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arXiv:1711.04970

Vortex dipole precession in a Fermi superfluid with Rashba spin-orbit coupling

L. A. Toikka

Published Nov 14, 2017• 0 citations
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Abstract

We present a closed-form expression for the time dynamics of a balanced Fermi superfluid with s-wave pairing and Rashba spin-orbit (SO) coupling. Solving the associated self-consistency conditions for an initial number density given by a Gaussian and an initial gap containing a vortex dipole, we show that Rashba SO coupling results in precession of the vortex dipole. The integrated self-consistent gap decays as a function of time, characterising a "transient Fermi superfluid". Our analytic solution forms a starting point for studies of vortex dynamics -- in particular braiding of Majorana fermions -- in Fermi superfluids in the presence of spin population imbalance and two-dimensional SO coupling, which are both required to realize a topological atomic Fermi gas in experiments.

DOI
10.48550/arxiv.1711.04970

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We present a closed-form expression for the time dynamics of a balanced Fermi superfluid with s-wave pairing and Rashba spin-orbit (SO) coupling. Solving the associated self-consistency conditions for an initial number density given by a Gaussian and an initial gap containing a vortex dipole, we show that Rashba SO coupling results in precession of the vortex dipole. The integrated self-consistent gap decays as a function of time, characterising a "transient Fermi superfluid". Our analytic solution forms a starting point for studies of vortex dynamics -- in particular braiding of Majorana fermions -- in Fermi superfluids in the presence of spin population imbalance and two-dimensional SO coupling, which are both required to realize a topological atomic Fermi gas in experiments.
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.
It has recently been shown that the spin-orbit coupling gives rise to topologically nontrivial and thermodynamically stable gapless superfluid phases when the pseudospin populations of an atomic Fermi gas are imbalanced, with the possibility of featuring Majorana zero-energy quasiparticles. In this paper, we consider a Rashba-type spin-orbit coupling, and use the Bogoliubov-de Gennes formalism to analyze a single vortex line along a finite cylinder with a periodic boundary condition. We show that the signatures for the appearance of core- and edge-bound states can be directly found in the density of single-particle states and particle-current density. In particular, we find that the pseudospin components counterflow near the edge of the cylinder, the strength of which increases with increasing spin-orbit coupling.
We theoretically investigate a three-dimensional Fermi gas with Rashba spin–orbit coupling in the presence of both out-of-plane and in-plane Zeeman fields. We show that, driven by a sufficiently large Zeeman field, either out-of-plane or in-plane, the superfluid phase of this system exhibits a number of interesting features, including inhomogeneous Fulde–Ferrell pairing, gapped or gapless topological order, and exotic quasi-particle excitations known as Weyl fermions that have linear energy dispersions in momentum space (i.e., massless Dirac fermions). The topological superfluid phase can have either four or two topologically protected Weyl nodes. We present the phase diagrams at both zero and finite temperatures and discuss the possibility of their observation in an atomic Fermi gas with synthetic spin–orbit coupling. In this context, topological superfluid phase with an imperfect Rashba spin–orbit coupling is also studied.
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 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 consider the time evolution of the magnetization in a Rashba spin-orbit coupled Fermi gas, starting from a fully polarized initial state. We model the dynamics using a Boltzmann equation, which we solve in the Hartree-Fock approximation. The resulting nonlinear system of equations gives rise to three distinct dynamical regimes with qualitatively different asymptotic behaviors of the magnetization at long times. The distinct regimes and the transitions between them are controlled by the ratio of interaction and spin-orbit coupling strength λ: for small λ, the magnetization decays to zero. For intermediate λ, it displays undamped oscillations about zero, and for large λ, a partially magnetized state is dynamically stabilized. The dynamics we find is a spin analog of interaction induced self-trapping in double-well Bose Einstein condensates. The predicted phenomena can be realized in trapped Fermi gases with synthetic spin-orbit interactions.