arXiv quant-ph/06102442006-10-30quant-ph

异质分子玻色-爱因斯坦凝聚体模型中的涌现量子相

Emergent quantum phases in a heteronuclear molecular Bose--Einstein condensate model

Melissa Duncan, Angela Foerster, Jon Links, Eduardo Mattei, Norman Oelkers, Arlei Prestes Tonel

备注：: 23 pages, 10 figures
DOI：: 10.1016/j.nuclphysb.2006.12.015

摘要：

本文研究了异质分子玻色-爱因斯坦凝聚体的三模哈密顿量。两种模式与两种可区分的原子成分相关联，它们可以结合形成由第三种模式表示的分子。从一个半经典的模拟模型，我们进行分析，以确定系统的相空间不动点。不动点的分叉自然地将耦合参数空间分成不同的区域。两个不同的情况下，发现，取决于原子模式的数量运营商之间的不平衡是零或非零。这一结果表明，模型的基态性质对原子不平衡表现出不寻常的敏感性。然后，我们测试这一发现的量子力学模型。具体地说，我们使用Bethe方法，基态期望值，量子动力学的特性，和基态波函数重叠来澄清基态相位的性质。由于量子涨落，跃迁的性质是平滑的，但我们仍然可以在零原子不平衡的极限下识别量子相界的出现。

英文摘要：

We study a three-mode Hamiltonian modelling a heteronuclear molecular Bose--Einstein condensate. Two modes are associated with two distinguishable atomic constituents, which can combine to form a molecule represented by the third mode. Beginning with a semi-classical analogue of the model, we conduct an analysis to determine the phase space fixed points of the system. Bifurcations of the fixed points naturally separate the coupling parameter space into different regions. Two distinct scenarios are found, dependent on whether the imbalance between the number operators for the atomic modes is zero or non-zero. This result suggests the ground-state properties of the model exhibit an unusual sensitivity on the atomic imbalance. We then test this finding for the quantum mechanical model. Specifically we use Bethe ansatz methods, ground-state expectation values, the character of the quantum dynamics, and ground-state wavefunction overlaps to clarify the nature of the ground-state phases. The character of the transition is smoothed due to quantum fluctuations, but we may nonetheless identify the emergence of a quantum phase boundary in the limit of zero atomic imbalance.

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