generated cells, depending on the length of the treatment, the concentration used and the region considered. The effects of estradiol in regenerative situations are presently incompletely studied and need more research that is currently in process.

Adverse effects of endocrine disruptors during early neurogenesis in zebrafish.

As described above, four different estrogen receptors (the three nuclear isoforms and the membrane receptor) are expressed in the adult brain of zebrafish. To follow the onset of estrogen receptors expression during embryogenesis, detailed studies based on RNA protection assay, real-time PCR and whole mount in situ hybridization have been performed [118][119][120][121]. These studies reported that maternally inherited estrogen receptors were detected early during the development. When embryonic transcription activity starts, esr1 (ER ), esr2a (ER 2), esr2b (ER 1) and gper genes expression dramatically increased from 24 hours postfertilization (hpf) to 48 hpf [119,121]. Interestingly, a significant rise in cyp19a1b expression was also obvious during this period, in parallel to that observed for the estrogen receptors [65,119]. Although esr1 expression is detected by PCR between 24 and 48 hpf, esr1 messengers were not detectable by in situ hybridization until 14 days post-fertilization. At this time, positive cells were observed in the ventral telencephalon and in the hypothalamus. The brain expression of esr2a and esr2b is clearly visible at 36 hpf and increases between 48 and 60 hpf in the forebrain and in the hypothalamus [119]. Whole mount in situ hybridization revealed that gper expression in the brain is detected after 18 hpf and is obvious at 36 hpf in the diencephalon, the midbrain and the mid-hindbrain boundary [122]. All estrogen receptors are doubtless fully functional at these stages of development as demonstrated by several studies.

Using the cyp19a1b-GFP or wild type embryos, we have shown that GFP or AroB is strongly induced by estradiol in RGCs at 24hpf, evidencing the functionality of estrogen receptors at early stages of development [75,119]. The strong increase in basal AroB expression at 24 hpf relies on estrogen receptors activation because treatment of zebrafish embryos with ICI 182780 strongly reduced the AroB expression rise [119] and it has been shown with the use of morpholino knock-down technology of the three nuclear receptors isoforms that the AroB expression is specifically induced through ER 2 receptors [123]. Knock-down experiments with Gper specific morpholinos induce profound alterations of apoptosis and proliferation that lead to morphological defect of the developing brain [122].

For several years now, there has been increasing concern about the deleterious impacts of many natural or synthetic molecules released in the environment on the development of aquatic species. Some of these molecules may interfere with the signalling pathways of sex For example, this is the case for compounds such as Bisphenol A (BPA) that is commonly found in food containers and receipt tickets. An increasing number of studies pointed out the deleterious impact of BPA on zebrafish central and peripheral developmental processes. Alterations of heart morphology, skeletal muscles organizations have been described in early-life BPA-treated zebrafish [125][126][127][128]. A recent study showed that zebrafish embryos exposed to BPA accumulate lipids, suggesting a role of BPA in the onset of overweight and obesity [129]. Centrally BPA treatments elicit an upregulation of AroB expression in zebrafish larvae [130,131], an estrogenic effect mediated by estrogen receptor binding and transcriptional activation [124]. BPA has been shown to impair the early brain regionalization processes as evidenced by an inappropriate neuronal markers expression during zebrafish embryogenesis [132] and BPA exposure has been associated with an increase of precocious hypothalamic neurogenesis [133].

Ethinylestradiol (EE2) was until recently the main compound of the contraceptive pill.

The above-mentioned data (i.e. estradiol effects on adult neurogenesis, functionality of estrogen receptors at the onset of the brain development) raised the question of the alterations induced by such molecules on early developmental stages, which could be influenced by many exogenous factors and the subsequent impacts in adulthood physiology. Studies dedicated to the impacts of EE2 in the brain of fish are very scarse. When larvae are exposed to EE2, the early development of the forebrain GnRH neurons circuitry is impaired with an increase in the number of GnRH neurons, a reduction in the size of their soma and a modification of their migration [134,135]. Taking advantage of the cyp19a1b-GFP transgenic zebrafish line (GFP expression restricted to RGCs and the strong susceptibility of the cyp19a1b promoter to estrogens), it has been shown that EE2 were approximately 50 times more potent than estradiol to induced fluorescence in RGCs of zebrafish larvae treated during 5 days [124]. Recent exposure experiments (6 days) performed in our laboratory showed that low concentrations of EE2 (EE2 at 10 -11 M, 10 -10 M, 10 -9 M) impaired the development of larvae and EE2-treated animals were smaller in size than the controls (Figure 3A).

Quantitative PCR assays carried out on RNA extracts isolated from the head of EtOH or EE2treated zebrafish revealed that the transcripts level for AroB were dose-dependently and significantly increased (Figure 3B) and expression of PCNA tends to decrease but the difference were not significant (Figure 3C). Even if those recent data need to be reinforced and complete with neuroanatomical approaches, they strongly suggest that EE2 disrupts the proliferative activity in the brain of 6 days treated-larvae, an effect that is consistent with the inhibitory action of estradiol described in the brain of adult zebrafish.

