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We report on observations of the extended environment of the bright Be star $\gamma$-Cas performed using intensity interferometry measurements within its H$\alpha$ emission line. These observations were performed using a modified version of the I2C intensity interferometry instrument installed onto the 1.54 meter M\'{e}O optical metrology telescope and a portable 1-meter telescope (T1M). In order to better constrain the extent of the H$\alpha$ envelope, observations were performed for two different positions of the T1M telescope, corresponding to an intermediate and long baselines in which the extended region was partially and fully resolved. We find that the observed data are consistent with past interferometric observations of $\gamma$-Cas. These observations demonstrate the capability to equip optical telescopes of different optical designs with intensity interferometry capabilities and illustrate the potential to scale a similar system onto many additional telescopes.

Considering light-mediated long-range interactions between cold atoms in a magneto-optical trap (MOT), we present numerical evidence of a nonequilibrium steady state (NESS) for sufficiently large number of atoms (> 10^8). This state manifests itself as the appearance of an anisotropic distribution of velocity when a MOT approaches the threshold beyond which self-oscillating instabilities occur. Our three-dimensional (3D) spatiotemporal model with nonlocal spatial dependencies stemming from the interatomic interactions has recently been compared successfully to predict different instability thresholds and regimes in experiments with rubidium atoms. The behavior of the NESS is studied as a function of the main MOT parameters, including its spatiotemporal characteristics., Comment: 10 pages, 8 figures

The Siegert relation relates field and intensity temporal correlations. After a historical review of the Siegert relation and the Hanbury Brown and Twiss effect, we discuss the validity of this relation in two different domains. We first show that this relation can be used in astrophysics to determine the fundamental parameters of stars, and that it is especially important for the observation with stellar emission lines. Second, we verify the validity of this relation for moving quantum scatterers illuminated by a strong driving field.

We present the current status of the I2C stellar intensity interferometer used towards high angular resolution observations of stars in visible wavelengths. In these proceedings, we present recent technical improvements to the instrument, and share results from ongoing campaigns using arrays of small diameter optical telescopes. A tip-tilt adaptive optics unit was integrated into the optical system to stabilize light injection into an optical fiber. The setup was successfully tested with several facilities on the Calern Plateau site of the Observatoire de la C\^ote d'Azur. These include one of the 1 m diameter telescopes of the C2PU observatory, a portable 1 m diameter telescope, and also the 1.5 m M\'eO telescope. To better constrain on-sky measurements, the spectral transmission of instrument was characterized in the laboratory using a high resolution spectrograph. The system was also tested with two of the auxiliary telescopes of the VLTI resulting in successful temporal and spatial correlation measurements of three stars.

In this paper we report on spatial intensity interferometry measurements within the H$\alpha$ line on two stars: the Luminous Blue Variable supergiant \PCygni\,and the late-type B supergiant Rigel. The experimental setup was upgraded to allow simultaneous measurement of two polarization channels, instead of one in our previous setup, and the zero baseline correlation function on-sky to validate independent estimates obtained from the stellar spectrum and the instrumental spectral throughput. Combined with simultaneous spectra measurements and based on radiative transfer models calculated with the code CMFGEN, we were able to fit our measured visibility curves to extract the stellar distances. Our distance determinations for both \PCygni\ (1.61 $\pm$ 0.18 kpc) and Rigel (0.26 $\pm$ 0.02 kpc) agree very well with the values provided by astrometry with the Gaia and Hipparcos missions, respectively. This result for Rigel was obtained by adopting a stellar luminosity of $L_{\star}$ = 123000 $L_{\odot}$, which is reported in the literature as being consistent with the Hipparcos distance to Rigel. However, due to the lack of consensus on Rigel's luminosity, we also explore how the adoption of the stellar luminosity in our models affects our distance determination for Rigel. In conclusion, we support, in an independent way, the distance to Rigel as the one provided by the Hipparcos mission, when taking the luminosity of 123000 $L_{\odot}$ at face value. This study is the first successful step towards extending the application of the Wind Momentum Luminosity Relation method for distance calibration from an LBV supergiant to a more normal late-type B supergiant., Comment: Monthly Notices of the Royal Astronomical Society: Letters, Oxford Journals, In press

A large cloud of $^{87}$Rb atoms confined in a magneto-optical trap exhibits, in a certain regime of parameters, spatio-temporal instabilities with a dynamics resembling that of a turbulent fluid. We apply the methods of turbulence theory based on structure function analysis to extract scaling exponents which are compared to known turbulent regimes. This analysis also allows us to make a clear distinction between different instability regimes., Comment: 5 pages, 3 Figures

