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arXiv:cond-mat/0502061 · Physical Review A

Coherent spin mixing dynamics in a spin-1 atomic condensate

Wenxian Zhang, D. L. Zhou, M.-S. Chang, Michael Chapman, Li You

Published Jul 5, 2005• 188 citations
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Abstract

We study the coherent off-equilibrium spin mixing inside an atomic condensate. Using mean-field theory and adopting the single-spatial-mode approximation, the condensate spin dynamics is found to be well described by that of a nonrigid pendulum and displays a variety of periodic oscillations in an external magnetic field. Our results illuminate several recent experimental observations and provide critical insights into the observation of coherent interaction-driven oscillations in a spin-1 condensate.

DOI
10.1103/physreva.72.013602

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We study the coherent off-equilibrium spin mixing inside an atomic condensate. Using mean-field theory and adopting the single-spatial-mode approximation, the condensate spin dynamics is found to be well described by that of a nonrigid pendulum and displays a variety of periodic oscillations in an external magnetic field. Our results illuminate several recent experimental observations and provide critical insights into the observation of coherent interaction-driven oscillations in a spin-1 condensate.
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We study the spin mixing dynamics of a spin-orbit coupled spin-1 Bose–Einstein condensate. Using mean-field theory and adopting plane wave solutions, the spin mixing dynamics can be well described by an internal Josephson equation. In order to establish the role of the different terms in spin mixing dynamics clearly, we consider the equilibrium state firstly, which shows that the spin-orbit coupling can significantly modify the dispersion relation and change the property of ground state of the condensate. For the non-equilibrium state, the spin-orbit coupling plays an important role in the spin mixing dynamics. Moreover, the oscillation period of spin mixing dynamics is determined by the coupled effects of momentum, magnetization, spin-dependent atomic interaction and spin-orbit coupling. When spin-orbit coupling is less than a critical value, it can prolong the oscillation period of spin mixing dynamics. Conversely, when the spin-orbit coupling is larger than the critical value, it can shorten the oscillation period of spin mixing dynamics. Particularly, when spin-orbit coupling is equal to the critical value, the period tends to infinity. Our study provides a complete spin mixing dynamics of spin-orbit coupled spin-1 BEC, which can be used to explore the spin mixing dynamics experimentally.
Compared to single-component Bose-Einstein condensates, spinor Bose-Einstein condensates display much richer dynamics. In addition to density oscillations, spinor Bose-Einstein condensates exhibit intriguing spin dynamics that is associated with population transfer between different hyperfine components. This paper analyzes the validity of the widely employed single-mode approximation when describing the spin dynamics in response to a quench of the system Hamiltonian. The single-mode approximation assumes that the different hyperfine states all share the same time-independent spatial mode. This implies that the resulting spin Hamiltonian only depends on the spin interaction strength and not on the density interaction strength. Taking the spinor sodium Bose-Einstein condensate in the f=1f=1f=1 hyperfine manifold as an example and working within the mean-field theory framework, it is found numerically that the single-mode approximation misses, in some parameter regimes, intricate details of the spin and spatial dynamics. We develop a physical picture that explains the observed phenomenon. Moreover, using that the population oscillations described by the single-mode approximation enter into the effective potential felt by the mean-field spinor, we derive a semiquantitative condition for when dynamical mean-field induced corrections to the single-mode approximation are relevant. Our mean-field results have implications for a variety of published and planned experimental studies.
We investigate the quantum dynamics of number fluctuations inside an atomic condensate during coherent spin mixing among internal states of the ground state hyperfine manifold, by quantizing the semiclassical nonrigid pendulum model in terms of the conjugate variable pair: the relative phase and the atom number. Our result provides a theoretical basis that resolves the resolution limit, or the effective "shot-noise" level, for counting atoms that is needed to clearly detect quantum correlation effects in spin mixing.
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