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Journal of the Physical Society of Japan

Location of Spin-1 Condensate Magnetization in a Double-Well Potential under External Field

Lei Tan, Xiaofei Zang, Li Ju-Ping, Liwei Liu, Cai-Ying Ding, Qirong Li, Xiang Gao

Published Mar 26, 2008• 5 citations
Publisher

Abstract

The dynamics of magnetization of a spin-1 Bose-Einstein condensate trapped in a double-well potential under external fields is investigated, focusing on the effects induced by the nonlinear self-interaction and the external magnetic field. Our numerical calculations show that the larger the external magnetic field is, the stronger the macroscopic quantum location of the condensate magnetization becomes.

DOI
10.1143/jpsj.77.044704

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In this thesis we investigate the static, dynamic, and thermodynamic properties\nof atomic spin-1 Bose gases in external magnetic fields. At low magnetic fields\nthe properties of single-component, or scalar condensates, are essentially\nunaffected but can become significantly altered for spinor Bose condensates as\nshown by our studies.\n\nWe first study the Bose-Einstein condensation of trapped spin-1 Bose gases by\nemploying the Hartree-Fock approximation and the two-fluid model within a mean\nfield approximation. Our detailed investigation reveals that the\nferromagnetically interacting spin-1 condensates exhibit triple condensations\nwhile the antiferromagnetically interacting ones show double condensations.\n\nThe ground state structure of homogeneous and trapped spin-1 Bose condensates\nwith ferromagnetic and antiferromagnetic interactions at zero temperature in\nmagnetic fields are then investigated systematically. We further illuminate the\nimportant effect of quadratic Zeeman shift which causes a preferred occupation\nof the $|m_F=0\nangle$ state through spin exchange collisions, $2|m_F=0\nangle\nleftrightarrow |m_F=1\nangle + |m_F=-1\nangle$.\n\nWe also present detailed studies of the off-equilibrium coherent dynamics of\nspin-1 Bose condensates in magnetic fields within the single spatial mode\napproximation. Dynamical instabilities of the off-equilibrium oscillations are\nshown to be responsible for the formation of multiple domains as recently\nobserved in several $^{87}$Rb experiments.\n\nFinally, we discuss briefly excited condensate states, or soliton-like states,\nin cigar-shaped spin-1 Bose condensates with an effective quasi-1D description,\nusing the developed nonpolynomial Schr"odinger equation.

•Sep 22, 2005•0 citations
The dynamics of magnetization of a spin-1 Bose-Einstein condensate trapped in a double-well potential under external fields is investigated, focusing on the effects induced by the nonlinear self-interaction and the external magnetic field. Our numerical calculations show that the larger the external magnetic field is, the stronger the macroscopic quantum location of the condensate magnetization becomes.
We have investigated the effect of an external periodic driving to the macroscopic quantum tunneling of spin-1 condensates in a double-well potential. By manipulating the frequencies of the external magnetic fields, a rich set of phenomena can be studied, and dynamical localization and self-trapping in spin states can be realized using time-dependent magnetic field. We have shown that a relatively high-frequency field may induce a fast oscillation of the macroscopic quantum localization. The larger the periodic magnetic field frequency is, the faster oscillation of the spin condensate magnetization goes. By applying a lower-frequency field to the spin-condensate, one can find that the dynamical properties of the magnetization appears similar behaviors to the results of the modulations of a constant external magnetic field. A possible realization in experiments is also presented.
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.
Abstract We investigate the macroscopic quantum self-trapping (MQST) phenomenon of a spin–orbit-coupled Bose–Einstein condensate (BEC) in a double-well potential, emphasizing the critical behavior at the transition to MQST. We show that as the nonlinear parameter characterizing the atomic interaction increases, the spin–orbit-coupled BEC appears as MQST, manifesting an asymmetric distribution of the atom in two wells. Then, the effect of the initial condition on the critical behavior at the transition to MQST is given. Analytic expressions for the dependence of the transition parameters on the system parameters and the initial condition are derived, which are in agreement with our numerical simulations.
Dynamic response of the F=2F=2F=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.
In this thesis we investigate the static, dynamic, and thermodynamic properties\nof atomic spin-1 Bose gases in external magnetic fields. At low magnetic fields\nthe properties of single-component, or scalar condensates, are essentially\nunaffected but can become significantly altered for spinor Bose condensates as\nshown by our studies.\n\nWe first study the Bose-Einstein condensation of trapped spin-1 Bose gases by\nemploying the Hartree-Fock approximation and the two-fluid model within a mean\nfield approximation. Our detailed investigation reveals that the\nferromagnetically interacting spin-1 condensates exhibit triple condensations\nwhile the antiferromagnetically interacting ones show double condensations.\n\nThe ground state structure of homogeneous and trapped spin-1 Bose condensates\nwith ferromagnetic and antiferromagnetic interactions at zero temperature in\nmagnetic fields are then investigated systematically. We further illuminate the\nimportant effect of quadratic Zeeman shift which causes a preferred occupation\nof the $|m_F=0\nangle$ state through spin exchange collisions, $2|m_F=0\nangle\nleftrightarrow |m_F=1\nangle + |m_F=-1\nangle$.\n\nWe also present detailed studies of the off-equilibrium coherent dynamics of\nspin-1 Bose condensates in magnetic fields within the single spatial mode\napproximation. Dynamical instabilities of the off-equilibrium oscillations are\nshown to be responsible for the formation of multiple domains as recently\nobserved in several 87^{87}87Rb experiments.\n\nFinally, we discuss briefly excited condensate states, or soliton-like states,\nin cigar-shaped spin-1 Bose condensates with an effective quasi-1D description,\nusing the developed nonpolynomial Schr"odinger equation.