This article discusses self-organization in cold atoms via light-mediated interactions induced by feedback from a single retro-reflecting mirror. Diffractive dephasing between the pump beam and the spontaneous sidebands selects the lattice period. Spontaneous breaking of the rotational and translational symmetry occur in the 2D plane transverse to the pump. We elucidate how diffractive ripples couple sites on the self-induced atomic lattice. The nonlinear phase shift of the atomic cloud imprinted onto the optical beam is the parameter determining coupling strength. The interaction can be tailored to operate either on external degrees of freedom leading to atomic crystallization for thermal atoms and supersolids for a quantum degenerate gas, or on internal degrees of freedom like populations of the excited state or Zeeman sublevels. Using the light polarization degrees of freedom on the Poincar{\'e} sphere (helicity and polarization direction), specific irreducible tensor components of the atomic Zeeman states can be coupled leading to spontaneous magnetic ordering of states of dipolar and quadrupolar nature. The requirements for critical interaction strength are compared for the different situations. Connections and extensions to longitudinally pumped cavities, counterpropagating beam schemes and the CARL instability are discussed.

We propose a new approach, based on the Hanbury Brown and Twiss intensity interferometry, to transform a Cherenkov telescope to its equivalent optical telescope. We show that, based on the use of photonics components borrowed from quantum-optical applications, we can recover spatial details of the observed source down to the diffraction limit of the Cherenkov telescope, set by its diameter at the mean wavelength of observation. For this, we propose to apply aperture synthesis techniques from pairwise and triple correlation of sub-pupil intensities, in order to reconstruct the image of a celestial source from its Fourier moduli and phase information, despite atmospheric turbulence. We examine the sensitivity of the method, i.e. limiting magnitude, and its implementation on existing or future high energy arrays of Cherenkov telescopes. We show that despite its poor optical quality compared to extremely large optical telescopes under construction, a Cherenkov telescope can provide diffraction limited imaging of celestial sources, in particular at the visible, down to violet wavelengths., Comment: 8 pages, 7 figures

Large clouds of cold atoms prepared in a magneto-optical trap can develop spatio-temporal instabilities when the frequency of the trapping lasers is brought close to the atomic resonance. This system bears close similarities with trapped plasmas, whereby effective Coulomb interactions are induced by the exchange of scattered photons and lead to collective nonlinear dynamics of the trapped atoms. We report in this paper a detailed experimental study of the instability threshold, and comparisons with three-dimensional simulations of the interacting, laser-driven cloud., Comment: 8 pages, 6 figures

Recent advances in photonics have revived the interest in intensity interferometry for astronomical applications. The success of amplitude interferometry in the early 1970s, which is now mature and producing spectacular astrophysical results (e.g. GRAVITY, MATISSE, CHARA, etc.), coupled with the limited sensitivity of intensity interferometry stalled any progress on this technique for the past 50 years. However, the precise control of the optical path difference in amplitude interferometry is constraining for very long baselines and at shorter wavelengths. Polarization measurements are also challenging in amplitude interferometry due to instrumental effects. The fortuitous presence of strong groups in astronomical interferometry and quantum optics at Universite Cote d'Azur led to the development of a prototype experiment at Calern Observatory, allowing the measure of the temporal correlation g(2)(\tau, r=0) in 2016 and of the spatial correlation g^(2)(r) in 2017 with a gain in sensitivity (normalized in observing time and collecting area) of a factor ~100 compared to Hanbury Brown and Twiss's original Narrabri Interferometer. We present possible ways to further develop this technique and point to possible implementations on existing facilities, such as CTA, the VLTI ATs or the summit of Maunakea, which offer a unique scientific niche., Comment: SPIE Conference proceedings, 12 pages

We propose different experimental methods to measure the analog of the Debye length in a very large Magneto-Optical Trap, which should characterize the spatial correlations in the atomic cloud. An analytical, numerical and experimental study of the response of the atomic cloud to an external modulation potential suggests that this Debye length, if it exists, is significantly larger than what was expected., Comment: 12 pages, 6 figures. v2 Clarify the paper presentation + correct minor points

When applying a red-detuned retro-reflected laser beam to a large cloud of cold atoms, we observe the spontaneous formation of 2D structures in the transverse plane corresponding to high contrast spatial modulations of both light field and atomic spins. By applying a weak magnetic field, we explore the rich resulting phase space and identify specific phases associated with both dipolar and quadrupolar terms of the atomic magnetic moment. In particular we demonstrate spontaneous structures in optically induced ground state coherences representing magnetic quadrupoles., Comment: 8 pages, 5 figures

