Phase diagrams of 2D and 3D disordered Bose gases in the local density approximation

We study the superfluid transitions in bidimensional (2D) and tridimensional (3D) disordered and interacting Bose gases. We work in the limit of long-range correlated disorder such that it can be treated in the local density approximation. We present the superfluid transition curves both in the disorder-temperature plane well as in the disorder-entropy plane in 2D and 3D Bose gases. Surprisingly, we find that a small amount of disorder is always favorable to the apparition of a superfluid. Our results offer a quantitative comparison with recent experiments in 2D disordered ultra-cold gases, for which no exact theory exists.Comment: LCF-O

All optical cooling of 39^{39}K to Bose Einstein condensation

We report the all-optical production of Bose Einstein condensates (BEC) of $^{39}$K atoms. We directly load $3 \times 10^{7}$ atoms in a large volume optical dipole trap from gray molasses on the D1 transition. We then apply a small magnetic quadrupole field to polarize the sample before transferring the atoms in a tightly confining optical trap. Evaporative cooling is finally performed close to a Feshbach resonance to enhance the scattering length. Our setup allows to cross the BEC threshold with $3 \times 10^5$ atoms every 7s. As an illustration of the interest of the tunability of the interactions we study the expansion of Bose-Einstein condensates in the 1D to 3D crossover

Effect of disorder close to the superfluid transition in a two-dimensional Bose gas

We experimentally study the effect of disorder on trapped quasi two-dimensional (2D) 87Rb clouds in the vicinity of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. The disorder correlation length is of the order of the Bose gas characteristic length scales (thermal de Broglie wavelength, healing length) and disorder thus modifies the physics at a microscopic level. We analyze the coherence properties of the cloud through measurements of the momentum distributions, for two disorder strengths, as a function of its degeneracy. For moderate disorder, the emergence of coherence remains steep but is shifted to a lower entropy. In contrast, for strong disorder, the growth of coherence is hindered. Our study is an experimental realization of the dirty boson problem in a well controlled atomic system suitable for quantitative analysis

A quantum trampoline for ultra-cold atoms

We have observed the interferometric suspension of a free-falling Bose-Einstein condensate periodically submitted to multiple-order diffraction by a vertical 1D standing wave. The various diffracted matter waves recombine coherently, resulting in high contrast interference in the number of atoms detected at constant height. For long suspension times, multiple-wave interference is revealed through a sharpening of the fringes. We use this scheme to measure the acceleration of gravity

Observing the Formation of Long-range Order during Bose-Einstein Condensation

We have experimentally investigated the formation of off-diagonal long-range order in a gas of ultracold atoms. A magnetically trapped atomic cloud prepared in a highly nonequilibrium state thermalizes and thereby crosses the Bose-Einstein condensation phase transition. The evolution of phase coherence between different regions of the sample is constantly monitored and information on the spatial first-order correlation function is obtained. We observe the growth of the spatial coherence and the formation of long-range order in real time and compare it to the growth of the atomic density. Moreover, we study the evolution of the momentum distribution during the nonequilibrium formation of the condensate.Comment: 4 pages, 4 figure

Cavity QED with a Bose-Einstein condensate

Cavity quantum electrodynamics (cavity QED) describes the coherent interaction between matter and an electromagnetic field confined within a resonator structure, and is providing a useful platform for developing concepts in quantum information processing. By using high-quality resonators, a strong coupling regime can be reached experimentally in which atoms coherently exchange a photon with a single light-field mode many times before dissipation sets in. This has led to fundamental studies with both microwave and optical resonators. To meet the challenges posed by quantum state engineering and quantum information processing, recent experiments have focused on laser cooling and trapping of atoms inside an optical cavity. However, the tremendous degree of control over atomic gases achieved with Bose-Einstein condensation has so far not been used for cavity QED. Here we achieve the strong coupling of a Bose-Einstein condensate to the quantized field of an ultrahigh-finesse optical cavity and present a measurement of its eigenenergy spectrum. This is a conceptually new regime of cavity QED, in which all atoms occupy a single mode of a matter-wave field and couple identically to the light field, sharing a single excitation. This opens possibilities ranging from quantum communication to a wealth of new phenomena that can be expected in the many-body physics of quantum gases with cavity-mediated interactions.Comment: 6 pages, 4 figures; version accepted for publication in Nature; updated Fig. 4; changed atom numbers due to new calibratio

Bosons and Fermions near Feshbach resonances

Near Feshbach resonances, $n|a|^3\gg 1$, systems of Bose and Fermi particles become strongly interacting/dense. In this unitary limit both bosons and fermions have very different properties than in a dilute gas, e.g., the energy per particle approach a value $\hbar^2n^{2/3}/m$ times an universal many-body constant. Calculations based upon an approximate Jastrow wave function can quantitatively describe recent measurements of trapped Bose and Fermi atoms near Feshbach resonances. The pairing gap between attractive fermions also scales as $\Delta\sim\hbar^2n^{2/3}/m$ near Feshbach resonances and is a large fraction of the Fermi energy - promising for observing BCS superfluidity in traps. Pairing undergoes several transitions depending on interaction strength and the number of particles in the trap and can also be compared to pairing in nuclei.Comment: Revised version extended to include recent molecular BEC-BCS result

Thermodynamic Measurements in a Strongly Interacting Fermi Gas

We conduct a series of measurements on the thermodynamic properties of an optically-trapped strongly interacting Fermi gas, including the energy $E$, entropy $S$, and sound velocity $c$. Our model-independent measurements of $E$ and $S$ enable a precision study of the finite temperature thermodynamics. The $E(S)$ data are directly compared to several recent predictions. The temperature in both the superfluid and normal fluid regime is obtained from the fundamental thermodynamic relation $T=\partial E/\partial S$ by parameterizing the $E(S)$ data. Our $E(S)$ data are also used to experimentally calibrate the endpoint temperatures obtained for adiabatic sweeps of the magnetic field between the ideal and strongly interacting regimes. This enables the first experimental calibration of the temperature scale used in experiments on fermionic pair condensation. Our calibration shows that the ideal gas temperature measured for the onset of pair condensation corresponds closely to the critical temperature estimated in the strongly interacting regime from the fits to our $E(S)$ data. The results are in very good agreement with recent predictions. Finally, using universal thermodynamic relations, we estimate the chemical potential and heat capacity of the trapped gas from the $E(S)$ data.Comment: 29 pages, 12 figures. To appear in JLTP online, and in the January, 2009 volum

The Unitary Gas and its Symmetry Properties

The physics of atomic quantum gases is currently taking advantage of a powerful tool, the possibility to fully adjust the interaction strength between atoms using a magnetically controlled Feshbach resonance. For fermions with two internal states, formally two opposite spin states, this allows to prepare long lived strongly interacting three-dimensional gases and to study the BEC-BCS crossover. Of particular interest along the BEC-BCS crossover is the so-called unitary gas, where the atomic interaction potential between the opposite spin states has virtually an infinite scattering length and a zero range. This unitary gas is the main subject of the present chapter: It has fascinating symmetry properties, from a simple scaling invariance, to a more subtle dynamical symmetry in an isotropic harmonic trap, which is linked to a separability of the N-body problem in hyperspherical coordinates. Other analytical results, valid over the whole BEC-BCS crossover, are presented, establishing a connection between three recently measured quantities, the tail of the momentum distribution, the short range part of the pair distribution function and the mean number of closed channel molecules.Comment: 63 pages, 8 figures. Contribution to the Springer Lecture Notes in Physics "BEC-BCS Crossover and the Unitary Fermi gas" edited by Wilhelm Zwerger. Revised version correcting a few typo