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We report on a combined experimental and theoretical study of the low-entropy Mott transition for interacting bosons trapped in a three-dimensional (3D) cubic lattice -- namely, the interaction-induced superfluid-to-normal phase transition in the vicinity of the zero-temperature Mott transition. Our analysis relies on the measurement of the 3D momentum distribution, which allows us to extract the momentum-space density $\rho({\bf k}={\bf 0})$ at the center of the Brillouin zone. Upon varying the ratio between the interaction $U$ and the tunnelling energy $J$ across the superfluid transition, we observe that $\rho({\bf k}={\bf 0})$ exhibits a sharp transition at a value of $U/J$ consistent with the bulk prediction from quantum Monte Carlo. In addition, the variation of $\rho({\bf k}={\bf 0})$ with $U/J$ exhibits a critical behavior consistent with the expected 3D XY universality class. Our results show that the tomographic reconstruction of the momentum distribution of ultracold bosons can reveal traits of the critical behavior of the superfluid transition even in an inhomogeneous trapped system., Comment: 5 pages, 4 figures

Quantum fluctuations play a central role in the properties of quantum matter. In non-interacting ensembles, they manifest as fluctuations of non-commuting observables, quantified by Heisenberg inequalities. In the presence of interactions, additional quantum fluctuations appear, from which many-body correlations and entanglement arise. In the context of many-body physics, the Bogoliubov theory provides us with an illuminating microscopic picture of how this occurs for weakly-interacting bosons, with the appearance of the quantum depletion formed by pairs of bosons with opposite momenta. Here, we report the observation of these atom pairs in the depletion of an equilibrium interacting Bose gas. A quantitative study of atom-atom correlations, both at opposite and close-by momenta, allows us to fully characterise the equilibrium many-body state. We show that the atom pairs share the properties of two-mode squeezed states, including relative number squeezing. Our results illustrate how interacting systems acquire non-trivial quantum correlations as a result of the interplay between quantum fluctuations and interactions, 5 pages, 4 figures + supplementary material

International audience; We measure the lifetime of the cesium $5^2D_{5/2}$ state using a time-resolved single-photon-counting method. We excite atoms in a hot vapor cell via an electric quadrupole transition at a wavelength of $685\,\mathrm{nm}$ and record the fluorescence of a cascade decay at a wavelength of $852\,\mathrm{nm}$. We extract a lifetime of $1353(5)\,\mathrm{ns}$ for the $5^2D_{5/2}$ state, in agreement with a recent theoretical prediction. In particular, the observed lifetime is consistent with the literature values of the polarizabilities of the cesium $6P$ states. Our measurement contributes to resolving a long-standing disagreement between a number of experimental and theoretical results.

