We introduce the Global Spin Model to study the static and dynamic properties of the ultracold fermionic gas near the broad Feshbach resonance. We show that the problem of molecular production, in a single-mode approximation, is reduced to the linear Landau-Zener problem for operators. The strong interaction leads to significant renormalization of the gap between adiabatic levels. In contrast to static problem the close vicinity of exact resonance does not play substantial role. Two main physical results of our theory is the high sensitivity of molecular production to the initial value of magnetic field and generation of a large BCS condensate distributed over a broad range of momenta in a wide range of parameters. We calculate the amplitude of the condensate as function of the initial detuning and the rate of the magnetic field sweep.
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.
Thermodynamic properties of an ultracold Fermi gas in a harmonic trap are calculated within a local density approximation, using a conserving many-body formalism for the BCS to Bose-Einstein condensate crossover problem, which has been developed by Haussmann et al. [Phys. Rev. A 75, 023610 (2007)]. We focus on the unitary regime near a Feshbach resonance and determine the local density and entropy profiles and the global entropy
S(E) as a function of the total energy
E. Our results are in good agreement with both experimental data and previous analytical and numerical results for the thermodynamics of the unitary Fermi gas. The value of the Bertsch parameter at
T=0 and the superfluid transition temperature, however, differ appreciably. We show that, well in the superfluid regime, removal of atoms near the cloud edge enables cooling far below temperatures that have been reached so far.
Ultracold atomic Fermi gases close to Feshbach resonances represent the ideal platform to study strongly correlated fermionic states [1]. Up to now, most of the experimental efforts have been dedicated to the study of the famous BEC-BCS crossover, i.e. the transition from a Bose-Einstein condensate of tightly bound molecules to a BCS superfluid of long-range fermion pairs. However, such fermionic gases are the ideal environment to explore also the effects of strong, repulsive interactions. The interest in studying repulsive Fermi gases is manifold, since many phase transitions are driven by the strong repulsion between electrons in solids. One notable example is represented by the onset of itinerant ferromagnetism in metals, as envisioned by Stoner almost ninety years ago.
We consider a single vortex in a superfluid Fermi gas in the BCS-BEC crossover regime near a Feshbach resonance. The effect of the molecular Bose-Einstein condensate upon the vortex structure is discussed within the mean field approximation at zero temperature. Using the self-consistent Bogoliubov-de Gennes equation of the fermion-boson coupled model, we calculate density distributions of atoms and molecules. As the number of the molecules increases, both atomic and molecular density changes from BCS-like distribution to BEC-like. We also study the change of the vortex core size in the crossover regime.
A self-consistent theory is derived to describe the BCS--Bose-Einstein-condensate crossover for a strongly interacting Fermi gas with a Feshbach resonance. In the theory the fluctuation of the dressed molecules, consisting of both preformed Cooper pairs and ``bare'' Feshbach molecules, has been included within a self-consistent
T-matrix approximation, beyond the Nozi\`eres and Schmitt-Rink strategy considered by Ohashi and Griffin. The resulting self-consistent equations are solved numerically to investigate the normal-state properties of the crossover at various resonance widths. It is found that the superfluid transition temperature
Tc increases monotonically at all widths as the effective interaction between atoms becomes more attractive. Furthermore, a residue factor
Zm of the molecule's Green function and a complex effective mass have been determined to characterize the fraction and lifetime of Feshbach molecules at
Tc. Our many-body calculations of
Zm agree qualitatively well with recent measurments of the gas of
6Li atoms near the broad resonance at
834G. The crossover from narrow to broad resonances has also been studied.