Conclusion

Zebrafish provides a unique model for studying the impact of steroids on neurogenesis and also the potential effects of endocrine disruptors on this critical mechanism. Obviously, fish differ from other vertebrates in several respects that are probably linked to each other.

The most intriguing feature certainly is the massive expression of aromatase in RGCs, the function of which is still unclear in terms of evolution and adaptation. To our knowledge, there is no equivalent situation in other vertebrates where aromatase is expressed mostly in neurons and does not seem to be so sensitive to estradiol. Our current hypothesis is that, given the high neurogenic activity of the brain of adult fish and the fact that fish do not perform somatic growth and gonadal growth at the same time, cell proliferation has to be turned down when there is a high demand of energy, i.e. when fish are entering gametogenesis. In fish this process is accompanied by a rise in steroid production and either directly from the gonad or indirectly through aromatization of androgens. In any case, what this shows is that sex steroids certainly have the potential to affect neurodevelopment in fish, with the consequence that endocrine disruptors with hormone mimetic effects may also disrupt the neurogenic activity.

Legends

  proliferation)[17]. Finally, when zebrafish are sacrificed long time after BrdU exposure (30 days), we demonstrated by performing double staining with BrdU and Hu and acetylatedtubulin (two known neuronal markers) that new-generated cells moving away from the ventricles differentiate into neurons in many regions of the forebrain (Figure1H-1J) [17].More caudally, in the caudal part of the hypothalamus, a structure that concentrates numerous dopaminergic and serotoninergic neurons, we have shown that AroB-RGCs are also local source of new-generated cells and some of them differentiate into serotoninergic neurons (Figure1G)[100]. However, presently, we cannot claim that all newborn born cells in the brain of adult zebrafish differentiate into neurons and we cannot rule out the possibility that some of those new cells become glial cells or undergo apoptotic process[101].

  steroids [124]. Using one of the property of cyp19a1b-GFP transgenic zebrafish (ie the high sensitivity of the gene to estrogens), Brion et al., have screened the estrogenic activities of 45 different chemical compounds and demonstrated that half of them stimulate GFP fluorescence in larvae [124].

Figure 1 :F:

 1 Figure 1: Aromatase B and neurogenesis in the brain of adult zebrafish. A and B: AroB-positive RGCs in the preoptic area (POA) and at the level of the nucleus of the posterior recess (NPR). (A) In the POA, RGCs soma is closed to the ventricle (V). RGCs send a short cytoplasmic extension toward the ventricle and a long one in the direction of the

Figure 2 :

 2 Figure 2: Estradiol and neurogenesis in constitutive and reparative conditions.A and B: BrdU (12 hours exposure) labeling at the junction between olfactory bulbs (OB) and telencephalon (Tel) in a male treated with EtOH (A) or with estradiol (E2, B) (10 -7 M, 28 days). Animals were sacrificed immediately after E2-treatment (28 days). Estradiol inhibits the migration of newborn cells that tends to stay along the ventricle. Scale bar: 25 µm.C, D, E and F, G, H: transverse sections showing AroB immunohistochemistry (C, F) 72 hours after telencephalon injury. Nuclei have been labeled with DAPI (D, G). (C, D and E: adult male N°1; F, G and H: adult male N°2). Some parenchymal cells express AroB (arrows) following the injury. Scale bar: 50 µm.

Figure 3 :

 3 Figure 3: Impacts of EE2 treatment on the zebrafish larvae.

Acknowledgments

The ANR PROOF (CES-2008-11), the Post-Grenelle grant NEMO and the TC2N Program supported this research.

!"# $ % & ' % ( % ) % **+ ,*-"+ "+"."/0 !*# 1 )

% & $ % $ 2 % 3 % 4/ ,*-"/ 0-4.0+0 !+# 5 % $ ) ) % % 5 % "*/ ,"467 +"4.++7 !/# 8 $ % 9 : % : % % % 3 : 8 ; 8 % <-,"4<+ *+4-.*+4/ !7# & ' 1 = % % : % "" ,"44+ "0+."<4 !6# ( 1 % .' % 3 % 3 : 8 ; 8 % 4-,"44+ *-0/.*-00 !0# $ % ( $ $ % : 2 % 5 2 8 : % ** ,*--* 6"4.6*+ !<# $ 1 & % 8 % % :

% *< ,*--7 **+.*7-!4# ) 1 % 8 ' = % 9 % > 5 ) :

% +-,*-"* 6"7.6*" !"-# & ? @ = % A % 5 8 9 % : 2 % 8

,: A =% : A % +"-,*--7 604.6<+ !""# 9 % ) % & & 3 .( % 5 & $ .? % : % ' % % 7< ,*--" *06.*47 !"*# 1 )B % ) ' % 3 ( % 3 % C % ' % "/-7 ,*-"" +"./< !"+# 1 3 % ? @ ( = % ; % % >> % ( % *0" ,"44+ +7".+6* !"/# $ @ D % % ' ' % 7< ,*--" *7-.*07 !"7# 3 = % ( & 5 % 1 & E % ? , % 5 % /+6 ,*--" 4*.""-!"6# ' % 3 (

