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arXiv:1503.02131 · Physical Review A

Collisionless spin dynamics in a magnetic field gradient

Junjun Xu, Qiang Gu, Erich J. Mueller

Published Apr 10, 2015• 6 citations
arXivHTMLPDF

Abstract

We study the collisionless spin dynamics of a harmonically trapped Fermi gas in a magnetic field gradient. In the absence of interactions, the system evolution is periodic: the magnetization develops twists, which evolve into a longitudinal polarization. Recurrences follow. For weak interaction, the exchange interactions lead to beats in these oscillations. We present an array of analytic and numerical techniques for studying this physics.

DOI
10.1103/physreva.91.043613

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We study the collisionless spin dynamics of a harmonically trapped Fermi gas in a magnetic field gradient. In the absence of interactions, the system evolution is periodic: the magnetization develops twists, which evolve into a longitudinal polarization. Recurrences follow. For weak interaction, the exchange interactions lead to beats in these oscillations. We present an array of analytic and numerical techniques for studying this physics.
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We study the transverse spin dynamics of trapped polarized Fermi gases in the high-temperature limit. In the non-interacting collisionless regime, a magnetic-field gradient induces collective spin wave oscillations. In the strongly interacting collisional regime, the dynamics are governed by spin diffusion. These two limits have been extensively studied both experimentally and theoretically, but the crossover between them has received less attention. In this paper, we use a quantum Boltzmann equation to study transverse spin dynamics and show how the excitations evolve from dispersive to diffusive in the high-temperature limit. We provide analytical solutions in the two limiting regimes, which agree well with our numerical results.
We study the spin-mixing dynamics of ultracold spin-1 atoms in a weak nonuniform magnetic field with field gradient GGG, which can flip the spin from +1+1+1 to $\ensuremath{-}1$ so that the magnetization $m={\ensuremath{\rho}}_{+}\ensuremath{-}{\ensuremath{\rho}}_{\ensuremath{-}}$ is not a constant anymore. The dynamics of mF=0{m}_{F}=0mF​=0 Zeeman component ${\ensuremath{\rho}}_{0}$, as well as the system magnetization mmm, are illustrated for both ferromagnetic and polar interaction cases in the mean-field theory. We find that the dynamics of system magnetization can be tuned between the Josephson-like oscillation similar to the case of double well and the interesting self-trapping regimes, i.e., the spin-mixing dynamics sustains a spontaneous magnetization. Meanwhile, the dynamics of ${\ensuremath{\rho}}_{0}$ may be sufficiently suppressed for initially imbalanced number distribution in the case of polar interaction. A ``beat-frequency''oscillation of the magnetization emerges in the case of balanced initial distribution for polar interaction, which vanishes for ferromagnetic interaction.
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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.
Experiments at JILA on the collisions between two oscillating spin-polarized components of a Fermi gas of 40K atoms have shown that this setup is an important tool for studying the dynamics of quantum gases. We have developed advanced numerical methods to solve the Vlasov–Landau equations for a binary mixture of atomic Fermi gases inside a harmonic trap at very low temperatures. In particular, a locally adaptive importance-sampling technique allows us to handle collisional interactions several orders of magnitude more efficiently than in standard Monte Carlo calculations. These methods have been applied to study the dynamical and transport properties of a fermion mixture in the presence of mean-field interactions and of collisions between its components for system parameters ranging from the collisionless to the hydrodynamic regime.