International audience; We realize a mechanical analogue of the Dicke model, achieved by coupling the spin of individual neutral atoms to their quantized motion in an optical trapping potential. The atomic spin states play the role of the electronic states of the atomic ensemble considered in the Dicke model, and the in-trap motional states of the atoms correspond to the states of the electromagnetic field mode. The coupling between spin and motion is induced by an inherent polarization gradient of the trapping light fields, which leads to a spatially varying vector light shift. We experimentally show that our system reaches the ultra-strong coupling regime, i.e., we obtain a coupling strength which is a significant fraction of the trap frequency. Moreover, with the help of an additional light field, we demonstrate the in-situ tuning of the coupling strength. Beyond its fundamental interest, the demonstrated one-to-one mapping between the physics of optically trapped cold atoms and the Dicke model paves the way for implementing protocols and applications that exploit extreme coupling strengths. The quantum Rabi model (QRM) describes the interaction of a two-level emitter with a single quantized mode of the electromagnetic field. Together with its extension for an ensemble of emitters, i.e., the Dicke model (DM), it constitutes a cornerstone of quantum optics [1]. The physics predicted by the QRM and the DM strongly depends on the relative values of the mode frequency, ω, and the coupling strength between the two-level system (TLS) and the bosonic mode, g. For weak coupling, i.e., g/ω 1, the rotating wave approximation (RWA) applies. In this case, the QRM and the DM reduce to the Jaynes-Cummings and the Tavis-Cummings models, respectively. The RWA breaks down in the ultra-strong coupling regime (USC), i.e., for g/ω 0.1. When increasing the coupling strength further, one enters the deep-strong coupling regime (DSC) [2]. For such high values of g/ω, new phenomena are expected [3-7]. The existence of a quantum phase transition in the thermo-dynamic limit adds to the richness of the DM [8-10]. Furthermore, USC and DSC may enable novel protocols for quantum communication and quantum information processing [11-13]. Over the last decade, USC was reached using various experimental platforms [14-22]. More recently, DSC was achieved in circuit quantum electrodynamics [23, 24] as well as by coupling a THz metamaterial with cyclotron resonances in a two-dimensional electron gas [25]. While these systems reach record-high ratios of g/ω, the large coupling strengths make state preparation and read-out challenging. For this reason, alternative routes were proposed to achieve large coupling in experimental platforms that, at the same time, offer a high level of control and tunability. Following this path, the QRM in the USC and DSC regimes was simulated using circuit quantum elec-trodynamics [26, 27], and DSC was studied with single trapped ions [28]. Here, we implement a mechanical analogue of the Dicke model by coupling the spin of individual neutral atoms to their quantized motion in a trapping potential. In our approach, the coupling is enabled by spatial gradients of the vector light shift inherent to optical mi-crotraps. Fluorescence spectroscopy, which was recently used to measure the temperature of atoms in a nanofiber-based trap after degenerate Raman cooling [29], grants access to the energy spectrum of the system. We observe vacuum Rabi splittings and transitions between dressed states that both clearly and consistently reveal an ultra-strong spin-motion coupling in our experiment, i.e., the coupling strength is a significant fraction of the mode frequency. Furthermore, we demonstrate that the coupling strength can be readily tuned in situ using an additional laser light field.

Laser-cooled atoms coupled to nanophotonic structures constitute a powerful research platform for the exploration of new regimes of light-matter interaction. While the initialization of the atomic internal degrees of freedom in these systems has been achieved, a full preparation of the atomic quantum state also requires controlling the center of mass motion of the atoms at the quantum level. Obtaining such control is not straightforward, due to the close vicinity of the atoms to the photonic system that is at ambient temperature. Here, we demonstrate cooling of individual neutral Cesium atoms, that are optically interfaced with light in an optical nanofiber, preparing them close to their three-dimensional motional ground state. The atoms are localized less than 300nm away from the hot fiber surface. Ground-state preparation is achieved by performing degenerate Raman cooling, and the atomic temperature is inferred from the analysis of heterodyne fluorescence spectroscopy signals. Our cooling method can be implemented either with externally applied or guided light fields. Moreover, it relies on polarization gradients which naturally occur for strongly confined guided optical fields. Thus, this method can be implemented in any trap based on nanophotonic structures. Our results provide an ideal starting point for the study of novel effects such as light-induced self-organization, the measurement of novel optical forces, and the investigation of heat transfer at the nanoscale using quantum probes.

International audience; We report on high-resolution optical spectroscopy of interacting bosonic $^{174}$Yb atoms in deep optical lattices with negligible tunneling. We prepare Mott insulator phases with singly- and doubly-occupied isolated sites and probe the atoms using an ultra-narrow "clock" transition. Atoms in singly-occupied sites undergo long-lived Rabi oscillations. Atoms in doubly-occupied sites are strongly affected by interatomic interactions, and we measure their inelastic decay rates and energy shifts. We deduce from these measurements all relevant collisional parameters involving both clock states, in particular the intra- and inter-state scattering lengths.

Optical microtraps provide a strong spatial confinement for laser-cooled atoms. They can, e.g., be realized with strongly focused trapping light beams or the optical near fields of nano-scale waveguides and photonic nanostructures. Atoms in such traps often experience strongly spatially varying AC Stark shifts which are proportional to the magnetic quantum number of the respective energy level. These inhomogeneous fictitious magnetic fields can cause a displacement of the trapping potential that depends on the Zeeman state.