More than sixty years after the first intensity correlation experiments by Hanbury Brown and Twiss, there is renewed interest for intensity interferometry techniques for high angular resolution studies of celestial sources. We report on a successful attempt to measure the bunching peak in the intensity correlation function for bright stellar sources with 1 meter telescopes (I2C project). We propose further improvements of our preliminary experiments of spatial interferometry between two 1 m telescopes, and discuss the possibility to export our method to existing large arrays of telescopes., Comment: 14 pages, 3 figures

Nonlinear oscillations and synchronisation phenomena are ubiquitous in nature. We study the synchronization of self oscillating magneto-optically trapped cold atoms to a weak external driving. The oscillations arise from a dynamical instability due the competition between the screened magneto-optical trapping force and the inter-atomic repulsion due to multiple scattering of light. A weak modulation of the trapping force allows the oscillations of the cloud to synchronize to the driving. The synchronization frequency range increases with the forcing amplitude. The corresponding Arnold tongue is experimentally measured and compared to theoretical predictions. Phase-locking between the oscillator and drive is also observed., Comment: Corrected typos

When applying two counter-propagating laser beams to a cold cloud of Rubidium atoms, we observe the spontaneous formation of intensity patterns associated with a spatial structuration of the atomic spins. We study the average number of defects in these patterns as a function of the sweep time employed to cross the transition threshold. We observe a power-law decrease of the number of defects with increasing sweep time, typical of the Kibble-Zurek mechanism. The measured exponent is consistent with the prediction for a supercritical bifurcation., Comment: 5 pages, 4 Figures

We investigate the scaling behavior of a very large magneto-optical trap (VLMOT) containing up to $1.4 \times 10^{11}$ Rb$^{87}$ atoms. By varying the diameter of the trapping beams, we are able to change the number of trapped atoms by more than 5 orders of magnitude. We then study the scaling laws of the loading and size of the VLMOT, and analyze the shape of the density profile in this regime where the Coulomb-like, light-mediated repulsive interaction between atoms is expected to play an important role., Comment: 9 pages, 10 figures

We study the center-of-mass motion in systems of trapped interacting particles with space- and velocity-dependent friction and anharmonic traps. Our approach, based on a dynamical ansatz assuming a fixed density profile, allows us to obtain information at once for a wide range of binary interactions and interaction strengths, at linear and nonlinear levels. Our findings are first tested on different simple models by comparison with direct numerical simulations. Then, we apply the method to characterize the motion of the center of mass of a magneto-optical trap and its dependence on the number of trapped atoms. Our predictions are compared with experiments performed on a large Rb85 magneto-optical trap., Comment: 9 pages, 8 figures

The rapidly developing field of optomechanics aims at the combined control of optical and mechanical (solid-state or atomic) modes. In particular, laser cooled atoms have been used to exploit optomechanical coupling for self-organization in a variety of schemes where the accessible length scales are constrained by a combination of pump modes and those associated to a second imposed axis, typically a cavity axis. Here, we consider a system with many spatial degrees of freedom around a single distinguished axis, in which two symmetries - rotations and translations in the plane orthogonal to the pump axis - are spontaneously broken. We observe the simultaneous spatial structuring of the density of a cold atomic cloud and an optical pump beam. The resulting patterns have hexagonal symmetry. The experiment demonstrates the manipulation of matter by opto-mechanical self-assembly with adjustable length scales and can be potentially extended to quantum degenerate gases., Comment: 20 pages, 6 figures

Starting from a microscopic theory for atomic scatterers, we describe the scattering of light by a single atom and study the coherent propagation of light in a cold atomic cloud in the presence of a magnetic field B in the mesoscopic regime. Non-pertubative expressions in B are given for the magneto-optical effects and optical anisotropy. We then consider the multiple scattering regime and address the fate of the coherent backscattering (CBS) effect. We show that, for atoms with nonzero spin in their ground state, the CBS interference contrast can be increased compared to its value when B=0, a result at variance with classical samples. We validate our theoretical results by a quantitative comparison with experimental data., Comment: 16 pages, 7 figures

We study experimentally and numerically the quasi-bidimensional transport of a $^{87}$Rb Bose-Einstein condensate launched with a velocity $v_0$ inside a disordered optical potential created by a speckle pattern. A time-of-flight analysis reveals a pronounced enhanced density peak in the backscattering direction $-v_0$, a feature reminiscent of coherent backscattering. Detailed numerical simulations indicate however that other effects also contribute to this enhancement, including a "backscattering echo" due to the position-momentum correlations of the initial wave packet., Comment: 5 pages, 4 figures

