Trapped Superfluid Fermi Gas Research Articles

Higgs Mode in a Trapped Superfluid Fermi Gas

In quantum many-body systems with spontaneous breaking of a continuous symmetry, Higgs modes emerge as collective amplitude oscillations of order parameters. Recently, Higgs modes have been observed in superconductors and in Bose gases in optical lattices. However, it has yet to be observed in Fermi gases. In the present paper, we use the time-dependent Bogoliubov–de Gennes equations to investigate Higgs amplitude oscillations of the superfluid order parameter in a trapped Fermi gas induced by a sudden changes of the \({ s}\)-wave scattering length. In particular, we investigate the Higgs mode with different values of the initial scattering length and discuss how the frequency and damping of the Higgs mode changes around the unitarity regime.

Vortex of an anomalous mode in Fermi gas near unitarity limit

We investigate the dynamics of a quantized vortex in a trapped superfluid Fermi gas near the unitarity limit. By taking a trial wave function for the order-parameter of a condensate in a rotating axisymmetric trap confinement and using a time-dependent variational analysis we obtain the equations of motion and their solutions for anomalous mode. The results show that the critical rotating frequency of the trap increases when the system ranges from the left to the right side of the unitarity limit, while the period of the vortex decreases in this regime.

Inhomogeneous Pseudogap Phenomenon in the BCS-BEC Crossover Regime of a Trapped Superfluid Fermi Gas

We investigate pseudogap phenomena in the unitarity limit of a trapped superfluid Fermi gas. Including effect of strong pairing fluctuations within a T-matrix approximation, as well as effects of a harmonic trap within the local density approximation (LDA), we calculate the local superfluid density of states below the superfluid phase transition temperature Tc. We show that the spatial region where single-particle excitations are dominated by the pseudogap may still exist even below Tc, due to inhomogeneous pairing fluctuations caused by the trap potential. From the temperature dependence of the pseudogapped density of states, we identify the pseudogap regime of the unitarity Fermi gas with respect to the temperature and spatial position. We also show that the combined T-matrix theory with the LDA can quantitatively explain the local pressure which was recently observed in the unitarity limit of a 6Li Fermi gas.

Sound Velocity and Eigenfrequencies of a Disk-Shaped Harmonically Trapped Superfluid Fermi Gas in the BCS-BEC Crossover

The analytical expressions for the zero-temperature sound velocity and low-energy eigenfrequencies of a disk-shaped harmonically trapped three-dimensional superfluid Fermi gas are derived on the basis of the hydrodynamic theory in the regimes along the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. Theoretically, by plotting the sound velocity as a function of 1/(k F a), it finds that there is an obvious flat behavior for the sound velocity in a disk-shaped trap around unitarity. However, there is no such flat behavior for a cigar-shaped Fermi gas at the same superfluid regime. Here, k F is the Fermi wave vector and a is the s-wave scattering length.

Finite vortex numbers and symmetric vortex structures in a rotating trapped Fermi gas in the BCS-BEC crossover

The ground state of a three-dimensional (3D) rotating trapped superfluid Fermi gas in the BCS-BEC crossover is mapped to finite Nv-body vortex states by a simple ansatz. The total vortex energy is measured from the ground-state energy of the system in the absence of the vortices. The vortex state is stable since the vortex potential and rotation energies are attractive while the vortex kinetic energy and interaction between vortices are repulsive. By combining the analytical and numerical works for the minimal vortex energy, the 2D configurations of Nv vortices are studied by taking into account of the finite size effects both on xy-plane and on z-direction. The calculated vortex numbers as a function of the interaction strength are appropriate to the renew experimental results by Zwierlein in [High-temperature superfluidity in a ultracold Fermi gas, Ph.D. thesis, Massachusetts Institute of Technology, 2006]. The numerical results show that there exist two types of vortex structures: the trap center is occupied and unoccupied by a vortex, even in the case of Nv < 10 with regular polygon and in the case of Nv≥ 10 with finite triangle lattice. The rotation frequency dependent vortex numbers with different interaction strengths are also discussed.

Dynamics of Dark Solitons in a Trapped Superfluid Fermi Gas

We study soliton oscillations in a trapped superfluid Fermi gas across the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. We derive an exact equation for the oscillation period in terms of observable quantities, which we confirm by solving the time-dependent Bogoliubov-de Gennes equations. Hence we reveal the appearance and dynamics of solitons across the crossover, and show that the period dramatically increases as the soliton becomes shallower on the BCS side of the resonance. Finally, we propose an experimental protocol to test our predictions.

Gradient corrections to the local-density approximation for trapped superfluid Fermi gases

Two species superfluid Fermi gas is investigated on the BCS side up to the Feshbach resonance. Using the Greens's function technique gradient corrections are calculated to the generalized Thomas-Fermi theory including Cooper pairing. Their relative magnitude is found to be measured by the small parameter $(d/R_{TF})^4$, where $d$ is the oscillator length of the trap potential and $R_{TF}$ is the radial extension of the density $n$ in the Thomas-Fermi approximation. In particular at the Feshbach resonance the universal %constant $A_{TF}$ has the %correction in the center $A=A_{TF}+A_2(d/R_{TF})^4+\...$ corrections to the local density approximation are calculated and a universal prefactor $\kappa_W=7/27$ is derived for the von Weizs\"acker type correction $\kappa_W(\hbar^2/2m)(\nabla^2 n^{1/2}/n^{1/2})$.