% 9 $ % : % : % / ,"44< "+"+."+"0

% E @ % % 5 : % +/ ,*-"" /7.76

% % "/* ,*--" 0/-.07-!66# = % $ ? ( % > (A3"4 3/7-% % "+4 ,"44< *"04.*"<4 !60# C ( % @ % ' 8 = % @ .@ % ( ( 8 = % A : % % :

,E % $ % "/" ,*--7 "-".""7

% /<7 ,*--7 +-/.+*-!06# & &H % 3 ( % : ) % ( ? % ' % & = % ( 8 1 % E @ % 1 '

.( % ; 8 % % $ % 7< ,*-"-<0-.<<< !00# 8 @ % @ & % & G @ % 3 % & & $ % 9 ' % E @ % ' ( ( % "4 " . , ' $93 % $ % /0 ,*--4 60.0+ !0<# : ) % A 1 3 % @ & % 8 @ % 3 % ( ? % > % 9 ' % 9 3 = % ' ( ( % E @ % 2 % % 9 % +" ,*-"-"0*."4* !04# 5 ' % 3 % 9 % & % : % $ 9 ' % ) .

, 2 % 5 : % +" ,"446 "*4."/< !<-# 5 ' % $ 9 ' % : , % : % *" ,"44< */+.*/4 !<"# 3 ( % E @ % ( "4 " , C % 5 % *6 ,*-"/ **6.*+6 !<*# @ & % 5 5 1 % 8 @ % A 1 3 % ( ? % 3 % 9 3 = % ' ( ( % E @ % > % , "4 " % ) ) % ,*--4

,( % % "*0 ,*---7*7+.7*6+ !47# 8 ( :

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

% % "7/ ,*-"+ /"7<./"64 !"*/# 9 ' % A 1 3 % ' 3 % E ( % 8 @ % ' ( ( % E @ % 8 , "4 " .$93 % 3 8 % 0 ,*- % "+4 ,*-"/ /<.7< !"+-# @ 3 % 9 % E @ % 9 ' % 8 8 % @ % , "4 " .$93 % F , % : % "+<."+4 ,*-"+ <<.40 !"+"# 5 G % C 8 % A ) % ' D % , 3/7-, "4 ,)

% 5 3 % J M % /6 ,*-"" 46-.460 !"+*# G @ % ' A % G % ( @ G % % ' % * ,*-"+ /66./0" !"++# ( ) @ % @ > % 5 5 % % ) & @ % 1 . 8 % 3 : 8 ; 8 % ""* ,*-"7 "/07."/<-!"+/# & ? % A 1 3 % ' ( ( % A ( % 5 & 3 % E @ % 9 ' % "0 . $ % F , % : % 44 ,*-"-/04./4" !"+7# & ? % E @ % : % ( % A 1 3 % A ( % 5 & 3 % 9 ' % "0 . $ . % % ++ ,*-"* "4<.*-/


Marion Delehaye

Sébastien Laurent

Igor Ferrier-Barbut

Shuwei Jin

Frédéric Chevy

Christophe Salomon

Critical Velocity and Dissipation of an ultracold Bose-Fermi Counterflow

Keywords: numbers: 03.75.Kk, 03.75.Ss, 37.10.Gh

come   L'archive ouverte pluridisciplinaire

Superconductivity and superfluidity are spectacular macroscopic manifestations of quantum physics at low temperature. Besides liquid helium 4 and helium 3, dilute quantum gases have emerged over the years as a versatile tool to probe superfluid properties in diverse and controlled situations. Frictionless flows have been observed with both bosonic and fermionic atomic species, in different geometries and in a large range of interaction parameters from the weakly interacting Bose gas to strongly correlated fermionic systems [1][2][3][4][5][6]. Several other hallmarks of superfluidity such as quantized vortices or second sound were also observed in cold atoms [7][8][9].

A peculiar feature of superfluid flows is the existence of a critical velocity above which dissipation arises. In Landau's original argument, this velocity is associated with the threshold for creation of elementary excitations in the superfluid: for a linear dispersion relation, it predicts that the critical velocity is simply given by the sound velocity in the quantum liquid. This critical velocity has been measured both in superfluid helium [START_REF] Wilks | An introduction to liquid helium[END_REF] and ultracold atoms [1,[4][5][6][START_REF] Dries | [END_REF]. However the recent production of a Bose-Fermi double superfluid [12] raised new questions on Bose-Fermi mixtures [13][14][15][16] and interrogations on the validity of Landau's argument in the case of superfluid counterflow [17][18][19][20][21][22].

