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arXiv:cond-mat/0203066 · Physical Review Letters

Macroscopic Spin Tunneling and Quantum Critical Behavior of a Condensate in a Double-Well Potential

Han Pu, Weiping Zhang, Pierre Meystre

Published Aug 7, 2002• 48 citations
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Abstract

In a previous work [H. Pu, W. Zhang, and P. Meystre, Phys. Rev. Lett. 87, 140405 (2001)]], we have shown that a spinor condensate confined in a periodic or double-well potential exhibits ferromagnetic behavior due to the magnetic dipole-dipole interactions between different wells, and in the absence of external magnetic field, the ground state has a twofold degeneracy. In this work, we demonstrate the possibility of observing macroscopic quantum spin tunneling between these two degenerate states and show how the tunneling rate critically depends on the strength of the transverse field.

DOI
10.1103/physrevlett.89.090401

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In a previous work [H. Pu, W. Zhang, and P. Meystre, Phys. Rev. Lett. 87, 140405 (2001)]], we have shown that a spinor condensate confined in a periodic or double-well potential exhibits ferromagnetic behavior due to the magnetic dipole-dipole interactions between different wells, and in the absence of external magnetic field, the ground state has a twofold degeneracy. In this work, we demonstrate the possibility of observing macroscopic quantum spin tunneling between these two degenerate states and show how the tunneling rate critically depends on the strength of the transverse field.
We study the macroscopic quantum tunneling of magnetization of the F=1F=1F=1 spinor condensate interacting through dipole-dipole interaction with an external magnetic field applied along the longitudinal or transverse direction. We show that the ground state energy and the effective magnetic moment of the system exhibit an interesting macroscopic quantum oscillation phenomenon originating from the oscillating dependence of thermodynamic properties of the system on the vacuum angle. Tunneling between two degenerate minima are analyzed by means of an effective potential method and the periodic instanton method.
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 investigate the macroscopic quantum spin coherence of a spinor condensate confined in an anisotropic potential. Under the single-mode approximation, we show that a spin-1 Rb condensate can be modeled as a biaxial quantum magnet. A direct consequence of the biaxial anisotropy is that the tunneling splitting oscillates as a function of the external magnetic field applied along the hard axis. We also propose an experimental scheme to detect the oscillatory behavior of the tunneling splitting by employing the Landau-Zener tunneling.
We study macroscopic quantum phenomena for an atomic condensate in a double-well potential as realized in recent experiments by Albiez et al. [Phys. Rev. Lett. 95, 010402 (2005)] and Shin et al. [Phys. Rev. Lett 95, 170402 (2005)]. By keeping the leading correction in the usually adopted mapping to an anisotropic spin model, we find that the topological Berry phase, a parity effect due to the even and odd atom numbers of a condensate, can be observed in the tunnel splitting. Our investigation suggests a cleaner, perhaps significantly improved, alternative for observing macroscopic quantum coherence (MQC) in large spin models.
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.