Unitarity Schrödinger Equation and Ground State Properties of the Finite Trapped Superfluid Fermi Gases in a BCS-BEC Crossover

On the basis of quantum hydrodynamical equations we derive a unitarity Schrödinger equation of a finite trapped superfluid Fermi gas valid in the whole interaction regime from BCS superfluid to BEC. This equation is just the Ginzburg–Laudau-type equation for the fermionic Cooper pairs in the BCS side, the Gross–Pitaevskii-type equation for the bosonic dimers in the BEC side, and a unitarity equation for a strongly interacting Fermi superfluid in the unitarity limit. By taking a modified Gauss-like trial wave function, we solve the unitarity Schrödinger equation, calculate the energy, chemical potential, sizes and profiles of the ground-state condensate, and discuss the properties of the ground state in the entire BCS-BEC crossover regimes.

Scattering resonances in a degenerate Fermi gas

We consider elastic single-particle scattering from a one-dimensional trapped two-component superfluid Fermi gas when the incoming projectile particle is identical to one of the confined species. Our theoretical treatment is based on the Hartree-Fock ground state of the trapped gas and a configuration-interaction description of the excitations. We determine the scattering phase shifts for the system and predict Fano-type scattering resonances that are a direct consequence of interatomic pairing. We describe the main characteristics of the scattering resonances and make a comparison with the results of BCS mean-field theory.

The quantum pressure correction to the excitation spectrum of the trapped superfluid Fermi gases in a BEC-BCS crossover

Using quantum hydrodynamic approaches, we study the quantum pressure correction to the collective excitation spectrum of the interacting trapped superfluid Fermi gases in the BEC-BCS crossover. Based on a phenomenological equation of state, we derive hydrodynamic equations of the system in the whole BEC-BCS crossover regime. Beyond the Thomas–Fermi approximation, expressions of the frequency corrections of collective modes for both spherical and axial symmetric traps excited in the BEC-BCS crossover are given explicitly. The corrections of the eigenfrequencies due to the quantum pressure and their dependence on the inverse interaction strength, anisotropic parameter and particle numbers of the condensate are discussed in detail.

Collective modes of trapped superfluid Fermi gases in the BCS-BEC crossover beyond the mean-field approximation

A perturbation method is developed for calculating the oscillating frequencies of collective modes of trapped superfluid Fermi gases from Bardeen-Cooper-Schrieffer (BCS) superfluid to Bose-Einstein condensation (BEC). Based on the complete and orthogonal eigenfunction set obtained recently and a series expansion of the equation of state beyond the mean-field approximation, the corrections of eigenfrequencies and eigenfunctions of all collective modes are given systematically, which are valid for various superfluid regimes in the BCS-BEC crossover beyond the mean-field approximation. Expressions of frequency correction of the collective modes for both spherical and axial symmetric traps excited near the BCS, BEC, and unitarity limits are provided explicitly, and their dependence on interatomic interaction strength and anisotropic trapping parameter is also discussed in detail.

Collective Excitations of Trapped Superfluid Fermi Gases in a BCS-BEC Crossover with Arbitrary Atom Numbers

We investigate the collective excitations of an axially-symmetric harmonically trapped superfluid Fermi gas in the BCS-BEC crossover, focusing on the dependence of the frequency of the collective modes on the atom number. Starting from a phenomenological equation of state valid for the whole BCS-BEC crossover regime and the time-dependent Gross-Pitaevskii equation of the condensed fermionic superfluid, we obtain analytically the chemical potential and ground-state wavefunction of the paired fermions with arbitrary atom numbers by use of variational method. We solve the generalized Bogoliubov-de Gennes equations numerically and discuss the properties of low-lying excitations when the system consists with Fermi atoms of several hundreds or thousands. Our numerical results reveal some new properties of the small system in the excited states.

Dipole Polarizability of a Trapped Superfluid Fermi Gas

The polarization produced by the relative displacement of the potentials trapping two spin species of a dilute Fermi gas with N=N is calculated at unitarity by assuming phase separation between the superfluid and a polarized phase at zero temperature. Because of the energy cost associated with pair breaking, the dipole polarizability is strongly quenched and exhibits important deviations from the ideal gas behavior even for nonlinear displacements of the order of the size of the atomic cloud. The behavior in the presence of different trapping frequencies (monopole polarization) for the two spin species is also discussed. Our results suggest new experimental perspectives to explore the quantum phases of interacting Fermi gases.

Analytical expressions of collective excitations for trapped superfluid Fermi gases in a BCS-BEC crossover

We investigate the collective excitations of a harmonically trapped superfluid Fermi gas at varying coupling strengths across a BCS-BEC crossover. Using a hydrodynamic approach, we solve analytically the eigenvalue problem of collective modes and provide explicit expressions for all eigenvalues and eigenfunctions, which are valid for both BCS and BEC limits and also for the whole crossover regime. Both spherical- and axial-symmetric traps are taken into account, and the features of these collective modes in the BCS-BEC crossover are discussed and compared with available experimental and numerical data.

Vortices in trapped superfluid fermi gases.

We consider a superfluid of trapped fermionic atoms and study the single vortex solution in the Ginzburg-Landau regime. We define simple analytical estimates for the main characteristics of the system, such as the vortex core size, temperature regimes for the existence of a vortex, and the effects of rotation and interactions with normal fermions. The parameter dependence of the vortex core size (healing length) is found to be essentially different from that of the healing length in metallic superconductors or in trapped atomic Bose-Einstein condensation in the Thomas-Fermi limit. This is an indication of the importance of the confining geometry for the properties of fermionic superfluids.