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arXiv 1004.3520cond-mat.quant-gasphysics.atom-ph
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双势阱中玻色-费米混合体系的自发对称性破缺

Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials

S. K. Adhikari, B. A. Malomed, L. Salasnich, F. Toigo

摘要:

研究了双势阱中超流玻色-费米(BF)混合体系的自发对称性破缺。玻色子的Gross-Pitaevskii方程(GPE)与费米超流体的序参量方程相耦合,后者是从幺正性极限下的密度泛函导出的(类似的模型也适用于BCS体系)。简并费米气体中的直接单边带是不可能的,因为它需要一个有吸引力的自相互作用,而费米气体中的固有非线性是排斥的。尽管如此,我们证明了对称性破缺在费米子和玻色子之间存在吸引力的混合物中是可能的,如40 K和87 Rb。数值结果表示的依赖性的不对称参数的两个组件的混合物,N_F和N_B的粒子数,并在(N_F,N_B)平面,它显示对称和不对称的基态区域的相图。由单阱势逐渐转变为双阱势引起的单边带的动力学图象也被报道。当玻色子波函数的GPE可以用TF近似处理时,本文提出了一种解析近似。在N_F和N_B之间的一个特殊的线性关系下,TF近似允许我们把模型简化为一个包含相互竞争的排斥和吸引非线性项的费米子函数的单一方程。后者直接显示了费米超流体中有效吸引力的产生机制,它是由混合物中的玻色子成分介导的。

英文摘要:

We study the spontaneous symmetry breaking (SSB) of a superfluid Bose-Fermi (BF) mixture in a double-well potential (DWP). The mixture is described by the Gross-Pitaevskii equation (GPE) for the bosons, coupled to an equation for the order parameter of the Fermi superfluid, which is derived from the respective density functional in the unitarity limit (a similar model applies to the BCS regime too). Straightforward SSB in the degenerate Fermi gas loaded into a DWP is impossible, as it requires an attractive self-interaction, while the intrinsic nonlinearity in the Fermi gas is repulsive. Nonetheless, we demonstrate that the symmetry breaking is possible in the mixture with attraction between fermions and bosons, like 40K and 87Rb. Numerical results are represented by dependencies of asymmetry parameters for both components on particle numbers of the mixture, N_F and N_B, and by phase diagrams in the (N_F,N_B) plane, which displays regions of symmetric and asymmetric ground states. The dynamical picture of the SSB, induced by a gradual transformation of the single-well potential into the DWP, is reported too. An analytical approximation is proposed for the case when GPE for the boson wave function may be treated by means of the Thomas-Fermi (TF) approximation. Under a special linear relation between N_F and N_B, the TF approximation allows us to reduce the model to a single equation for the fermionic function, which includes competing repulsive and attractive nonlinear terms. The latter one directly displays the mechanism of the generation of the effective attraction in the Fermi superfluid, mediated by the bosonic component of the mixture.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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