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arXiv:cond-mat/0703500 · Physical Review Letters

Nonequilibrium Spin Dynamics in a Trapped Fermi Gas with Effective Spin-Orbit Interactions

Tudor D. Stanescu, Chuanwei Zhang, Victor M. Galitski

Published Sep 14, 2007• 128 citations
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Abstract

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.

DOI
10.1103/physrevlett.99.110403

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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 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 propose a mechanism to realize nontrivial spin dynamics in a one-dimensional spin-orbit-coupled Bose-Einstein condensate by abruptly shaking the harmonic trap. Continuously varying the shaking strength, it is found that the Bose-Einstein condensate may exhibit exotic nonequilibrium spin dynamics. Specifically, at some special values of the shaking strength, the time-averaged spin polarization shows sharp resonant peaks, whereas it tends to be zero at any other positions. Furthermore, the spacings between any two nearest peaks depend only on the system parameters and are thus identical to each other. By simplifying this time-dependent system to an exactly solvable ``quantum quench'' model, we show that the essential physics behind the exotic spin dynamics comes from periodic suppressing and enhancing of the out-of-phase interference. It is further shown that the presented physical picture persists under weak atomic interactions. This work may shed light on the ongoing research of spin-based quantum control and quantum information.
We theoretically investigate the momentum-resolved radio-frequency spectroscopy of a harmonically trapped atomic Fermi gas near a Feshbach resonance in the presence of equal Rashba and Dresselhaus spin-orbit coupling. The system is qualitatively modeled as an ideal gas mixture of atoms and molecules, in which the properties of molecules, such as the wave function, binding energy, and effective mass, are determined from the two-particle solution of two interacting atoms. We calculate separately the radio-frequency response from atoms and molecules at finite temperatures by using the standard Fermi golden rule and take into account the effect of harmonic traps within local density approximation. The total radio-frequency spectroscopy is discussed as functions of temperature and spin-orbit coupling strength. Our results give a qualitative picture of radio-frequency spectroscopy of a resonantly interacting spin-orbit-coupled Fermi gas and can be directly tested in atomic Fermi gases of 40{}^{40}40K atoms at Shanxi University and 6{}^{6}6Li atoms at the Massachusetts Institute of Technology.
We propose an experimental scheme to observe spin-orbit coupling effects of a two-dimensional Fermi atomic gas cloud by coupling its internal electronic states (pseudospins) to radiation in a Lambda configuration. The induced spin-orbit coupling can be of the Dresselhaus and Rashba type with a Zeeman term. We show that the optically induced spin-orbit coupling can lead to a spin-dependent effective mass under appropriate conditions with one of them able to be tuned between positive and negative effective masses. As a direct observable we show that in the expansion dynamics of the atomic cloud the initial atomic cloud splits into two clouds for the positive effective mass case regime, and into four clouds for the negative effective mass regime.
Motivated by recent experimental breakthroughs in generating spin-orbit coupling in ultracold Fermi gases using Raman laser beams, we present a systematic study of spin-orbit-coupled Fermi gases confined in a quasi-one-dimensional trap in the presence of an in-plane Zeeman field (which can be realized using a finite two-photon Raman detuning). We find that a topological Fulde-Ferrell state will emerge, featuring finite-momentum Cooper pairing and zero-energy Majorana excitations localized near the edge of the trap based on the self-consistent Bogoliubov--de Gennes (BdG) equations. We find analytically the wave functions of the Majorana modes. Finally, using the time-dependent BdG, we show how the finite-momentum pairing field manifests itself in the expansion dynamics of the atomic cloud.
We review our recent experimental realization and investigation of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) and quantum degenerate Fermi gas. By using two counter-propagating Raman lasers and controlling the different frequency of two Raman lasers to engineer the atom-light interaction, we first study the SO coupling in BEC. Then we study SO coupling in Fermi gas. We observe the spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state as hallmarks of SO coupling in a Fermi gas. To clearly reveal the property of SO coupling Fermi gas, we also study the momentum-resolved radio-frequency spectroscopy which characterizes the energy-momentum dispersion and spin composition of the quantum states. We observe the change of fermion surfaces in different helicity branches with different atomic density, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system. At last, we study the momentum-resolved Raman spectroscopy of an ultracold Fermi gas.