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arXiv:cond-mat/0210252 · Physical Review A

Dynamics of the spin-2 Bose condensate driven by external magnetic fields

Ping Zhang, C. K. Chan, Xiang‐Gui Li, Qi‐Kun Xue, Xian-Geng Zhao

Published Oct 10, 2002• 17 citations

Abstract

Dynamic response of the $F=2$ spinor Bose-Einstein condensate (BEC) under the influence of external magnetic fields is studied. A general formula is given for the oscillation period to describe population transfer from the initial polar state to other spin states. We show that when the frequency and the reduced amplitude of the longitudinal magnetic field are related in a specific manner, the population of the initial spin-0 state will be dynamically localized during time evolution. The effects of external noise and nonlinear spin-exchange interaction on the dynamics of the spinor BEC are studied. We show that while the external noise may eventually destroy the Rabi oscillations and dynamic spin localization, these coherent phenomena are robust against the nonlinear atomic interaction.

DOI: 10.1103/physreva.66.043606

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Dynamic response of the

F=2

spinor Bose-Einstein condensate (BEC) under the influence of external magnetic fields is studied. A general formula is given for the oscillation period to describe population transfer from the initial polar state to other spin states. We show that when the frequency and the reduced amplitude of the longitudinal magnetic field are related in a specific manner, the population of the initial spin-0 state will be dynamically localized during time evolution. The effects of external noise and nonlinear spin-exchange interaction on the dynamics of the spinor BEC are studied. We show that while the external noise may eventually destroy the Rabi oscillations and dynamic spin localization, these coherent phenomena are robust against the nonlinear atomic interaction.

We have studied the interaction of spinor Bose condensate with a combination of static and sinusoidal magnetic field . We find that the tunneling current among spin 0 and spin , spin 0 and spin , spin and spin may exhibit the incremental oscillation behavior, which depends on the field parameters of the reduced amplitudes of the transverse and the longitudinal magnetic fields respectively. This means that the dynamics spin localization can be adjusted experimentally by selecting the less values of the reduced amplitudes of the transverse magnetic field and those of the longitudinal magnetic field .

In this letter, we have studied the interaction of F=2 spinor Bose condensate with a combination of staticand sinusoidal magnetic field bl(t) = b0 + bcos(ωt). We find that the tunneling current among spin 0 and spin ±l,spin 0 and spin ±2, spin ±1 and spin ±2 may exhibit the incremental oscillation behavior, which depends on the fieldparameters of the reduced amplitudes of the transverse and the longitudinal magnetic fields respectively. This meansthat the dynamics spin localization can be adjusted experimentally by selecting the less values of the reduced amplitudesof the transverse magnetic field bx/ω and those of the longitudinal magnetic field b/ω.

In this paper, we study the dynamics properties of three-component antiferromagnetic dipolar Bose–Einstein condensates with external magnetic field. Our results are obtained by numerical simulations of the spinor Gross–Pitaevskii equation. We find that the population of the spin components is seriously influenced by magnetic field. The dynamical evolution process is accelerated in the presence of magnetic field. As a result, the periodic oscillation of spin exchange dynamics emerges and the components [Formula: see text] have the same amplitude. In addition, the density profile displays that the influences of dipolar interaction are masked by magnetic field. Moreover, we introduce an order parameter to characterize the disorder-order crossover, where it is seen that the system develops toward the disordered state with strong dipole strength when magnetic field is included.

We present measurements and a theoretical model for the interplay of spin-dependent interactions and external magnetic fields in atomic spinor condensates. We highlight general features such as quadratic Zeeman dephasing and its influence on coherent spin mixing processes by focusing on a specific coherent superposition state in a

F=1

^{87}\mathrm{Rb}

Bose-Einstein condensate. In particular, we observe the transition from coherent spinor oscillations to the thermal equilibration.

In this letter, we have studied the influence of the external magnetic fields on tunneling of the spin-1 Bose condensate. We find that the population transfer between spin-0 and spin-±1 exhibits the step structure under the external cosinusoidal magnetic field and a combination of static and cosinusoidal one, respectively. Compared with the longitudinal component of the external magnetic field, the smaller the transverse component of the magnetic field is, the larger the time scale of exhibiting the step structure does. The tunneling current may exhibit periodically oscillation behavior when the ratio of the transverse component of the magnetic field is smaller than that of the longitudinal component, otherwise it exhibits a damply oscillating behavior. This means that the dynamical spin localization can be adjusted by the external magnetic fields.