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arXiv:1703.04808 · Physical Review A

Core filling and snaking instability of dark solitons in spin-imbalanced superfluid Fermi gases

Matthew D. Reichl, Erich J. Mueller

Published May 26, 2017• 9 citations
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Abstract

We use the time-dependent Bogoliubov--de Gennes equations to study dark solitons in three-dimensional spin-imbalanced superfluid Fermi gases. We explore how the shape and dynamics of dark solitons are altered by the presence of excess unpaired spins which fill their low-density core. The unpaired particles broaden the solitons and suppress the transverse snake instability. We discuss ways of observing these phenomena in cold-atom experiments.

DOI
10.1103/physreva.95.053637

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We use the time-dependent Bogoliubov--de Gennes equations to study dark solitons in three-dimensional spin-imbalanced superfluid Fermi gases. We explore how the shape and dynamics of dark solitons are altered by the presence of excess unpaired spins which fill their low-density core. The unpaired particles broaden the solitons and suppress the transverse snake instability. We discuss ways of observing these phenomena in cold-atom experiments.
We present an investigation of generation, dynamics, and stability of dark solitons in anisotropic Fermi gases for a range of particle numbers and trap aspect ratios within the framework of the order-parameter equation. We calculate the periods of dark solitons oscillating in a trap and find good agreement with the results based on the Bogoliubov--de Gennes equations. By studying the stability of initially off-center dark solitons under various tight transverse confinements in the unitarity limit, we not only give the criterion of dynamical stability, but also find that the soliton and a hybrid of solitons and vortex rings can be characterized by different oscillation periods. The stability criterion is not fulfilled by the parameters of the recent experiment of Yefsah et al. [Nature (London) 499, 426 (2013)]. Therefore, instead of a very slow oscillation as observed experimentally, we find that the created dark soliton undergoes a transverse snake instability with a collapse into vortex rings, which propagate in solitonlike manner with a nearly 2 times larger period.
In this paper the properties of dark solitons in superfluid Fermi gases with spin imbalance are studied by means of a recently developed effective field theory [Eur. Phys. J. B 88, 122 (2015)] suitable to describe the BEC-BCS crossover in ultracold gases in an extended range of temperatures as compared to the usual Ginzburg--Landau treatments. The spatial profiles for the total density and for the density of the excess-spin component, and the changes of their properties across the BEC-BCS crossover are examined in different conditions of temperature and imbalance. The presence of population imbalance is shown to strongly affect the structure of the soliton excitation by filling its core with unpaired atoms. This in turn influences the dynamical properties of the soliton since the additional particles in the core have to be dragged along thus altering the effective mass.
Cold atoms experiments offer invaluable information on superfluid dynamics, including decay cascades of topological defects. While the cascade properties are well established for Bose systems, our understanding of their behavior in Fermi counterparts is very limited, in particular in spin-imbalanced systems, where superfluid (paired) and normal (unpaired) particles naturally coexist giving rise to complex spatial structure of the atomic cloud. Here we show, based on a newly developed microscopic approach, that the decay cascades of topological defects are dramatically modified by the spin polarization. We demonstrate that decay cascades end up at different stages: "dark soliton," "vortex ring," or "vortex line," depending on the polarization. We reveal that it is caused by sucking of unpaired particles into the soliton's internal structure. As a consequence vortex reconnections are hindered and we anticipate that quantum turbulence phenomenon can be significantly affected, indicating new physics induced by polarization effects.
We present numerical calculations of the snake instability in a Fermi superfluid within the Bogoliubov-de Gennes theory of the Bose-Einstein condensate (BEC) to BCS crossover using the random-phase approximation complemented by time-dependent simulations. We examine the snaking behavior across the crossover and quantify the time scale and length scale of the instability. While the dynamics shows extensive snaking before eventually producing vortices and sound on the BEC side of the crossover, the snaking dynamics is preempted by decay into sound due to pair breaking in the deep BCS regime. At the unitarity limit, hydrodynamic arguments allow us to link the rate of snaking to the experimentally observable ratio of inertial to physical mass of the soliton. In this limit we witness an unresolved discrepancy between our numerical estimates for the critical wave number of suppression of the snake instability and recent experimental observations with an ultracold Fermi gas.
Families of dark solitons exist in superfluid Fermi gases. The energy-velocity dispersion and number of depleted particles completely determine the dynamics of dark solitons on a slowly varying background density. For the unitary Fermi gas, we determine these relations from general scaling arguments and conservation of local particle number. We find solitons to oscillate sinusoidally at the trap frequency reduced by a factor of 1/31/\sqrt{3}1/3​. Numerical integration of the time-dependent Bogoliubov--de Gennes equation determines spatial profiles and soliton-dispersion relations across the BEC-BCS crossover, and proves consistent with the scaling relations at unitarity.
Dark solitons in superfluid Bose gases decay through the snake instability mechanism, unless they are strongly confined. Recent experiments in superfluid Fermi gases have also interpreted soliton decay via this mechanism. However, we show using both an effective field numerical simulation and a perturbative analysis that there is a qualitative difference between soliton decay in the BEC and BCS regimes. On the BEC side of the interaction domain, the characteristic snaking deformations are induced by fluctuations of the amplitude of the order parameter, while on the BCS side, fluctuations of the phase destroy the soliton core through the formation of local Josephson currents without the presence of snaking deformations. The latter mechanism is qualitatively different from the snaking instability and this difference should be experimentally detectable.