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arXiv:1507.08681 · Physical Review A

Nonadiabatic dynamics of superfluid spin-orbit-coupled degenerate Fermi gas

Maxim Dzero, Ammar A. Kirmani, Emil A. Yuzbashyan

Published Nov 25, 2015• 7 citations
arXivHTMLPDF

Abstract

We study a problem of nonadiabatic superfluid dynamics of spin-orbit-coupled neutral fermions in two spatial dimensions. We focus on the two cases when the out-of-equilibrium conditions are initiated by either a sudden change of the pairing strength or the population imbalance. For the case of a zero-population imbalance and within the mean-field approximation, the nonadiabatic evolution of the pairing amplitude in a collisionless regime can be found exactly by employing the method of Lax vector construction. Our main finding is that the presence of the spin-orbit coupling significantly reduces the region in the parameter space where a steady state with periodically oscillating pairing amplitude is realized. For the collisionless dynamics initiated by a sudden disappearance of the population imbalance, we obtain an exact expression for the steady-state pairing amplitude. In the general case of quenches to a state with finite population imbalance, we show that there is a region in the steady-state phase diagram where at long times the pairing amplitude dynamics is governed by the reduced number of the equations of motion in full analogy with the exactly integrable case.

DOI
10.1103/physreva.92.053626

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We study a problem of nonadiabatic superfluid dynamics of spin-orbit-coupled neutral fermions in two spatial dimensions. We focus on the two cases when the out-of-equilibrium conditions are initiated by either a sudden change of the pairing strength or the population imbalance. For the case of a zero-population imbalance and within the mean-field approximation, the nonadiabatic evolution of the pairing amplitude in a collisionless regime can be found exactly by employing the method of Lax vector construction. Our main finding is that the presence of the spin-orbit coupling significantly reduces the region in the parameter space where a steady state with periodically oscillating pairing amplitude is realized. For the collisionless dynamics initiated by a sudden disappearance of the population imbalance, we obtain an exact expression for the steady-state pairing amplitude. In the general case of quenches to a state with finite population imbalance, we show that there is a region in the steady-state phase diagram where at long times the pairing amplitude dynamics is governed by the reduced number of the equations of motion in full analogy with the exactly integrable case.
We use the self-consistent mean-field theory to analyze the effects of Rashba-type spin-orbit coupling (SOC) on the ground-state phase diagram of population-imbalanced Fermi gases throughout the BCS-Bose-Einstein condensate evolution. We find that the SOC and population imbalance are counteracting, and that this competition tends to stabilize the uniform superfluid phase against the phase separation. However, we also show that the SOC stabilizes (destabilizes) the uniform superfluid phase against the normal phase for low (high) population imbalances. In addition, we find topological quantum phase transitions associated with the appearance of momentum-space regions with zero quasiparticle energies, and study their signatures in the momentum distribution.
We study the dynamics of a nondegenerate, harmonically trapped Fermi gas following a sudden ramp of the spin-orbit coupling strength using a Boltzmann equation approach. In the absence of interactions and a Zeeman field, we solve the spin-orbit-coupled Boltzmann equation analytically and derive expressions for the phase-space and temporal dynamics of an arbitrary initial spin state. For a fully spin-polarized initial state, the total magnetization exhibits collapse and revival dynamics in time with a period set by the trapping potential. In real space, this corresponds to oscillations between a fully polarized state and a spin helix. To make predictions relevant to current experiments on spin-orbit-coupled Fermi gases, we then numerically study the dynamics in the presence of an additional momentum-independent Zeeman field. We find that the spin helix is robust for weak magnetic fields but disappears for stronger field strengths. Finally, we explore the spin dynamics in the presence of interactions and find that weak interactions enhance the amplitude of the spin helix.
The spin–orbit-coupled degenerate Fermi gas provides a new platform for realizing topological superfluids and related topological excitations. However, previous studies have been mainly focused on the topological properties of the stationary ground state. Here, we investigate the quench dynamics of a spin–orbit-coupled two-dimensional Fermi gas in which the Zeeman field serves as the major quench parameter. Three post-quench dynamical phases are identified according to the asymptotic behaviour of the order parameter. In the undamped phase, a persistent oscillation of the order parameter may support a topological Floquet state with multiple edge states. In the damped phase, the magnitude of the order parameter approaches a constant via a power-law decay, which may support a dynamical topological phase with one edge state at the boundary. In the overdamped phase, the order parameter decays to zero exponentially although the condensate fraction remains finite. These predictions can be observed in the strong-coupling regime. Spin–orbit-coupled Fermi gases have been shown to support exotic topological quantum states. Here, the authors investigate quench dynamics of these gases in two dimensions, and find that three different phases with different topological properties emerge depending on the behaviour of the order parameter.
We present detailed numerical and analytical investigations of the nonequilibrium dynamics of spin-polarized ultracold Fermi gases following a sudden switching on of the atom-atom pairing coupling strength. Within a time-dependent mean-field approach we show that on increasing the imbalance it takes longer for pairing to develop, the period of the nonlinear oscillations lengthens, and the maximum value of the pairing amplitude decreases. As expected, dynamical pairing is suppressed by the increase of the imbalance. Eventually, for a critical value of the imbalance the nonlinear oscillations do not even develop. Finally, we point out an interesting temperature-reentrant behavior of the exponent characterizing the initial instability.
We investigate the ground state of a uniform two-dimensional polarized Fermi gas with Rashba spin-orbit coupling at zero temperature. We construct the phase diagram by comparing the thermodynamic potential of superfluid and phase-separated states in detail. Due to the competition between polarization and spin-orbit coupling, we find that phase-separated states in the phase diagram can be topologically trivial and nontrivial. These two topologically distinct phase-separated states can not be connected without topological phase transition. The spin-orbit coupling reduces the effect of the population imbalance. Therefore, the phase-separated states are unstable to the superfluid phases for a large spin-orbit coupling.
Topological superfluid state is different from the normal superfluid one due to the excitation energy gap on the boundary. How to obtain the topological superfluid state by using spin–orbit coupling to control the s-waves paired mass-imbalanced Fermi gas is a recent novel topic. In this paper, we study the topological superfluid phase diagram of two-dimensional mass-imbalanced Fermi gas with Rashba spin–orbit coupling at zero temperature. We find that due to the competition among mass imbalance, pairing interaction and spin–orbit coupling, there is a double-well structure in the thermodynamic potential, which affects the properties of the ground state of the system. We comprehensively give the phase diagrams of the system on the plane of spin–orbit coupling and chemical potential, and the phase diagrams on the plane of the reduced mass ratio and two-body binding energy. This study not only points out the stable region of topological superfluid state of mass-imbalanced Fermi gas, but also provides a detailed theoretical basis for better observation of topological superfluid state in experiments.