Exploring the Kibble-Zurek mechanism with homogeneous Bose gases

Out-of-equilibrium phenomena is a subject of considerable interest in many fields of physics. Ultracold quantum gases, which are extremely clean, well-isolated and highly controllable systems, offer ideal platforms to investigate this topic. The recent progress in tailoring trapping potentials now allows the experimental production of homogeneous samples in custom geometries, which is a key advance for studies of the emergence of coherence in interacting quantum systems. Here we review recent experiments in which temperature quenches have been performed across the Bose-Einstein condensation (BEC) phase transition in an annular geometry and in homogeneous 3D and quasi-2D gases. Combined, these experiments give a comprehensive picture of the Kibble-Zurek (KZ) scenario through complementary measurements of correlation functions and topological defects density. They also allow the measurement of KZ scaling laws, the direct confirmation of the "freeze-out" hypothesis that underlies the KZ theory, and the extraction of critical exponents of the Bose-Einstein condensation transition.Comment: 11 pages, 6 figures; topical revie

Collective Oscillations of an Imbalanced Fermi Gas: Axial Compression Modes and Polaron Effective Mass

We investigate the low-lying compression modes of a unitary Fermi gas with imbalanced spin populations. For low polarization, the strong coupling between the two spin components leads to a hydrodynamic behavior of the cloud. For large population imbalance we observe a decoupling of the oscillations of the two spin components, giving access to the effective mass of the Fermi polaron, a quasi-particle composed of an impurity dressed by particle-hole pair excitations in a surrounding Fermi sea. We find $m^*/m=1.17(10)$, in agreement with the most recent theoretical predictions.Comment: 4 pages, 4 figures, submitted to PR

The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions

Interacting fermions are ubiquitous in nature and understanding their thermodynamics is an important problem. We measure the equation of state of a two-component ultracold Fermi gas for a wide range of interaction strengths at low temperature. A detailed comparison with theories including Monte-Carlo calculations and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids is presented. The low-temperature phase diagram of the spin imbalanced gas reveals Fermi liquid behavior of the partially polarized normal phase for all but the weakest interactions. Our results provide a benchmark for many-body theories and are relevant to other fermionic systems such as the crust of neutron stars.Comment: 28 pages, 7 figure

Lifetime of the Bose Gas with Resonant Interactions

We study the lifetime of a Bose gas at and around unitarity using a Feshbach resonance in lithium~7. At unitarity, we measure the temperature dependence of the three-body decay coefficient $L_{3}$. Our data follow a $L_3 {=} \lambda_{3} / T^{2}$ law with \lambda_{3} = 2.5(3)_{stat}_(6)_{sys} 10^{-20} (\mu K)^2 cm^6 s^{-1} and are in good agreement with our analytical result based on the zero-range theory. Varying the scattering length $a$ at fixed temperature, we investigate the crossover between the finite-temperature unitary region and the previously studied regime where $|a|$ is smaller than the thermal wavelength. We find that $L_{3}$ is continuous across resonance, and over the whole $a {<} 0$ range our data quantitatively agree with our calculation

Dobiński relations and ordering of boson operators

We introduce a generalization of the Dobiński relation, through which we define a family of Bell-type numbers and polynomials. Such generalized Dobiński relations are coherent state matrix elements of expressions involving boson ladder operators. This may be used in order to obtain normally ordered forms of polynomials in creation and annihilation operators, both if the latter satisfy canonical and deformed commutation relations

Metastability in spin polarised Fermi gases and quasiparticle decays

We investigate the metastability associated with the first order transition from normal to superfluid phases in the phase diagram of two-component polarised Fermi gases.We begin by detailing the dominant decay processes of single quasiparticles.Having determined the momentum thresholds of each process and calculated their rates, we apply this understanding to a Fermi sea of polarons by linking its metastability to the stability of individual polarons, and predicting a region of metastability for the normal partially polarised phase. In the limit of a single impurity, this region extends from the interaction strength at which a polarised phase of molecules becomes the groundstate, to the one at which the single quasiparticle groundstate changes character from polaronic to molecular. Our argument in terms of a Fermi sea of polarons naturally suggests their use as an experimental probe. We propose experiments to observe the threshold of the predicted region of metastability, the interaction strength at which the quasiparticle groundstate changes character, and the decay rate of polarons

Longitudinal Momentum Fraction X_L for Two High P_t Protons in pp->ppX Reaction

We present an analysis of new data from Experiment E850 at BNL. We have characterized the inclusive cross section near the endpoint for pp exclusive scattering in Hydrogen and in Carbon with incident beam energy of 6 GeV. We select events with a pair of back-to-back hadrons at large transverse momentum. These cross sections are parameterized with a form $\frac{d \sigma}{d X_{L}}$ $\sim(1-X_{L})^{p}$, where ${X_{L}}$ is the ratio of the longitudinal momentum of the observed pair to the total incident beam momentum. Small value of $p$ may suggest that the number of partons participating in the reaction is large and reaction has a strong dependence on the center-of-mass energy. We also discuss nuclear effects observed in our kinematic region.Comment: 4 pages, 2 figures, to be published in Proceedings of CIPANP2000, Quebec, May 22-28, 2000, requires aipproc.sty(included

The equation of state of ultracold Bose and Fermi gases: a few examples

We describe a powerful method for determining the equation of state of an ultracold gas from in situ images. The method provides a measurement of the local pressure of an harmonically trapped gas and we give several applications to Bose and Fermi gases. We obtain the grand-canonical equation of state of a spin-balanced Fermi gas with resonant interactions as a function of temperature. We compare our equation of state with an equation of state measured by the Tokyo group, that reveals a significant difference in the high-temperature regime. The normal phase, at low temperature, is well described by a Landau Fermi liquid model, and we observe a clear thermodynamic signature of the superfluid transition. In a second part we apply the same procedure to Bose gases. From a single image of a quasi ideal Bose gas we determine the equation of state from the classical to the condensed regime. Finally the method is applied to a Bose gas in a 3D optical lattice in the Mott insulator regime. Our equation of state directly reveals the Mott insulator behavior and is suited to investigate finite-temperature effects.Comment: 14 pages, 6 figure