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Journal of Physics B Atomic Molecular and Optical Physics

Interference between two superfluid Fermi gases

Wen Wen, Hui‐jun Li

Published Jan 28, 2013• 4 citations
Publisher

Abstract

We investigate the interference of the superfluid Fermi gases released from a double-well potential in the crossover from the unitarity limit to the Bose–Einstein condensate (BEC) limit. For two initially coupled Fermi superfluids, we show the formation of the clear and nonuniform interference fringes, in which the fringe spacing grows linearly in the evolution time, and the expansion velocity of the fringes increases significantly from the BEC limit to the unitarity limit. For two spatially separated Fermi superfluids, however, we show that in the strongly interacting regime, the interference patterns are characterized by the complicated spatial structures. By studying the interferences in the unitarity limit under different values of the strength of the double-well potential, we find that these complicated structures actually originate from the formations of spontaneous vortex rings, due to the transverse instability.

DOI
10.1088/0953-4075/46/3/035302

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We investigate the interference of the superfluid Fermi gases released from a double-well potential in the crossover from the unitarity limit to the Bose–Einstein condensate (BEC) limit. For two initially coupled Fermi superfluids, we show the formation of the clear and nonuniform interference fringes, in which the fringe spacing grows linearly in the evolution time, and the expansion velocity of the fringes increases significantly from the BEC limit to the unitarity limit. For two spatially separated Fermi superfluids, however, we show that in the strongly interacting regime, the interference patterns are characterized by the complicated spatial structures. By studying the interferences in the unitarity limit under different values of the strength of the double-well potential, we find that these complicated structures actually originate from the formations of spontaneous vortex rings, due to the transverse instability.
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 investigate tunneling and self-trapping of superfluid Fermi gases under a two-mode ansatz in different regimes of the crossover from Bardeen—Cooper—Schrieffer (BCS) superfluid to Bose—Einstein condensates (BEC). Starting from a generalized equation of state, we derive the coupled equations of relative atom-pair number and relative phase about superfluid Fermi gases in a double-well system and then classify the different oscillation behaviors by the tunneling strength and interactions between atoms. Tunneling and self-trapping behaviors are considered in the whole BCS-BEC crossover in the case of a symmetric double-well potential. We show that the nonlinear interaction between atoms makes the self-trapping more easily realized in BCS regime than in the BEC regime and stability analysis is also given.
The interference pattern of two Bose—Einstein condensates released from a double-well potential for different holding times is theoretically investigated using a decoupled two-mode Bose—Hubbard model. For two coherently separated condensates, the interference displays a periodic behavior, which is closely related to the atomic interaction. A remarkable parity effect is found in the interference patterns. For certain holding times, the even/odd total number of atoms would result in different interference fringes. The influences of different initial conditions on the evolution of interference and the observation of parity effects are discussed.
In the mean-field theory and two-mode approximation, we study the self-trapping of superfluid Fermi gases in the BEC regime and in unitarity by observing the evolution of the population imbalance with time and the variation of the average of population imbalance with several non-linear interaction parameters. The high-frequency modulations of both the symmetric double-well potential and the potential well are studied. The boundary conditions of the self-trapping and non-self-trapping are given. We find that high-frequency modulation in a certain range of modulation can make the self-trapping phenomenon easier to achieve. Finally, we study the influence of the initial value on self-trapping, and find that the increase of the absolute of the initial value can make the self-trapping more conducive to the realization.
We study the super Efimovian expansions of a superfluid Fermi gas in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC), by using superfluid hydrodynamic equations with the equation of state fitting from the experimental data and a scaling approach. We find that in an isotropic trap, the super Efimovian expansion of the Fermi superfluid in the unitary limit is characterized by the double-log periodicity, while for an axially symmetric trap, the double-log periodicity only emerges in the longer direction for a large anisotropy of the trapping frequencies. Away from unitarity where the scale invariance is broken, the super Efimovian expansions of the superfluid Fermi gases deviate from the double-log oscillations. The oscillations in the BCS regime deviate upward from the double-log oscillations, whereas the oscillations in the BEC regime deviate downward and the deviation in the BEC limit is the most significant. This difference can be used to discriminate different superfluid regimes.