In this letter, we study the dynamics of a Bose-Fermi superfluid counterflow in the BEC-BCS crossover and at finite temperature. We show how friction arises when the relative velocity of the Bose and Fermi clouds increases and we confirm that damping occurs only above a certain critical relative velocity v c . We compare our measurements to Landau's prediction and its recent generalization v c = c F s +c B s where c F s and c B s are the sound velocities of the fermionic and bosonic components respectively [18]. Finally, we study finite temperature damping of the counterflow and we show that the system can be mapped onto a Caldeira-Leggett-like model [23] of two quantum harmonic oscillators coupled to a bath of excitations. This problem has been recently studied as a toy model for decoherence in quantum networks [24] or for heat transport in crystals [25] and we show here that the emergence of dissipation between the two clouds leads to a Zeno-like effect which locks their relative motions.

Our Bose and Fermi double-superfluid set-up was previously described in [12]. We prepare vapors of bosonic (B) 7 Li atoms spin-polarized in the second-to-lowest energy state and fermionic (F) 6 Li atoms prepared in a balanced mixture of the two lowest spin states noted |↑ , |↓ . The two species are kept in the same cigar-shaped hybrid magnetic-optical trap in which evaporative cooling is performed in the vicinity of the 832 G 6 Li Feshbach resonance [26]. The final number of fermions N F = 2.5 × 10 5 greatly exceeds that of the bosons N B ∼ 2.5 × 10 4 and the temperature of the sample is adjusted by stopping the evaporation at different trap depths. The thermal pedestal surrounding the 7 Li Bose-Einstein Condensate (BEC) provides a convenient low temperature thermometer for both species after sufficiently long thermalization time (∼ 1 second). The lowest temperature achieved in this study corresponds to almost entirely superfluid clouds with T /T c,α=B,F ≤ 0.5, where T c,α is the superfluidity transition temperature of species α.

The magnetic field values used in the experiment (780 -880 G) enable us to scan the fermion-fermion interaction within a range -0.5 ≤ 1/k F a F ≤ 1. Here, a F is the s-wave scattering length between | ↑ and | ↓ fermions and the Fermi momentum k F is defined by

2 k 2 F /2m F = ω(3N F ) 1/3
with ω the geometric mean of the trap frequencies, and N F the total number of fermions of mass m F . In our shallowest traps, typical trap frequencies for 6 Li are ω x = ω y = 2π × 550 Hz and ω z = 2π × 17 Hz. Since the bosonic and fermionic isotopes experience the same trapping potentials, the oscillation frequencies of the two species are within a ratio 6/7 0.9.

We excite the dipole modes of the system by displac- ing adiabatically the centers of mass of the clouds from their initial position by a distance z 0 along the weakly confined z direction, and abruptly releasing them in the trap. The two clouds evolve for a variable time t before in situ absorption images perpendicular to z direction are taken. The measurement of their doubly integrated density profiles gives access to axial positions and atom numbers of both species. Typical time evolutions of the centers of mass are shown in Fig. 1 for different parameter values. Since the Bose and Fermi components oscillate at different frequencies, they oscillate in quadrature after a few periods. By changing z 0 , we can thus tune the maximum relative velocity between the two clouds and probe the critical superfluid counterflow.

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 0 -1 1 � � • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 0 100 200 300 400 0 -1 1 ω � � � � (�) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 0 -1 1 � � • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 0 100 200 300 0 -1 1 ω � � � � (�) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 0 -1 1 � � • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 0 50 100 0 -1 1 ω � � � � (�)
v max v F Γ B s 1 1 k F a F 0.42 1 k F a F 0 1 k F a F 0
As shown in Fig. 1 a, the superfluid counterflow exhibits no visible damping on a 5 s time scale for very low temperature and small initial displacement. A striking feature is the beat note on the 7 Li oscillation amplitude due to the coherent mean-field coupling to the 6 Li cloud [12]. For larger relative velocities, 7 Li oscillations are initially damped (Fig. 1 b) until a steady-state regime as in Fig. 1 a is reached. We fit the time evolution of the cloud position using the phenomenological law

z B (t) = d(t) [a cos(ω B t) + b cos(ω F t)] , (1)
d(t) = d 1 + d 2 exp(-γ B t).
We measure the damping rate γ B as a function of relative velocity for six different values of magnetic field, exploring a large region of the crossover going from the BCS (1/k F a F = -0.42, B = 880 G) to the BEC side (1/k F a F = 0.68, B = 780 G), see Fig. 2. For these magnetic field values, the Bose gas remains in the weakly interacting (repulsive) regime and the Bose-Fermi scattering length is a BF 41a 0 , constant in this magnetic field range, and equal for both |↑ and |↓ spin states.

