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arXiv:1305.2443 · Physical Review A

Spin dynamics in a spin-orbit-coupled Fermi gas

Stefan S. Natu, S. Das Sarma

Published Sep 11, 2013• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.88.033613

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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.
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.
We consider a trapped atomic system in the presence of spatially varying laser fields. The laser-atom interaction generates a pseudospin degree of freedom (referred to simply as spin) and leads to an effective spin-orbit coupling for the fermions in the trap. Reflections of the fermions from the trap boundaries provide a physical mechanism for effective momentum relaxation and nontrivial spin dynamics due to the emergent spin-orbit coupling. We explicitly consider evolution of an initially spin-polarized Fermi gas in a two-dimensional harmonic trap and derive nonequilibrium behavior of the spin polarization. It shows periodic echoes with a frequency equal to the harmonic trapping frequency. Perturbations, such as an asymmetry of the trap, lead to the suppression of the spin echo amplitudes. We discuss a possible experimental setup to observe spin dynamics and provide numerical estimates of relevant parameters.
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 Bogoliubov-de Gennes (BdG) theory to study the interplay between the Zeeman field, spin-orbit coupling (SOC) and resultant skyrmion-like polarization textures in harmonically trapped two-dimensional Fermi gases. Our primary finding is that, in sharp contrast to the no-SOC case where only an easy-axis polarization is possible beyond a threshold Zeeman field (depending on the interaction strength), any non-zero combination of the Zeeman field and Rashba SOC induces not only an easy-axis polarization everywhere in the system but also a spatially-modulated transverse one near the edges. Our secondary finding is that the ground states of Rashba spin-orbit coupled systems are revealed to have stronger Fulde-Ferrell type non-uniform superfluid characters (i.e. phase modulations) but not a Larkin-Ovchinnikov one (i.e. amplitude modulations) under the in-plane Zeeman field, for which the phases of the superfluid order parameters modulate near the edges and most prominently along the transverse direction. The effects of the interaction, temperature, SOC anisotropy and Zeeman field anisotropy on the intricate polarization textures and superfluid order parameter are also discussed.
In this Letter, we investigate spin dynamics of a two-component Bose gas with spin-orbit coupling realized in cold atom experiments. We derive coupled hydrodynamic equations for number and spin densities as well as their associated currents. Specializing to the quasi-one-dimensional situation, we obtain analytic solutions of the spin helix structure and its dynamics in both adiabatic and diabatic regimes. In the adiabatic regime, the transverse spin decays parabolically in the short-time limit and exponentially in the long-time limit, depending on initial polarization. In contrast, in the diabatic regime, transverse spin density and current oscillate in a way similar to the charge-current oscillation in an undamped LC circuit. The effects of Rabi coupling on the short-time spin dynamics is also discussed. Finally, using realistic experimental parameters for ^{87}Rb, we show that the timescales for spin dynamics is of the order of milliseconds to a few seconds and can be observed experimentally.