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arXiv:0809.4307 · Physical Review Letters

Non-Abelian Josephson Effect between Two F=2 Spinor Bose-Einstein Condensates in Double Optical Traps

Ran Qi, Xiao-Lu Yu, Zhibing Li, W. M. Liu

Published May 4, 2009• 136 citations
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Abstract

We investigate the non-Abelian Josephson effect in F=2 spinor Bose-Einstein condensates with double optical traps. We propose a real physical system which contains non-Abelian Josephson effect and has very different density and spin tunneling characters compared with the Abelian case. We calculate the frequencies of the pseudo Goldstone modes in different phases between two traps, respectively, which are the crucial feature of the non-Abelian Josephson effect. We also give an experimental protocol to observe this novel effect in future experiments.

DOI
10.1103/physrevlett.102.185301

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We investigate the non-Abelian Josephson effect in F=2 spinor Bose-Einstein condensates with double optical traps. We propose a real physical system which contains non-Abelian Josephson effect and has very different density and spin tunneling characters compared with the Abelian case. We calculate the frequencies of the pseudo Goldstone modes in different phases between two traps, respectively, which are the crucial feature of the non-Abelian Josephson effect. We also give an experimental protocol to observe this novel effect in future experiments.
We investigate the non-Abelian Josephson effect in F=2 spinor Bose-Einstein condensates with double optical traps. We propose a real physical system which incorporates the non-Abelian Josephson effect and has very different density and spin tunneling characteristics compared with the Abelian case. We calculate the frequencies of the pseudo Goldstone modes in different phases between two traps, which are the crucial feature of the non-Abelian Josephson effect. We also give an experimental protocol to observe this novel effect in future experiments.
We review our theoretical advances in quantum tunneling of Bose-Einstein condensates in optical traps and in microcavities. By employing a real physical system, the frequencies of the pseudo Goldstone modes in different phases between two optical traps are studied respectively, which are the crucial feature of the non-Abelian Josephson effect. When the optical lattices are under gravity, we investigate the quantum tunneling in the “Wannier-Stark localization” regime and “Landau-Zener tunneling” regime. We finally get the total decay rate and the rate is valid over the entire range of temperatures. At high temperatures, we show how the decay rate reduces to the appropriate results for the classical thermal activation. At intermediate temperatures, the results of the total decay rate are consistent with the thermally assisted tunneling. At low temperatures, we obtain the pure quantum tunneling ultimately. And we study the alternating-current and direct-current (ac and dc) photonic Josephson effects in two weakly linked microcavities containing ultracold two-level atoms, which allows for direct observation of the effects. This enables new investigations of the effect of many-body physics in strongly coupled atom-cavity systems and provides a strategy for constructing novel interference devices of coherent photons. In addition, we propose the experimental protocols to observe these quantum tunneling of Bose-Einstein condensates.
The Josephson effect can be observed in a Bose-Einstein condensate in a double-well potential, which is attributed to the tunneling of bosons between two wells. We propose a multi-mode theory to investigate the dynamics of local excitations in a one-dimensional condensate in a double-well potential. We show that the system can be described by two independent two-mode models. The Josephson oscillation and the self-trapping of local collective excitations are predicted analytically and confirmed by numerical simulation.
We investigate the quantum dynamics of an experimentally realized spin-orbit-coupled Bose-Einstein condensate in a double-well potential. The spin-orbit coupling can significantly enhance the atomic interwell tunneling. We find the coexistence of internal and external Josephson effects in the system, which are moreover inherently coupled in a complicated form even in the absence of interatomic interactions. Moreover, we show that the spin-dependent tunneling between two wells can induce a net atomic spin current referred as spin Josephson effects. Such spin Josephson effects can be observable under realistic conditions.
We analyze theoretically Josephson oscillations in a mixture of two Zeeman states of a spinor Bose-Einstein condensate in a double-well potential. We find that in the strongly polarized case, the less populated component exhibits a complex dynamics with an anti-Josephson behavior, i.e., oscillates in phase with the more populated one. In the balanced population case, the Josephson oscillations unveil a dependence with the different spin collision channels. This effect could be used to experimentally measure the distinct scattering lengths entering in the description of a spinor condensate. Our numerical results are in close agreement with an analytical description of the binary mixture using a two-mode model.
We theoretically study the internal Josephson effect, which is driven by spin-exchange interactions and magnetic dipole-dipole interactions, in a three-level system for spin-1 Bose--Einstein condensates, obtaining novel spin dynamics. We introduce single spatial mode approximations into the Gross--Pitaevskii equations and derive the Josephson-type equations, which are analogous to tunneling currents through three junctions between three superconductors. From an analogy with two interacting nonrigid pendulums, we identify unique varied oscillational modes, called the $0--\ensuremath{\pi}$, 0−−running0--\mathit{running}0−−running, running−−running\mathit{running}--\mathit{running}running−−running, $2n\ensuremath{\pi} & \mathit{running}--2\ensuremath{\pi}$, singlenonrigidpendulum\mathit{single nonrigid pendulum}singlenonrigidpendulum, and tworigidpendulums\mathit{two rigid pendulums}tworigidpendulums phase modes. These Josephson modes in the three states are expected to be found in real atomic Bose gas systems.