We study an atom-cavity system in which the cavity has several degenerate transverse modes. Mode-resolved cavity transmission spectroscopy reveals well-resolved atom-cavity resonances for several cavity modes, a signature of collective strong coupling for the different modes. Furthermore, the experiment shows that the cavity modes are coupled via the atomic ensemble contained in the cavity. The experimental observations are supported by a detailed theoretical analysis. The work paves the way to the use of interacting degenerate modes in cavity-based quantum information processing, where qubits corresponding to different cavity modes interact via an atom shared by the two modes. Our results are also relevant to the experimental realization of quantum spin glasses with ultracold atoms.

We propose an experimental realization of a time crystal using an atomic Bose-Einstein condensate in a high finesse optical cavity pumped with laser light detuned to the blue side of the relevant atomic resonance. By mapping out the dynamical phase diagram, we identify regions in parameter space showing stable limit cycle dynamics. Since the model describing the system is time-independent, the emergence of a limit cycle phase indicates the breaking of continuous time translation symmetry. Employing a semiclassical analysis to demonstrate the robustness of the limit cycles against perturbations and quantum fluctuations, we establish the emergence of a time crystal.

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Using a model system, we demonstrate both experimentally and theoretically that coherent scattering of light can be robust in hot atomic vapors despite a significant Doppler effect. By operating in a linear regime of far-detuned light scattering, we also unveil the emergence of interference triggered by inelastic Stokes and anti-Stokes transitions involving the atomic hyperfine structure.Wave propagation in disordered media is at the focus of intense investigations in many different fields of research, including condensed matter [1], astrophysics [2], acoustics [3], optics [4], atomic physics [5] and ultracold atoms [6]. Often, many parameters of the system under study are not fully controlled and are described by effective parameters, including for instance the strength of disorder or decoherence. Similarly, the internal structure of atoms is often put aside and a simplified two-level model is used to describe the qualitative behavior of observed phenomena. Interestingly, in cases when the detailed structure is taken into account, not only the quantitative description can be improved, but new qualitative features can emerge, such as Sisyphus cooling [7], slow light [8] and quantum memories [9]. Doppler broadening in room temperature vapors adds to the complexity of a microscopic description of coherent light propagation and a radiative transfer equation is often used as a simplified model [5]. This however prevents the description of coherence phenomena in nearby coupled dipoles [10][11][12][13][14] or the anomaly of polarization at the D1 line of the solar spectrum [15]. Even though Doppler-free spectroscopy in room temperature atomic vapors has seen important results, the development of laser cooling of atoms allowed for an impressive improvement of high-precision measurements. Presently, we witness a renewed interest in precision measurements with hot atoms, including applications on electric-field sensors [16] and quantum information science [17][18][19][20]. In this Letter we report on a coherent light scattering experiment with a hot atomic vapor in which thermal decoherence is largely circumvented. We also show that the internal multi-level structure of the atoms gives rise to qualitatively new interference features which emerge as a result of inelastic scattering and can be described with a quantitatively accurate microscopic theory.The scheme of our experiment is shown in Fig. 1. A collimated laser beam (waist w = 10 mm) is sent through a slab-shaped glass cell containing a natural mixture of rubidium vapor at an oven-regulated temperature/density. The wavelength λ = 780 nm is set to the D2 transition of rubidium. Two different cells were used, one with a metallic mirror clipped to the back side, and FIG. 1: (Color online) Scheme of the experiment (for clarity polarization elements are not shown). A collimated laser beam is sent via a beamspitter (bs) through a glass cell (width L ≃ 8 mm, chamber thickness L ′ ≃ 6 mm) containing a hot mixture of rubidium atoms. An oven with a cold 'finger' is used to re...

The field of quantum turbulence is related to the manifestation of turbulence in quantum fluids, such as liquid helium and ultracold gases. The concept of turbulence in quantum systems was conceived more than 70 years ago by Onsager and Feynman, but the study of turbulent ultracold gases is very recent. Although it is a young field, it already provides new approaches to the problem of turbulence. We review the advances and present status, of both theory and experiments, concerning atomic Bose-Einstein condensates (BECs). We present the difficulties of characterizing turbulence in trapped BECs, if compared to classical turbulence or turbulence in liquid helium. We summarize the challenges ahead, mostly related to the understanding of fundamental properties of quantum turbulence, including what is being done to investigate them.

Stable laser sources at 461 nm are important for optical cooling of strontium atoms. In most existing experiments this wavelength is obtained by frequency doubling infrared lasers, since blue laser diodes either have low power or large emission bandwidths. Here, we show that injecting less than 10 mW of monomode laser radiation into a blue multimode 500 mW high power laser diode is capable of slaving at least 50% of the power to the desired frequency. We verify the emission bandwidth reduction by saturation spectroscopy on a strontium gas cell and by direct beating of the slave with the master laser. We also demonstrate that the laser can efficiently be used within the Zeeman slower for optical cooling of a strontium atomic beam.

The theoretical description of the external degrees of freedom of atoms trapped inside a magnetooptical trap (MOT) often relies on the decoupling of the evolution of the internal and external degrees of freedom. That is possible thanks to much shorter timescales typically associated with the first ones. The electronic structure of alkaline-earth atoms, on the other hand, presents ultra-narrow transitions and metastable states that makes such an approximation invalid in the general case. In this article, we report on a model based on open Bloch equations for the evolution of the number of atoms in a magneto-optical trap. With this model we investigate the loading of the strontium blue magnetooptical trap under different repumping schemes, either directly from a Zeeman slower, or from an atomic reservoir made of atoms in a metastable state trapped in the magnetic quadrupolar field. The fluorescence observed on the strong 461 nm transition is recorded and quantitatively compared with the results from our simulations. The comparison between experimental results and calculations within our model allowed to identify the existence of the decay paths between the upper level of the repumping transition and the dark strontium metastable states, which could not be explained by electric dipole transition rates calculated in the literature. Moreover, our analysis pinpoints the role of the atomic movement in limiting the efficiency of the atomic repumping of the Sr metastable states.

We investigate the possibility of cooling an atomic gas enclosed in an optical cavity using blue-detuned laser light of sufficient intensity that excitation of the atoms cannot be neglected. We consider an ensemble of two-level atoms confined inside a simple Fabry-Perot cavity in two different geometric configurations: in one ('cavity-pump' configuration) the pump field is directed along the cavity axis and in the other ('atom-pump' configuration) the pump field is directed perpendicular to the cavity axis. Numerical simulations of the semi-classical models for each configuration are compared. Both configurations demonstrate cooling using a blue-detuned pump field. It is shown that in the cavity-pump configuration there is no collective enhancement of the cooling rate over that of free space blue-cooling. In contrast, the atom-pump configuration demonstrates collective enhancement of the cooling rate and intracavity field intensity