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Acta Physica Sinica

Nonlinear dynamical properties of susceptibility of a spinor Bose-Einstein condensate with dipole-dipole interaction in a double-well potential

Xiao-Fei Zang, Li Ju-Ping, Lei Tan, 兰州大学理论物理研究所，兰州 730000

Published Jan 1, 2007• 16 citations
Publisher

Abstract

Based on mean-field theory and single spatial mode approximation，we study the nonlinear dynamical properties of the susceptibility of total spin F=1 Bose-Einstein condensate with dipole-dipole interaction in a double-well potential. For certain initial states，we find that the susceptibility oscillation appears when λA+2λd=0. When λA+2λd≠0, the dynamical behavior of the system shows both oscillation and self-trapping of susceptibility.

DOI
10.7498/aps.56.4348

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Based on mean-field theory and single spatial mode approximation，we study the nonlinear dynamical properties of the susceptibility of total spin F=1 Bose-Einstein condensate with dipole-dipole interaction in a double-well potential. For certain initial states，we find that the susceptibility oscillation appears when λA+2λd=0. When λA+2λd≠0, the dynamical behavior of the system shows both oscillation and self-trapping of susceptibility.
We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.
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.
The quantum self-trapping phenomenon of a Bose-Einstein condensate (BEC) represents a remarkable nonlinear effect of wide interest. By considering a purely dipolar BEC in a double-well potential, we study how the dipole orientation affects the ground-state structure and the transition between self-trapping and Josephson oscillations in dynamics. Three-dimensional numerical results and an effective two-mode model demonstrate that the onset of self-trapping of a dipolar BEC can be radically modified by the dipole orientation. We also analyze the failure of the two-mode model in predicting the rate of Josephson oscillations. We hope that our results can motivate experimental work as well as future studies of self-trapping of ultracold dipolar gases in optical lattices.
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.
The properties of an F=1F=1F=1 spinor Bose-Einstein condensate trapped in a double-well potential are discussed using both a mean-field two-mode approach and a two-site Bose-Hubbard Hamiltonian. We focus on the region of phase space in which spin effects lead to symmetry breaking of the system, favoring the spatial localization of the condensate in one well. To model this transition we derive, using perturbation theory, an effective Hamiltonian that describes N/2N/2N/2 spin singlets confined in a double-well potential.