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International Journal of Modern Physics B

EVOLUTION OF INTERFERENCE PATTERNS OF SUPERFLUID FERMI GASES RELEASED FROM A TWO-DIMENSIONAL OPTICAL LATTICE

Sujuan Liu, Wen Wen, Guoxiang Huang

Published Jan 30, 2012• 1 citation
Publisher

Abstract

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.

DOI
10.1142/s0217979212500178

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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 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 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.
For a Bose-condensed gas in a combined potential consisting of an axially-symmetric harmonic magnetic trap and one-dimensional (1D) optical lattice, using the mean-field Gross–Pitaevskii (G-P) equation and the propagator method, we obtain the analytical result of the order parameter for matter wave interference at any time. The evolution of the interference pattern under a variation of the relative phase Δϕ between successive subcondensates trapped on an optical lattices is also studied. For Δϕ = π, the interference pattern is symmetric with two sharp peaks, which are symmetrically located on a straight line on both sides of a vacant central peak and moving apart from each other. This work is in agreement with available experimental results.
We investigate the collective modes of a quasi-two-dimensional (Q2D) superfluid Fermi gas in Bardeen–Cooper–Schrieffer Bose–Einstein condensation (BCS-BEC) crossover. For solving a generalized Gross–Pitaevskii equation by using a time-dependent variational method, we take a trial wavefunction with the form of hybrid Gaussian-parabolic type, which not only reflects the Q2D character of the system and also allows an essentially analytical approach of the problem. We present a Q2D criterion that is valid for various superfluid regimes and displays clearly the relation between the maximum condensed particle number and the parameters of trapping potential as well as atom–atom interaction. We show that due to the small particle number in the Q2D condensate, the contribution to oscillating frequencies by the quantum pressure in the strong confinement direction is significant and hence a Thomas–Fermi approximation can not be used.
We use the path-integral formalism to investigate the vortex properties of a quasi-two dimensional (2D) Fermi superfluid system trapped in an optical lattice potential. Within the framework of mean-field theory, the cooper pair density, the atom number density, and the vortex core size are calculated from weakly interacting BCS regime to strongly coupled while weakly interacting BEC regime. Numerical results show that the atoms gradually penetrate into the vortex core as the system evolves from BEC to BCS regime. Meanwhile, the presence of the optical lattice allows us to analyze the vortex properties in the crossover from three-dimensional (3D) to 2D case. Furthermore, using a simple re-normalization procedure, we find that the two-body bound state exists only when the interaction is stronger than a critical one denoted by G c which is obtained as a function of the lattice potential’s parameter. Finally, we investigate the vortex core size and find that it grows with increasing interaction strength. In particular, by analyzing the behavior of the vortex core size in both BCS and BEC regimes, we find that the vortex core size behaves quite differently for positive and negative chemical potentials.
We investigate the average particle-number distribution of the atoms in the combined potential of 2D optical lattices and 3D harmonic magnetic trap based on the Gross–Pitaevskii equation. After the combined potential is switched off, and only the optical lattice is switched off, we give the analytical results of the wavefunction of the Bose-condensed gas at any time t by using a propagator method. For both disk-shaped and cigar-shaped Bose-condensed gas, we discuss the evolution process of the central and side peaks of the interference pattern.