Accuracy of the Gross–Pitaevskii Equation in a Double-Well Potential

IF 1.1 3区 物理与天体物理 Q4 PHYSICS, APPLIED
Asaad R. Sakhel, Robert J. Ragan, William J. Mullin
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Abstract

The Gross–Pitaevskii equation (GPE) in a double-well potential produces solutions that break the symmetry of the underlying non-interacting Hamiltonian, i.e., asymmetric solutions. The GPE is derived from the more general second-quantized Fock Schr\(\ddot{\textrm{o}}\)dinger equation (FSE). We investigate whether such solutions appear in the more general case or are artifacts of the GPE. We use two-mode analyses for a variational treatment of the GPE and to treat the Fock equation. An exact diagonalization of the FSE in dual condensates yields degenerate ground states that are very accurately fitted by phase-state representations of the degenerate asymmetric states found in the GPE. The superposition of degenerate asymmetrical states forms a cat state. An alternative form of cat state results from a change of the two-mode basis set.

Abstract Image

Abstract Image

双井电位中格罗斯-皮塔耶夫斯基方程的准确性
双阱势中的格罗斯-皮塔耶夫斯基方程(GPE)会产生打破底层非相互作用哈密顿对称性的解,即非对称解。GPE 是由更一般的二次量化福克-施林格方程(FSE)衍生而来的。我们研究了这种解是否出现在更一般的情况下,或者是 GPE 的伪命题。我们使用双模分析法对 GPE 进行变分处理,并对 Fock 方程进行处理。在对偶凝聚态中对 FSE 进行精确的对角化,可以得到退化的基态,这些基态与 GPE 中发现的退化非对称态的相态表示非常精确地拟合。退化不对称态的叠加形成了猫态。猫态的另一种形式产生于双模基集的改变。
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来源期刊
Journal of Low Temperature Physics
Journal of Low Temperature Physics 物理-物理:凝聚态物理
CiteScore
3.30
自引率
25.00%
发文量
245
审稿时长
1 months
期刊介绍: The Journal of Low Temperature Physics publishes original papers and review articles on all areas of low temperature physics and cryogenics, including theoretical and experimental contributions. Subject areas include: Quantum solids, liquids and gases; Superfluidity; Superconductivity; Condensed matter physics; Experimental techniques; The Journal encourages the submission of Rapid Communications and Special Issues.
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