We extract the critical velocity v c using an ad-hoc power-law fitting function

γ B = AΘ(v-v c )((v-v c )/v F ) α ,
where Θ is the Heaviside function and v F is the Fermi velocity given by v F = k F /m F . For details see [30]. v c in the BEC-BCS crossover is displayed in Fig. 3 dots) and compared to Landau's and Castin et al. [18] predictions. In this latter work, dissipation arises by creation of excitation pairs and yields a critical velocity v c = Min

p σ = f,b B (p)+ F σ (p) p
. In this expression, B (p) denotes the dispersion relation of excitations in the BEC and F σ (p) refers to the two possible branches of the Fermi superfluid, phonon-like (σ = b) and threshold for pair breaking excitations (σ = f) [31]. For homogeneous gases, at unitarity and on the BEC side of the crossover, this critical relative velocity turns out to be simply the sum of the respective sound velocities of the Bose and Fermi superfluids, v c = c F s +c B s . We thus plot in Fig. 3 the calculated sound velocities of both superfluids in an elongated geometry obtained by integration over the transverse direction [27,28,[32][33][34] (red dashed line c F s , blue bars c B s ). Typically c B s contributes 20 -25% to the sum shown as green squares in Fig. 3. Around unitarity and on the BCS side of the resonance, our experimental data is consistent with this interpretation as well as with a critical velocity v c = c F s that one would expect by considering the BEC as a single impurity moving inside the fermionic superfluid. By contrast, we clearly exclude the bosonic sound velocity as a threshold for dissipation.

Our measured critical velocities are significantly higher than those previously reported in pure fermionic systems which, for all interaction strengths, were lower than Landau's criterion [4,6]. The main difference with our study is the use of focused laser beams instead of a BEC as a moving obstacle. In [6], the laser beam is piercing the whole cloud including its non-superfluid part where the density is low, and its potential may create a strong density modulation of the superfluid. These effects make a direct comparison to Landau criterion difficult [35]. On the contrary, in our system the size of the BEC (Thomas Fermi radii of 73, 3, 3 µm) is much smaller than the typical size of the Fermi cloud (350, 13, 13 µm around unitarity). For oscillation amplitudes up to ±200 µm the BEC probes only the superfluid core of the fermionic cloud. During its oscillatory motion along z the Bose gas may explore the edges of the Fermi superfluid where the density is smaller. However it is easy to check that the ratio v/c F s is maximum when the centers of the two clouds coincide [30]. Finally, as the mean-field interaction between the two clouds is very small [30] our BEC acts as a weakly interacting local probe of the Fermi superfluid.

On the BEC side of the resonance (780 G) however, we observe a strong reduction of the measured critical velocity compared to the predicted values. The effect is strikingly seen in Fig. 2, dark blue dots (see also supplementary material [30]). This anomalously small value for positive scattering lengths is consistent with previous measurements [4,6]. Its origin is still unclear but several explanations can be put forward [35]. Firstly, it is well known that vortex shedding can strongly reduce superfluid critical velocity. However, this mechanism requires a strong perturbation. The density of the Bose gas and the mean-field interaction between the two clouds are probably too small for vortex generation through a collective nucleation process. Second, inelastic losses increase on the BEC side of a fermionic Feshbach resonance and heat up the system [36]. This hypothesis is supported by the presence of a clearly visible pedestal in the density profiles of the BEC taken at 780 G. At this value of the magnetic field, we measure a 60% condensed fraction, corresponding to a temperature T /T c,B 0.5. Even though the two clouds are still superfluids as demonstrated by the critical behaviour around v c , the increased temperature could be responsible for the decrease of v c .

We now present results of experiments performed at higher temperature (0.03 T /T F 0.5) for B = 835 G. For low temperatures (T /T F ≤ 0.2), the two clouds remain weakly coupled and, as observed in Fig. 4, the bosonic and fermionic components oscillate at frequencies in the expected ratio 0.9 6/7. A new feature emerges for T T c,B ≈ 0.34 T F > T c,F where both gases are in the normal phase. In this "high" temperature regime, the two clouds are locked in phase: 7 Li oscillates at 6 Li frequency (Fig. 4) and the two components are equally damped (Fig. 1.c). This remarkable behavior can be understood as a Zeno effect arising from the increased dissipation between the two components. Indeed the system can be described as a set of two harmonic oscillators describing respectively the macroscopic motion of the global center of mass of the system (Kohn's mode [37]) and the relative motion of the two clouds [30]. These two degrees of freedom are themselves coupled to the "bath" of the internal excitations of the two clouds (breathing mode, quadrupole modes, pair breaking excitations...).

In the spirit of the dressed-atom picture, we can represent the state of the two harmonic oscillators by the "radiative" cascade of Fig. 5. Here the states |N, n are labeled by the quantum numbers associated to Kohn's mode (N ) and relative motion (n) of the two clouds and we trace-out the degrees of freedom of the bath. On the one hand, Kohn's mode is not an eigenstate of the system for fermions and bosons of different masses; centerof-mass and relative-motion modes are coupled and this coherent coupling is responsible for the dephasing of the oscillations of the two clouds in the weakly interacting regime. On the other hand interspecies interactions do not act on the center of mass of the whole system, owing to Kohn's theorem, but on the contrary lead to an irreversible "radiative" decay of the relative motion at a rate γ.

