Abstract A monolayer of superfluid Fermi gas can be prepared within an optical dipole trap using the tight confinement along the chosen direction. In this case, Cooper pairs occupy the lowest state corresponding to the motion in the trapping potential. After switching off the trapping potential, the initially two-dimensional gas expands to the three-dimensional space. In the case of unitary s-wave interactions, the dynamics of Fermi gas expansion is treated in the framework of appropriately modified Gross–Pitaevskii equation. It is found that the superfluid gas expands significantly faster than the normal gas, in contrast to the situation characteristic of the initially three-dimensional gas. The available experimental data [P. Dyke et al., Phys. Rev. A 93, 011603 (2016)] are close to the predictions of the model under study.
We consider an expansion of the strongly interacting superfluid Fermi gas in a vacuum in the so-called unitary regime when the chemical potential $\ensuremath{\mu}\ensuremath{\propto}{\ensuremath{\hbar}}^{2}{n}^{2/3}/m$, where
n is the density of the Bose-Einstein condensate of Cooper pairs of fermionic atoms. At low temperatures $T\ensuremath{\rightarrow}0$, such an expansion can be described in the framework of the Gross-Pitaevskii equation (GPE). For such a dependence of the chemical potential on the density, the GPE has additional symmetries, resulting in the existence of the virial theorem, connecting the mean size of the gas cloud and its Hamiltonian. It leads asymptotically at $t\ensuremath{\rightarrow}\ensuremath{\infty}$ to the gas cloud expansion, linearly growing in time. We study such asymptotics and reveal the perfect match between the quasiclassical self-similar solution and the asymptotic expansion of the noninteracting gas. This match is governed by the virial theorem, derived through utilizing the Talanov transformation, which was first obtained for the stationary self-focusing of light in media with a cubic nonlinearity due to the Kerr effect. In the quasiclassical limit, the equations of motion coincide with three-dimensional hydrodynamics for the perfect monatomic gas with $\ensuremath{\gamma}=5/3$. Their self-similar solution describes, within the background of the gas expansion, the angular deformities of the gas shape in the framework of the Ermakov-Ray-Reid--type system.
Abstract. – We discuss the effects of collisions on the expansion of an ultracold normal Fermi gas, following the sudden removal of the confining trap. Using a Boltzmann equation approach, we calculate the time dependence of the aspect ratio and the temperature increase of the expanding atomic cloud. We find that for dilute gases and standard choices of the trap parameters the aspect ratio does not deviate significantly from the predictions of ballistic expansion. Conversely, if the trap is sufficiently elongated the thermal broadening of the density distribution can be quite large, revealing that even at zero temperature collisions are effective in a Fermi gas. The expansion of an atomic gas following the sudden removal of the confining trap is known to provide valuable information on the state of the system and on the role of interactions [1]. In particular in the superfluid phase, where the macroscopic dynamics of the gas are governed by the equations of hydrodynamics, one expects anisotropic expansion if the gas is released from an anisotropic trap. This peculiar feature, which should be contrasted with the isotropic ballistic expansion exhibited by a non interacting gas, was first discussed in [2,3] in the case
Abstract We present a study of static and expansion properties of strongly interacting Fermi superfluids containing a vortex initially trapped by cylindrically symmetric potentials. Based on the order-parameter equation in the framework of the Gross–Pitaevskii equation, a unified expression for the energy of a vortex line in the crossover from a Bardeen–Cooper–Schrieffer superfluid to a molecular Bose–Einstein condensate is analytically presented. Numerical simulations show that the combined effects of interactions and trap configurations lead to an interesting property that the free expansion rate of the vortex core radius is smaller than that of the radius of the superfluid in the radial direction, when the strongly interacting Fermi superfluid containing a vortex is released from a cigar-shaped trap. The effects of the trap anisotropy and vortex on the Efimovian expansions of a unitary Fermi superfluid in real experimental setups are also predicted.
We extend our recent work [Y. Endo et al., Phys. Rev. A 92, 023610 (2015)] for a parity-mixing effect in a model of two-dimensional lattice fermions to a realistic three-dimensional ultracold Fermi gas. Including effects of broken local spatial inversion symmetry by a trap potential within the framework of the real-space Bogoliubov-de Gennes theory at
T=0, we point out that an odd-parity
p-wave Cooper-pair amplitude is expected to have already been realized in previous experiments on an (even-parity)
s-wave superfluid Fermi gas with spin imbalance. This indicates that when one suddenly changes the
s-wave pairing interaction to an appropriate
p-wave one by using a Feshbach technique in this case, a nonvanishing
p-wave superfluid order parameter is immediately obtained, which is given by the product of the
p-wave interaction and the
p-wave pair amplitude that has already been induced in the spin-imbalanced
s-wave superfluid Fermi gas. Thus, by definition, the system is in the
p-wave superfluid state, at least just after this manipulation. Since the achievement of a
p-wave superfluid state is one of the most exciting challenges in cold Fermi gas physics, our results may provide an alternative approach to this unconventional pairing state. In addition, since the parity-mixing effect cannot be explained as far as one deals with a trap potential in the local density approximation (LDA), it is considered as a crucial example which requires us to go beyond the LDA.
The pair correlation function of an expanding gas is investigated with an emphasis on the BEC-BCS crossover of a superfluid Fermi gas at zero temperature. At unitarity quantum Monte Carlo simulations reveal the occurrence of a sizable bunching effect due to interactions in the spin up-down channel which, at short distances, is larger than that exhibited by thermal bosons in the Hanbury-Brown-Twiss effect. We propose a local equilibrium ansatz for the pair correlation function which we predict will remain isotropic during the expansion even if the trapping potential is anisotropic, in contrast with the behavior of the density. The isotropy of the pair correlation function is an experimentally accessible signature, which makes a clear distinction with respect to the case of noninteracting gases and can be understood as a consequence of the violation of scaling.