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Journal of Physics Conference Series

Macroscopic quantum tunnelling of magnetization in spinor Bose-Einstein condensates

Özgür Esat Müstecaplıoğlu, Li You

Published Apr 1, 2006• 0 citations
Publisher

Abstract

We investigate macroscopic quantum tunneling of magnetization in a a spinor Bose-Einstein condensate trapped in a double-well potential.Using the mean field theory applicable for large condensates, and employing the single spatial mode approximation we derive dynamical equations for magnetization, independent from density mode, for certain initial conditions.We show that they can be reduced to standard Josephson junction dynamics equations under certain conditions.

DOI
10.1088/1742-6596/36/1/022

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We study quantum dynamical properties of a spin-1 atomic Bose-Einstein condensate in a double-well potential. Adopting a mean field theory and single spatial mode approximation, we characterize our model system as two coupled spins. For certain initial states, we find full magnetization oscillations between wells not accompanied by mass (or atom numbers) exchange. We identify dynamic regimes of collective spin variables arising from nonlinear self-interactions that are different from the usual Josephson oscillations. We also discuss magnetization beats and incomplete oscillations of collective spin variables other than the magnetization. Our study points to an alternative approach to observe coherent tunnelling of a condensate through a (spatial) potential barrier.
It is well known that increasing the nonlinearity due to repulsive atomic interactions in a double-well Bose-Einstein condensate suppresses quantum tunneling between the two sites. Here we find analogous behavior in the dynamical tunneling of a Bose-Einstein condensate between period-one resonances in a single driven potential well. For small nonlinearities we find unhindered tunneling between the resonances, but with an increasing period as compared to the noninteracting system. For nonlinearities above a critical value we generally observe that the tunneling shuts down. However, for certain regimes of modulation parameters we find that dynamical tunneling reemerges for large enough nonlinearities, an effect not present in spatial double-well tunneling. We develop a two-mode model in good agreement with full numerical simulations over a wide range of parameters, which allows the suppression of tunneling to be attributed to macroscopic quantum self-trapping.
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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.
Macroscopic quantum tunneling of Bose-Einstein Condensate in a double-well potential is discussed in the frame of an experimentally realizable Hamiltonian with ϕ 6 interaction under the two-mode approximation. Concentrating on a special case Δ E = Λ = 0, we analyze the stationary states and dynamics of the system to find that such system possesses very small phase spaces for Josephson oscillation and usually lies in the macroscopic quantum self-trapping state (MQST). Importantly we obtain three kinds of MQSTs and in terms of them show the phase diagrams of the system.