In our experiments, the initial state is a pure center of mass excitation |N, 0 . If we neglect the interspecies coupling, the system evolves in the subspace spanned by |N -n, n n=0,..,N of the two coupled oscillators and the system oscillates at a frequency δω ω B -ω F as the centers of mass of the Bose and Fermi clouds dephase. If we now consider the opposite limit where the decay rate γ is larger than the dephasing frequency δω, the strong coupling to the bath prevents the conversion of the center of mass excitations into relative motion. As soon as the system is transferred into |N -1, 1 it decays towards state |N -1, 0 . Similarly to optical pumping in quantum optics, we can eliminate adiabatically the excited states of the relative motion and restrict the dynamics of the system to the subspace |N, 0 N =0..∞ of Kohn's excitations. This situation is reminiscent of the synchronization of two spins immersed in a thermal bath predicted in [38] or to phenomenological classical two-coupled oscillators model.

In this letter we have investigated how a Bose-Fermi superfluid flow is destabilized by temperature or relative velocity between the two clouds. In the limit of very low temperature the measured critical velocity for superfluid counterflow slightly exceeds the speed of sound of the elongated Fermi superfluid and decreases sharply towards the BEC side of the BEC-BCS crossover. In a future study, we will investigate the role of temperature, of the confining potential, and of the accelerated motion of the two clouds [35] that should provide a more accurate model for the damping rate versus velocity and more insights on the nature of the excitations. In particular the ab initio calculation of the damping rate will require to clarify the dissipation mechanism at play in a trapped system where the bandwidth of the excitation spectrum is narrow, in contrast to a genuine Caldeira-Leggett model [39].

Supplemental Information

DAMPING RATES IN THE BEC-BCS CROSSOVER

All the center of mass (CoM) damping rates measured in the BEC-BCS crossover and their respective fitting functions to extract v c are shown in Fig. 6. As indicated in the main text the fit function is

γ B = AΘ(v -v c )((v - v c )/v F ) α
, where Θ is the Heaviside function and v F is the Fermi velocity. The χ 2 test reveals that most of our data is consistent with α = 1 as in [4,6]. Due to the current absence of theoretical prediction for α in a trapped system, we allow α to vary between 0.5 and 2, and this induces a systematic correlation between the extracted α and v c that we include in our error bars on v c shown in Fig. 3. The fit results for α = 1 are displayed in Tab. I along with experimental parameters to produce Fig. 3. The error bars given for v c give the span of v c when changing α from 0.5 to 2 in the fit function. Note the strong decrease of the damping rate towards the BCS regime.

In addition, c B s depends on the Bose-Bose scattering length which varies with magnetic field and in particular diverges for a magnetic field of 845.5 G (corresponding to 1/k F a F = -0.13). We therefore show only the values of c B s at the six magnetic field values used in our experiments.

Following [17] the Bose-Fermi coupling can be characterized by the quantity ∆ = ∂µB ∂nF ∂µF ∂nB / ∂µB ∂nB ∂µF ∂nF . As ∆ increases, the interspecies interactions affect more and more the properties of the system and for ∆ = 1, the mixture is dynamically unstable at rest and demixes. For measurements presented here we typically have ∆ 15%. I: Experimental parameters, sound velocity at the center of the Bose gas in an elongated geometry cB = µB/2mB, critical velocity vc/vF, damping rate A(s -1 ), and vc/c F s for α = 1 in the BEC-BCS crossover. The typical number of bosons and fermions are constant in the crossover and are respectively 2.5 ± 0.5 × 10 4 and 2.5 ± 0.5 × 10 5 .

EVOLUTION OF THE VELOCITIES IN THE TRAP

We demonstrate here that for a Bose-Fermi superfluid mixture oscillating in a harmonic trap, the ratio v/c F s is maximum when the centers of two clouds coincide. This can be demonstrated in the general case using the equation of state in the BEC-BCS crossover [27], but we will derive it here for the simpler case of a polytropic equation of state.

In the frame of the Fermi cloud, we can describe the trajectory of the BEC by the simple harmonic oscillation

z B (t) = Z 0 cos(ω B t), (2)
where we have omitted the slow beating of the amplitude Z 0 due to the oscillation-frequency difference between bosons and fermions. The velocity of the BEC is then

v(z) = -Z 0 ω B sin(ω B t), hence v(z) v(z = 0) 2 = 1 - z 2 Z 2 0 , (3)
For a polytropic equation of state, the local sound velocity in the Fermi cloud is given by [33] c F s (z

) 2 = γ γ + 1 µ F (z) m F (4) c F s (z) 2 = γ γ + 1 µ F (0) m F 1 - z 2 z 2 TF , (5)
where z TF is the Thomas-Fermi radius of the cloud, and the local chemical potential µ F (z) was obtained using the local density approximation. Combining equations 3 and 5, we then obtain

v(z) 2 c F s (z) 2 = v(z = 0) 2 c F s (z = 0) 2 1 -z 2 /Z 2 0 1 -z 2 /z 2 TF , (6)
which is maximum for z = 0 when Z 0 ≤ z TF .

