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Light is characterized by its electric field, yet quantum optics has revealed the importance of monitoring photon-photon correlations at all orders. We here present a comparative study of two experimental setups, composed of cold and warm Rubidium atoms, respectively, which allow us to probe and compare photon correlations up to the fourth order. The former operates in the quantum regime where spontaneous emission dominates, whereas the latter exhibits a temperature-limited coherence time. While both setups present almost-chaotic light statistics, we discuss how the access to different orders of photon correlations allows one to better characterize the mechanisms responsible for deviations from those statistics.

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.

Light is a precious tool to probe matter, as it captures microscopic and macroscopic information on the system. We here report on the transition from a thermal (classical) to a spontaneous emission (quantum) mechanism for the loss of light coherence from a macroscopic atomic cloud. The coherence is probed by intensity-intensity correlation measurements realized on the light scattered by the atomic sample, and the transition is explored by tuning the balance between thermal coherence loss and spontaneous emission via the pump strength. Our results illustrate the potential of cold atom setups to investigate the classical-to-quantum transition in macroscopic systems., Comment: 9 pages (6 pages - main text, 3 pages - supplemental material), 3 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

We present a new method to obtain the first-order temporal correlation function, $g^{(1)} (\tau)$, of the light scattered by an assembly of point-like quantum scatterers, or equivalently its spectral power distribution. This new method is based on the mirror-assisted backscattering interferometric setup. The contrast of its angular fringes was already linked in the past to the convolution of $g^{(1)} (\tau)$ for different Rabi frequencies taking into account the incoming spatial intensity profile of the probe beam, but we show here that by simply adding a half waveplate to the interferometer in a specific configuration, the fringe contrast becomes $g^{(1)} (\tau)$ of the light scattered by atoms, which are now all subjected to the same laser intensity. This new method has direct application to obtain the saturated spectrum of quantum systems. We discuss some non-trivial aspects of this interferometric setup, and propose an analogy with a double Mach-Zehnder interferometer.

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

We investigate two-color photon correlations in the light emitted by strongly coupled two-level emitters. Spectral filtering allows us to manipulate the collected light statistics and we show that the resonances induced by dipole-dipole interactions give rise to specific correlations, where the time-symmetry of the correlations is broken. Based on the collective dressed states, our study encompasses both the case of real processes, where the photons are associated with specific resonances and classical correlations between each other, and virtual processes, where pairs of photons are emitted with non-classical correlations.

We study the growth of an elongated phase-fluctuating condensate from a non-equilibrium thermal cloud obtained by shock-cooling. We compare the growth of the condensate with numerical simulations, revealing a time delay and a reduction in the growth rate which we attribute to phase fluctuations. We measure the phase coherence using momentum Bragg spectroscopy, and thereby observe the evolution of the phase coherence as a function of time. Combining the phase coherence results with the numerical simulations, we suggest a simple model for the reduction of the growth rate based on the reduction of bosonic stimulation due to phase fluctuations and obtain improved agreement between theory and experiment.

We observe the suppression of the 1D transport of an interacting elongated Bose-Einstein condensate in a random potential with a standard deviation small compared to the typical energy per atom, dominated by the interaction energy. Numerical solutions of the Gross-Pitaevskii equation reproduce well our observations. We propose a scenario for disorder-induced trapping of the condensate in agreement with our observations., Comment: Proceedings of the 17th International Conference on Laser Spectroscopy (ICOLS 05), Cairngorms National Park, Scotland, 19-24 June 2005

We observe the suppression of the 1D transport of an interacting elongated Bose-Einstein condensate in a random potential with a standard deviation small compared to the typical energy per atom, dominated by the interaction energy. Numerical solutions of the Gross-Pitaevskii equation reproduce well our observations. We propose a scenario for disorder-induced trapping of the condensate in agreement with our observations., Comment: 23th August 2005

We measure the spatial correlation function of Bose-Einstein condensates in the cross-over region between phase-coherent and strongly phase-fluctuating condensates. We observe the continuous path from a gaussian-like shape to an exponential-like shape characteristic of one-dimensional phase-fluctuations. The width of the spatial correlation function as a function of the temperature shows that the condensate coherence length undergoes no sharp transition between these two regimes., Comment: 8 pages, 6 figure, submitted to EPJD

We have investigated experimentally the finite-temperature properties of a Bose-Einstein condensed cloud of $^{87}$Rb atoms in a harmonic trap. Focusing primarily on condensed fraction and expansion energy, we measure unambiguous deviations from ideal-gas thermodynamics, and obtain good agreement with a Hartree-Fock description of the mixed cloud. Our results offer for the first time clear evidence of the mutual interaction between the condensed and thermal components. To probe the low-temperature region unaccessible to the usual time-of-flight technique, we use coherent Bragg scattering as a filtering technique for the condensate. This allows us to separate spatially the condensed and normal components in time of flight, and to measure reliably temperatures as low as $0.2 T_{\rm c}^0$ and thermal fractions as low as 10%.Finally, we observe evidence for the limitations of the usual image analysis procedure, pointing out to the need for a more elaborate model of the expansion of the mixed cloud.

We report on measurements of the critical temperature of a harmonically trapped, weakly interacting Bose gas as a function of atom number. Our results exclude ideal-gas behavior by more than two standard deviations, and agree quantitatively with mean-field theory. At our level of sensitivity, we find no additional shift due to critical fluctuations. In the course of this measurement, the onset of hydrodynamic expansion in the thermal component has been observed. Our thermometry method takes this feature into account., Comment: version 2, 20 octobre 2003