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arXiv:cond-mat/0701181

Expansion of an ultra-cold lithium gas in the BEC-BCS crossover

Leticia Tarruell, Martin Teichmann, Jason McKeever, Thomas Bourdel, J. Cubizolles, Lev Khaykovich, Zhang, Jing, Nir Navon, Frédéric Chevy, Christophe Salomon

Published Jan 9, 2007• 1 citation
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Abstract

We present an experimental study of the time of flight properties of a gas of ultra-cold fermions in the BEC-BCS crossover. Since interactions can be tuned by changing the value of the magnetic field, we are able to probe both non interacting and strongly interacting behaviors. These measurements allow us to characterize the momentum distribution of the system as well as its equation of state. We also demonstrate the breakdown of superfluid hydrodynamics in the weakly attractive region of the phase diagram, probably caused by pair breaking taking place during the expansion.

DOI
10.48550/arxiv.cond-mat/0701181

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We present an experimental study of the time of flight properties of a gas of ultra-cold fermions in the BEC-BCS crossover. Since interactions can be tuned by changing the value of the magnetic field, we are able to probe both non interacting and strongly interacting behaviors. These measurements allow us to characterize the momentum distribution of the system as well as its equation of state. We also demonstrate the breakdown of superfluid hydrodynamics in the weakly attractive region of the phase diagram, probably caused by pair breaking taking place during the expansion.
We report on experimental studies on the collective behavior of a strongly interacting Fermi gas with tunable interactions and variable temperature. A scissors mode excitation in an elliptical trap is used to characterize the dynamics of the quantum gas in terms of hydrodynamic or near-collisionless behavior. We obtain a crossover phase diagram for collisional properties, showing a large region where a nonsuperfluid strongly interacting gas shows hydrodynamic behavior. In a narrow interaction regime on the BCS side of the crossover, we find a novel temperature-dependent damping peak, suggesting a relation to the superfluid phase transition.
We observe dramatic changes in the atomic momentum distribution of a Fermi gas in the crossover region between the BCS theory superconductivity and Bose-Einstein condensation (BEC) of molecules. We study the shape of the momentum distribution and the kinetic energy as a function of interaction strength. The momentum distributions are compared to a mean-field crossover theory, and the kinetic energy is compared to theories for the two weakly interacting limits. This measurement provides a unique probe of pairing in a strongly interacting Fermi gas.
We report on measurements of an elementary surface mode in an ultracold, strongly interacting Fermi gas of 6Li^{6}\mathrm{Li}6Li atoms. The radial quadrupole mode allows us to probe hydrodynamic behavior in the crossover from Bose-Einstein condensation (BEC) to the Bardeen-Cooper-Schrieffer (BCS) regime without being influenced by changes in the equation of state. We examine the frequency and damping of this mode, along with its expansion dynamics. In the unitarity limit and on the BEC side of the resonance, the observed frequencies agree with standard hydrodynamic theory. However, on the BCS side of the crossover, a striking downshift of the oscillation frequency is observed in the hydrodynamic regime as a precursor to an abrupt transition to collisionless behavior; this indicates coupling of the oscillation to fermionic pairs.
This thesis summarizes our study on the properties of ultracold Fermions near a Feshbach resonance. The Feshbach resonance allows for a continuous tuning of the interaction strength between the atoms. With this tunability, many properties predicted for the BCS-BEC crossover region in solids can be shown to exist in this ultracold Fermi gas. With the highly controllable parameters and the clean environment in the experiments, the study of the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein Condensation (BEC) crossover in ultracold Fermions provides valuable insights to the strongly interacting crossover region, which has never been achieved before in solids. We first examine the properties of 6 Li and 40 K gases. We find that in the unitary region the properties of the system do not depend on the atom species: outside the unitary region, the properties of the system do depend on the scattering properties of the different atom species. We study the dynamics of the ultracold Fermions in the crossover region in response to the variations in the external magnetic field. We find that the response depends on the time scale and the amplitude of the variations; which is in qualitative agreement with the experimental observations. We derive a set of dynamic mean-field equations for a Fermi gas in an arbitrary potential trap near a wide Feshbach resonance. The equations are more general than the local density approximation (LDA), and less demanding computationally as the Bogoliubov-de-Gennes (BdG) equation. We then analyze the solubility of the equations, as well as solve a simplified version of the equations for illustration and for self-consistency check on the assumptions made during the derivation. We systematically study the possible phases for a trapped Fermi gas with population imbalance near a Feshbach resonance. Our results agree qualitatively well with the recent experimental results, and predict the existence of two exotic non-BCS superfluid phases for the strongly interacting gas with population unbalance: the Breached Pair (BP) phase and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Finally, to guide the experimental efforts in the search of new quantum phases, we propose a detection scheme for the possible exotic phases.
We observe characteristic atomic behaviors in the Bose–Einstein-condensation-Bardeen–Cooper–Schrieffer (BECBCS) crossover, by accurately tuning the magnetic field across the Feshbach resonance of lithium atoms. The magnetic field is calibrated by measuring the Zeeman shift of the optical transition. A non-monotonic anisotropic expansion is observed across the Feshbach resonance. The density distribution is explored in different interacting regimes, where a condensate of diatomic molecules forms in the BEC limit with the indication of a bimodal distribution. We also measure the three-body recombination atom loss in the BEC-BCS crossover, and find that the magnetic field of the maximum atom loss is in the BEC limit and gets closer to the Feshbach resonance when decreasing the atom temperature, which agrees with previous experiments and theoretical prediction. This work builds up a controllable platform for the study on the strongly interacting Fermi gas.
This thesis reports on the preparation of a 2D Fermi gas in the BEC-BCS crossover and \nthe observation of the BKT transition into a quasi long-range ordered superfluid phase. \nThe pair momentum distribution of the gas is probed by means of a matter-wave \nfocusing technique which relies on time-of-flight evolution in a weak harmonic potential. \nThis distribution holds the coherence properties of the gas. \nThe quasi long-range ordered phase manifests itself as a sharp low-momentum peak. \nThe temperature where it forms is identified as the transition temperature. By tuning \nthe temperature and the interaction strength, the phase diagram of the 2D Fermi gas in \nthe BEC-BCS crossover is mapped out. \nThe phase coherence is investigated in a self-interference experiment. Furthermore, \nalgebraic decay of correlations is observed in the trap average of the first order corre- \nlation function, which is obtained from the Fourier transform of the pair momentum \ndistribution. This is in qualitative agreement with predictions of homogeneous theory \nfor the superfluid phase in a 2D gas. \nThe presented results provide a foundation for future experimental and theoretical \nstudies of strongly correlated 2D Fermi gases. They might thus help to elucidate complex \nsystems such as the electron gas in high-Tc superconductors.