LOMB-SCARGLE ALGORITHM

We use the fit-free Lomb-Scargle periodogram -or Least Square Spectral Analysis -to extract the spectral components of the oscillations for different temperatures [40,41]. This method is an adaptation of the Fourier transform to the case of unevenly spaced data. For N data points {h i = h(t i )} i=1,...,N taken at times {t i }, the periodogram is defined as where τ is given by tan(2ωτ ) = j sin 2ωtj j cos 2ωtj making the periodogram independent of the time origin. h = 1 2 are the mean and the variance of {h i } i . The periodogram, or power spectrum (see Fig. 7), gives access to the statistical significance (ie the probability of rejecting the null hypothesis when it is true) of each of the evaluated frequencies: noting P max = max ω P N (ω), the signifiance is proportional to e -Pmax , and here a value of 10 for the power represents typically a significance of 0.002. Fig. 4 of the main text displays the set of maxima of Fig. 7; error bars correspond to a significance increased by a factor of 10.

P N (ω) = 1 2σ 2 [ j (h j -h) cos ω(t j -τ )] 2 j cos 2 ω(t j -τ ) + [ j (h j -h) sin ω(t j -τ )] 2 j sin 2 ω(t j -τ ) (7)
N N i=1 h i and σ = 1 N -1 N i=1 (h i -h)

RADIATIVE CASCADE MODEL

Consider a mixture of two atomic species labeled by α = 1, 2 of identical masses m and confined in identical harmonic traps. According to Kohn's theorem [37], the single-species Hamiltonian can always be written as

H α = P 2 α 2M α + M α ω 2 X 2 α 2 + H (α) int , (8)
where P α is the total momentum of cloud α, X α the position of its center of mass and M α = N α m its total mass (N α being the number of atoms). H

int acts only on the internal excitation modes of the cloud and commutes with the center-of-mass variables.

Neglecting interspecies interactions, the total Hamiltonian of the system can be written as H = H 1 +H 2 . Introducing the center of mass/relative variables, we have then

H = H 1 + H 2 = P 2 2M + M ω 2 X 2 2 + p 2 2µ + µω 2 x 2 2 + H (1) int + H (2) int , (9)
with the usual definitions P

= P 1 + P 2 , X = (M 1 X 1 + M 2 X 2 )/M , p = µ(P 1 /M 1 -P 2 /M 2 ), x = x 1 -x 2 , M = M 1 + M 2 and µ = M 1 M 2 /M .
The dynamics of the center of mass and relative variables are described by independent harmonic oscillators decoupled from the internal degrees of freedom. The decoupled base can therefore be written as |N, n, ϕ , where N (resp. n) is the excitation number of the center-of-mass (resp. relative) motion, and ϕ describes the state of the internal excitation modes. Let's now add the interspecies interactions and the mass difference between the two species.

1. Interspecies coupling: interactions between the two species are described by the Hamiltonian

H 1,2 = i≤N1,j≤N2 U (x 1,i -x 2,j ). ( 10
)
where x i,α is the position of the i-th particle of species α and U is the interspecies interaction potential.

Owing to Kohn's theorem, this Hamiltonian commutes with P and X and therefore couples the internal degrees of freedom only to the relative variables (x, p).

2. Mass difference: assume that species α has a mass m α = m + α δm/2, with 1 = 1 and 2 = -1. This mass difference adds to the kinetic energy a term

δH K = - δm 2m i,α α p 2 i,α 2m . (11)
As before, we can isolate the center of mass contribution and write

δH K = - δm 2m P 2 1 2M 1 - P 2 2 M 2 + δH K,int , (12)
where δH K,int contributes to the internal energies of the clouds and commutes with the center-of-mass degrees of freedom.

Let's now insert these two contributions in the total Hamiltonian. We have

H = H CoM + H rel + H int + H 1,2 + H coh . (13)
with

H CoM = P 2 2M (1 -ρ δm 2m ) + M ω 2 2 X 2 (14)
H rel = p 2 2µ (1 + ρ δm 2m ) + µω 2 2 x 2 (15)
H int = H (1)
int + H

(2)

int + δH K,int , (16)
H coh = δm m P • p M , (17)
and ρ = (M 1 -M 2 )/M . This hamiltonian describes two harmonic oscillators (H CoM and H rel ) coupled to a thermal bath (H int ). The coupling is ensured by the P • p terms which couples only the center-of-mass and relative degrees of freedom, and H 1,2 that commutes with H CoM , owing to Kohn's theorem, and couples the relative motion to the internal degrees of freedom of the two clouds.

