Philippe Bouyer

Direct observation of Anderson localization of matter waves in a controlled disorder.

In 1958, Anderson predicted the localization of electronic wavefunctions in disordered crystals and the resulting absence of diffusion. It is now recognized that Anderson localization is ubiquitous in wave physics because it originates from the interference between multiple scattering paths. Experimentally, localization has been reported for light waves, microwaves, sound waves and electron gases. However, there has been no direct observation of exponential spatial localization of matter waves of any type. Here we observe exponential localization of a Bose–Einstein condensate released into a one-dimensional waveguide in the presence of a controlled disorder created by laser speckle. We operate in a regime of pure Anderson localization, that is, with weak disorder—such that localization results from many quantum reflections of low amplitude—and an atomic density low enough to render interactions negligible. We directly image the atomic density profiles as a function of time, and find that weak disorder can stop the expansion and lead to the formation of a stationary, exponentially localized wavefunction—a direct signature of Anderson localization. We extract the localization length by fitting the exponential wings of the profiles, and compare it to theoretical calculations. The power spectrum of the one-dimensional speckle potentials has a high spatial frequency cutoff, causing exponential localization to occur only when the de Broglie wavelengths of the atoms in the expanding condensate are greater than an effective mobility edge corresponding to that cutoff. In the opposite case, we find that the density profiles decay algebraically, as predicted in ref. 13. The method presented here can be extended to localization of atomic quantum gases in higher dimensions, and with controlled interactions.

Six-axis inertial sensor using cold-atom interferometry.

We have developed an atom interferometer providing a full inertial base. This device uses two counterpropagating cold-atom clouds that are launched in strongly curved parabolic trajectories. Three single Raman beam pairs, pulsed in time, are successively applied in three orthogonal directions leading to the measurement of the three axis of rotation and acceleration. In this purpose, we introduce a new atom gyroscope using a butterfly geometry. We discuss the present sensitivity and the possible improvements.

Three-dimensional localization of ultracold atoms in an optical disordered potential

We report a study of three-dimensional (3D) localization of ultracold atoms suspended against gravity, and released in a 3D optical disordered potential with short correlation lengths in all directions. We observe density profiles composed of a steady localized part and a diffusive part. Our observations are compatible with the self-consistent theory of Anderson localization, taking into account the specific features of the experiment, and in particular the broad energy distribution of the atoms placed in the disordered potential. The localization we observe cannot be interpreted as trapping of particles with energy below the classical percolation threshold.

Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials

We show that the expansion of an initially confined interacting 1D Bose-Einstein condensate can exhibit Anderson localization in a weak random potential with correlation length sigma(R). For speckle potentials the Fourier transform of the correlation function vanishes for momenta k>2/sigma(R) so that the Lyapunov exponent vanishes in the Born approximation for k>1/sigma(R). Then, for the initial healing length of the condensate xi(in)>sigma(R) the localization is exponential, and for xi(in)

Suppression of Transport of an Interacting Elongated Bose-Einstein Condensate in a Random Potential

We observe the suppression of the 1D transport of an interacting elongated Bose-Einstein condensate in a random potential with an amplitude that is small compared to the typical energy per atom, dominated by the interaction energy. Numerical calculations reproduce our observations well. We propose a scenario for disorder-induced trapping of the condensate in agreement with our findings.

Quantum Physics Exploring Gravity in the Outer Solar System: The SAGAS Project

We summarise the scientific and technological aspects of the Search for Anomalous Gravitation using Atomic Sensors (SAGAS) project, submitted to ESA in June 2007 in response to the Cosmic Vision 2015–2025 call for proposals. The proposed mission aims at flying highly sensitive atomic sensors (optical clock, cold atom accelerometer, optical link) on a Solar System escape trajectory in the 2020 to 2030 time-frame. SAGAS has numerous science objectives in fundamental physics and Solar System science, for example numerous tests of general relativity and the exploration of the Kuiper belt. The combination of highly sensitive atomic sensors and of the laser link well adapted for large distances will allow measurements with unprecedented accuracy and on scales never reached before. We present the proposed mission in some detail, with particular emphasis on the science goals and associated measurements and technologies.

Momentum Spectroscopy of 1D Phase Fluctuations in Bose-Einstein Condensates

We measure the axial momentum distribution of Bose-Einstein condensates with an aspect ratio of 152 using Bragg spectroscopy. We observe the Lorentzian momentum distribution characteristic of one-dimensional phase fluctuations. The temperature dependence of the width of this distribution provides a quantitative test of quasicondensate theory. In addition, we observe a condensate length consistent with the suppression of density fluctuations, even when phase fluctuations are large.

MICROWAVE SIGNAL GENERATION WITH OPTICAL INJECTION LOCKING

Two single-mode laser diodes have been injection locked to the +1 and -1 diffracted orders of a 4.6-GHz acousto-optical modulator. The measured locking bandwidth was 3 GHz for a locking gain of 35 dB. The microwave signal at 9.2 GHz had a measured linewidth of less than a few hertz. We used this system to drive stimulated Raman transitions between the cesium ground-state hyperfine levels. We observed Ramsey fringes and used them to characterize the microwave signal phase noise.

Ultracold Bose Gases in 1D Disorder: From Lifshits Glass to Bose-Einstein Condensate

We study an ultracold Bose gas in the presence of 1D disorder for repulsive interatomic interactions varying from zero to the Thomas-Fermi regime. We show that for weak interactions the Bose gas populates a finite number of localized single-particle Lifshits states, while for strong interactions a delocalized disordered Bose-Einstein condensate is formed. We discuss the schematic quantum-state diagram and derive the equations of state for various regimes.

Critical temperature of a trapped, weakly interacting Bose gas.

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.