Optical microtraps provide a strong spatial confinement for laser-cooled atoms. They can, e.g., be realized with strongly focused trapping light beams or the optical near fields of nano-scale waveguides and photonic nanostructures. Atoms in such traps often experience strongly spatially varying AC Stark shifts which are proportional to the magnetic quantum number of the respective energy level. These inhomogeneous fictitious magnetic fields can cause a displacement of the trapping potential that depends on the Zeeman state. Hitherto, this effect was mainly perceived as detrimental. However, it also provides a means to probe and to manipulate the motional state of the atoms in the trap by driving transitions between Zeeman states. Furthermore, by applying additional real or fictitious magnetic fields, the state-dependence of the trapping potential can be controlled. Here, using laser-cooled atoms that are confined in a nanofiber-based optical dipole trap, we employ this control in order to tune the microwave coupling of motional quantum states. We record corresponding microwave spectra which allow us to infer the trap parameters as well as the temperature of the atoms. Finally, we reduce the mean number of motional quanta in one spatial dimension to $\langle n\rangle=0.3 \pm 0.1$ by microwave sideband cooling. Our work shows that the inherent fictitious magnetic fields in optical microtraps expand the experimental toolbox for interrogating and manipulating cold atoms., Comment: 6 pages, 3 figures, comments welcome

Hybrid quantum systems are promising candidates for realizing a quantum network. A particularly interesting approach in this context relies on optical-nanofiber-based atom-photon interfaces [1]. Using a two-color evanescent field, cold neutral atoms are trapped about 200nm away from the nanofiber surface. This small distance allows evanescent coupling between the trapped atoms and additional fiber-guided light fields. The control of the atoms' internal degrees of freedom has already been demonstrated extensively in the nanofiber system, including the preparation of Zeeman states [2, 3] and coherent dark states [4]. However, for complete control, one should also be able to manipulate the external degrees of freedom at the quantum level. In order to characterize the motional states of the trapped atoms, we record microwave spectra of the atomic hyperfine ground state manifold. As the trapping potential is spin-state-dependent, we can drive microwave transitions between different motional states [5]. In this case, motional sidebands appear in the spectra as additional resonances which are separated by integer multiples of the trap frequency from the microwave carrier transition. We use microwave spectroscopy as a diagnostic tool in order to precisely infer the trap frequency and the temperature of the atoms in the nanofiber-based trap. Furthermore, we can cool the atoms by repeatedly driving microwave transitions to lower vibrational states. Once atoms are cooled, their coherence time is increased as the influence of position-dependent light shifts is reduced. Moreover, thanks to the improved localization, the coupling of the atoms to nanofiber-guided optical fields is even more precisely controlled. This is beneficial for realizing nanofiber-based quantum memories, which have the potential to become an important building block in future quantum networks.

Recently, a new generation of experiments with ultracold quantum gases has emerged where the many-body properties are probed and manipulated using ultra-narrow “clock” transitions. We describe here our experimental project, which aims at engineering a special kind of optical lattice realizing an effective magnetic field coupling to the atomic motion - the Hofstadter optical lattice. Our specific experimental scheme uses the ultra-narrow optical transition linking the ground state to a metastable excited state of 174 Ytterbium atoms. We present the current status of the experiment, including the observation of coherent Rabi oscillations between the ground and excited states.

We study the dynamics of a two-component Bose-Einstein condensate (BEC) of $^{174}$Yb atoms coherently driven on a narrow optical transition. The excitation transfers the BEC to a superposition of states with different internal and momentum quantum numbers. We observe a crossover with decreasing driving strength between a regime of damped oscillations, where coherent driving prevails, and an incoherent regime, where relaxation takes over. Several relaxation mechanisms are involved: inelastic losses involving two excited atoms, leading to a non-exponential decay of populations; Doppler broadening due to the finite momentum width of the BEC and inhomogeneous elastic interactions, both leading to dephasing and to damping of the oscillations. We compare our observations to a two-component Gross-Pitaevskii (GP) model that fully includes these effects. For small or moderate densities, the damping of the oscillations is mostly due to Doppler broadening. In this regime, we find excellent agreement between the model and the experimental results. For higher densities, the role of interactions increases and so does the damping rate of the oscillations. The damping in the GP model is less pronounced than in the experiment, possibly a hint for many-body effects not captured by the mean-field description., Comment: 7 pages, 4 figures; supplementary material available as ancillary file