The interaction between the relative degrees of freedom and the internal thermal bath described by H 1,2 int leads to an irreversible decay of the relative motion. By contrast, H coh reflects the coherent beating existing between the relative oscillations of the two species due to their oscillation-frequency difference. It can be expressed using the annihilation operators a and b for the center of mass and relative motions respectively. We have then

H coh = - δm m ω µ M a -a † b -b † . (18)
Using the rotating wave approximation, one can eliminate the non resonant terms and one finally gets

H coh δm 2m ω µ M a † b + ab † . ( 19
)
This Hamiltonian is similar to the generalized Caldeira-Leggett model [23] used in solid state physics to study heat transport by phonons in a crystal. The absence of coupling between the bath and Kohn's mode generalizes to the decomposition used in [24] for a bilinear coupling between the harmonic oscillators and the bath.

In the experiment, we excite the center of mass motion and the initial state is |N, 0, ϕ . The coherent coupling transfers the system to the state |N -1, 1, ϕ . If the coupling to the bath is strong, the relative motion decays very fast and the system falls into a state |N -1, 0, ϕ (actually, since several states of the bath are involved, it is more appropriate to describe the state of the two harmonic oscillators by a density matrix rather than a well-defined quantum state). In this case, just like for optical pumping, we can adiabatically eliminate the intermediate state |N -1, 1, ϕ and consider that the dynamics occurs only in the sub-space |N, 0, ϕ , where the relative motion is never excited and the centers of mass of the two clouds are locked. In some sense, this freezing of the system state in a pure motion of its center of mass can be considered as a manifestation of the quantum Zeno effect.

FIG. 1 :

 1 FIG.1: Center-of-mass oscillations of bosons (blue, top) and fermions (red, bottom), for different sets of parameters at unitarity. Solid lines: fits using Eq.1 for the bosons and a similar equation for the fermions. (a) T /TF = 0.03, T /T c,b ≤ 0.5, z0 = 10 µm. Superfluid regime, no damping is observed and ωB = 2π ×15.41(1) Hz ≈ 6/7 ωF. The observed beating at ωF -ωB is due to coherent energy exchange between the clouds. (b) T /TF = 0.03 and z0 = 150 µm. For a larger initial displacement, initial damping (γB = 2.4 s -1 ) is followed by steady-state evolution. ωB = 2π × 14.2(1) Hz ≈ 6/7 ωF. (c) T /TF = 0.4 and z0 = 80 µm. At higher temperature, phaselocking of the two frequencies is observed with ωF ≈ ωB = 2π × 17.9(3) Hz and γB = γF = 1.4(5) s -1 .

  FIG. 3: Critical velocity of the Bose-Fermi superfluid counterflow in the BEC-BCS crossover normalized to the Fermi velocity vF. Red dots: measurements. Red dot-dashed line: sound velocity c F s of an elongated homogeneous Fermi superfluid calculated from its equation of state [27, 28] after integration of the density in the transverse plane, and also measured in [29]. Blue bars: calculated sound velocity c B s of the elongated 7 Li BEC for each magnetic field, (880 G, 860 G, 832 G, 816 G, 800 G, 780 G). Green squares indicate the prediction vc = c F s + c B s . Error bars and c B s are discussed in [30].

FIG. 4 :

 4 FIG. 4: Ratio ωB/ωF versus temperature of the cloud. Blue circles: the two clouds are superfluids. Yellow squares: only the bosonic component is superfluid. Green open diamonds: the two components are normal. Above T ≈ Tc,B ≈ 0.34 TF > Tc,F, oscillations of the Bose and Fermi clouds become locked together at ωF. Oscillations frequencies are obtained using a Lomb-Scargle algorithm [30]. The lower dashed line is the prediction of a low temperature mean field model [12].

FIG. 5 :

 5 FIG.5: Radiative cascade of the center of mass motion. In |N, n , N (resp. n) refers to the center of mass (resp. relative) motion of the two clouds (see text). When the decay rate of the relative motion is larger than the oscillation frequency difference between the two species, the dynamics is restricted to the center of mass degree of freedom: in this Zeno-like process, dissipation prevents excitation of the relative motion and the center of mass modes of the Bose and Fermi gases do not dephase.

FIG. 6 :

 6 FIG.6: Damping rates of the center of mass oscillations versus maximal relative velocity in the BEC-BCS crossover in unit of the Fermi velocity vF. Red line: fit with α = 1. Orange zone: region spanned by the fitting function when varying α from 0.5 to 2.

FIG. 7 :

 7 FIG. 7: Power spectrum of the oscillations for different temperatures, obtained using the Lomb-Scargle algorithm of the centerof-mass displacement. Above T ≈ Tc,B ≈ 0.34 TF > Tc,F, oscillations of the Bose and Fermi clouds become locked together at ωF. A value of 10 for the power represents typically a significance of 0.002.

TABLE

The authors acknowledge support from Région Ile de France (Atomix Project), ERC (ThermoDynaMix Project) and Institut de France (Louis D. Prize). They thank I. Danaila, N. Proukakis, K.L. Lee and M. Pierce for insightful comments and discussions, and J. Dalibard, Y. Castin, S. Nascimbène and T. Yefsah for critical reading of the manuscript.