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Physical Review A

Interference patterns of superfluid Fermi gases in the BCS-BEC crossover released from optical lattices

Wen Wen, Yu Long Zhou, Guoxiang Huang

Published Mar 21, 2008• 28 citations
Publisher

Abstract

We study the interference patterns of a superfluid Fermi gas released from optical lattices below and above Feshbach resonance based on a simple phenomenological approach. We first solve the order-parameter equation valid for the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC) to obtain an initial distribution of subcondensates formed in an optical lattice. Then we investigate the coherent evolution of the subcondensates when both harmonic oscillator and optical lattice potentials are switched off. The interference patterns of the superfluid Fermi gas along the BCS-BEC crossover during a nearly ballistic expansion are calculated by means of Feynman propagator method combined with numerical simulations. The result obtained agrees with the recent experimental observation reported by the MIT group [J. K. Chin et al., Nature (London) 443, 961 (2006)].

DOI
10.1103/physreva.77.033623

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We study the interference patterns of a superfluid Fermi gas released from optical lattices below and above Feshbach resonance based on a simple phenomenological approach. We first solve the order-parameter equation valid for the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC) to obtain an initial distribution of subcondensates formed in an optical lattice. Then we investigate the coherent evolution of the subcondensates when both harmonic oscillator and optical lattice potentials are switched off. The interference patterns of the superfluid Fermi gas along the BCS-BEC crossover during a nearly ballistic expansion are calculated by means of Feynman propagator method combined with numerical simulations. The result obtained agrees with the recent experimental observation reported by the MIT group [J. K. Chin et al., Nature (London) 443, 961 (2006)].
We study interference patterns and their time evolution of a superfluid fermionic gas released from a two-dimensional (2D) optical lattice below and above Feshbach resonance. We calculate initial distribution of many subcondensates formed in a combined potential of a parabolic trap and a 2D optical lattice in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC). By using Feynman propagator method combined with numerical simulations we investigate the interference patterns of the subcondensates for two different cases. One is when both the parabolic trap and optical lattice are switched off. In this case, interference pattern displays a main peak and many secondary peaks. The distance between these interference peaks grows as time increases. The other one is when only the 2D optical lattice is switched off. The interference pattern in this case is found to display decay and revival, and such behavior repeats periodically with increasing time. In different regimes of the BCS-BEC crossover, coherent arrays of interference patterns show different features, which can be used to characterize experimentally different properties in different superfluid regimes of the BCS–BEC crossover.
We study multiple period states of a two-component unpolarized superfluid Fermi gas in an optical lattice along the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensate (BEC) crossover. The existence of states whose period is a multiple of the lattice spacing is a direct consequence of the nonlinear behavior of the gas, which is due to the presence of the order parameter associated with superfluidity. By solving Bogoliubov–de Gennes equations for a superfluid flow with finite quasimomentum, we find that, in the BCS side of the crossover, the multiple period states can be energetically favorable compared to the normal Bloch states and their survival time against dynamical instability drastically increases, suggesting that these states can be accessible in current experiments, in sharp contrast to the situation in BECs.
We study, both analytically and numerically, the formation and propagation of dark solitons in a superfluid Fermi gas in the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC). Starting from a superfluid order-parameter equation, we derive a Korteweg--de Vries equation for weak nonlinear excitations under quasi-one-dimensional and long-wavelength approximations. We present dark soliton solutions valid for both BCS and BEC limits and also for the crossover, and show that dark solitons in different superfluid regimes possess different features. Particularly, a dark soliton in the BCS (BEC) regime has larger (smaller) propagating velocity and smaller (larger) spatial width. Upon moving to the boundary of the condensate, it generally decelerates and generates small radiations, which display different behavior in different superfluid regimes. We study also a head-on collision between two dark solitons and demonstrate that the phase shift due to the collision changes nonmonotonically along the BCS-BEC crossover. All analytical results are checked by numerical simulations, and good agreement between them is found.
We investigate the dynamical behavior of large-amplitude collective modes in a superfluid Fermi gas in the crossover from Bardeen--Cooper--Schrieffer (BCS) superfluid to Bose--Einstein condensate (BEC) based on a hydrodynamic approach. We first solve the superfluid hydrodynamic equations that describe the time evolution of fermionic condensates in the BCS-BEC crossover and calculate explicitly the frequency shifts of the collective modes induced by nonlinear effects using the Lindstedt--Poincar\'e method. The result shows that the frequency shifts display different features in different superfluid regimes. We then study the second-harmonic generation of the collective modes under a phase-matching condition, which can be fulfilled by choosing appropriate parameters of the system. The analytical results obtained are checked by numerical simulations and good agreement is found.
We study the evolution of the interference patterns of strongly interacting Fermi gases in a harmonic trap after removal of the optical lattice, by numerically solving the superfluid order-parameter equation. We find that for the strongly interacting Fermi gas elastic collisions during the expansion blur the interference peaks. In order to obtain a nearly ballistic expansion, the fast magnetic field ramp technique is applied in experiment. We simulate the fast magnetic field ramp process before expansions of strongly interacting Fermi gases. We find that clear interference patterns are formed, and oscillate for a long time in the harmonic trap. We also calculate the interference patterns in different superfluid regimes, which accord with the experimental observations.
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.