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arXiv:1503.07976 · New Journal of Physics

Multiple period states of the superfluid Fermi gas in an optical lattice

Sukjin Yoon, F. Dalfovo, Takashi Nakatsukasa, Gentaro Watanabe

Published Jan 29, 2016• 6 citations
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Abstract

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.

DOI
10.1088/1367-2630/18/2/023011

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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 multiple period states (i.e., states whose period is a multiple of the lattice constant) of a two-component unpolarized superfluid Fermi gas in an optical lattice along the crossover between the Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensate (BEC) states. 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. This is in sharp contrast to the situation in BECs.
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 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.
We study the effects of an external periodic potential on the critical velocity of a superfluid Fermi gas in the crossover between the Bardeen-Cooper-Schrieffer (BCS) phase and Bose-Einstein condensation (BEC). We numerically solve the Bogoliubov--de Gennes equations to model a three-dimensional gas of ultracold atoms in the superfluid phase flowing through a one-dimensional optical lattice. We find that when the recoil energy is comparable to the Fermi energy, the presence of the periodic potential reduces the effect of pair-breaking excitations. This behavior is a consequence of the peculiar band structure of the quasiparticle energy spectrum in the lattice. When the lattice height is much larger than the Fermi energy, the periodic potential makes pairs of atoms to be strongly bound, even in the BCS regime, and pair-breaking excitations are further suppressed. We have also found that when the recoil energy is comparable to or larger than the Fermi energy, the critical velocity due to long-wavelength phonon excitations shows a nonmonotonic behavior along the BCS-BEC crossover.
We review our studies on Bose and Fermi superfluids of cold atomic gases in optical lattices at zero temperature. Especially, we focus on superfluid Fermi gases along the crossover between the Bardeen-Cooper-Schrieffer (BCS) and the Bose-Einstein condensate (BEC) states, which enable us to study the Bose and the Fermi superfluids in a unified point of view. We discuss basic static and long-wavelength properties (such as the equation of state, incompressibility, and effective mass), energetic stability, and energy band structures of the superfluid Fermi gases in an optical lattice periodic along one spatial direction. The periodic potential causes pairs of atoms to be strongly bound, and this can affect the static and long-wavelength properties and the stability of the superflow. Regarding the band structure, a peculiar loop structure called “swallowtail” can appear in superfluid Fermi gases and in the Bose case, but the mechanism of emergence in the Fermi case is very different from that in bosonic case. Other quantum phases that the cold atomic gases in optical lattices can show are also briefly discussed based on their roles as quantum simulators of Hubbard models.