We study, experimentally and theoretically, the controlled transfer of harmonically trapped ultracold gases between different quantum states. In particular we experimentally demonstrate a fast decompression and displacement of both a non-interacting gas and an interacting Bose-Einstein condensate which are initially at equilibrium. The decompression parameters are engineered such that the final state is identical to that obtained after a perfectly adiabatic transformation despite the fact that the fast decompression is performed in the strongly non-adiabatic regime. During the transfer the atomic sample goes through strongly out-of-equilibrium states while the external confinement is modified until the system reaches the desired stationary state. The scheme is theoretically based on the invariants of motion and scaling equations techniques and can be generalized to decompression trajectories including an arbitrary deformation of the trap. It is also directly applicable to arbitrary initial non-equilibrium states., Comment: 36 pages, 14 figures

We show that, for a near-resonant propagating beam, a large cloud of cold 87Rb atoms acts as a saturable Kerr medium and produces self-trapping of light. By side fluorescence imaging we monitor the transverse size of the beam and, depending on the sign of the laser detuning with respect to the atomic transition, we observe self-focusing or -defocusing, with the waist remaining stationary for an appropriate choice of parameters. We analyze our observations by using numerical simulations based on a simple 2-level atom model., Comment: 3 pages, 4 figures, submitted to Optics Letters

We present an investigation of the fast decompression of a three-dimensional (3D) Bose-Einstein condensate (BEC) at finite temperature using an engineered trajectory for the harmonic trapping potential. Taking advantage of the scaling invariance properties of the time-dependent Gross-Pitaevskii equation, we exhibit a solution yielding a final state identical to that obtained through a perfectly adiabatic transformation, in a much shorter time. Experimentally, we perform a large trap decompression and displacement within a time comparable to the final radial trapping period. By simultaneously monitoring the BEC and the non-condensed fraction, we demonstrate that our specific trap trajectory is valid both for a quantum interacting many-body system and a classical ensemble of non-interacting particles., Comment: 5 pages, 4 figures

We demonstrate a technique based on invariants of motion for a time-dependent Hamiltonian, allowing a fast transition to a final state identical in theory to that obtained through a perfectly adiabatic transformation. This method is experimentally applied to the fast decompression of an ultracold cloud of Rubidium 87 atoms held in a harmonic magnetic trap, in the presence of gravity. We are able to decompress the trap by a factor of 15 within 35 ms with a strong suppression of the sloshing and breathing modes induced by the large vertical displacement and curvature reduction of the trap. When compared to a standard linear decompression, we achieve a gain of a factor of 37 on the transition time., Comment: 5 pages, 4 figures, an error in Eq. (2) has been corrected

By using the coherent backscattering interference effect, we investigate experimentally and theoretically how coherent transport of light inside a cold atomic vapour is affected by the residual motion of atomic scatterers. As the temperature of the atomic cloud increases, the interference contrast dramatically decreases emphazising the role of motion-induced decoherence for resonant scatterers even in the sub-Doppler regime of temperature. We derive analytical expressions for the corresponding coherence time., Comment: 4 pages - submitted to Physical Review Letters

We have observed self-sustained radial oscillations in a large magneto-optical trap (MOT), containing up to $10^{10}$ Rb$^{85}$ atoms. This instability is due to the competition between the confining force of the MOT and the repulsive interaction associated with multiple scattering of light inside the cold atomic cloud. A simple analytical model allows us to formulate a criterion for the instability threshold, in fair agreement with our observations. This criterion shows that large numbers of trapped atoms $N>10^9$ are required to observe this unstable behavior., Comment: submitted to Phys. Rev. Lett. 4 pages, 3 figures

We study the effect of an external magnetic field on coherent backscattering of light from a cool rubidium vapor. We observe that the backscattering enhancement factor can be {\it increased} with $B$. This surprising behavior shows that the coherence length of the system can be increased by applying a magnetic field, in sharp contrast with ususal situations. This is mainly due to the lifting of the degeneracy between Zeeman sublevels. We find good agreement between our experimental data and a full Monte-Carlosimulation, taking into account the magneto-optical effects and the geometry of the atomic cloud.

Coherent backscattering (CBS) of quasi-resonant light by cold atoms presents some specific features due to the internal structure of the atomic scatterers. We present the first quantitative comparison between the experimentally observed CBS cones and Monte-Carlo calculations which take into account the shape of the atomic cloud as well as the internal atomic structure., Comment: 5 pages, 3 figures, to appear in Eur. Phys. Lett