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arXiv 1508.04553quant-ph
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经典哈密顿量的压缩

Squeezing with classical Hamiltonians

Tomáš Opatrný

摘要:

导出了压缩过程初始阶段的最大压缩率的一个简单公式:压缩率仅与经典哈密顿量的二阶偏导数有关。规则的相空间的最佳旋转被发现,以保持最佳的状态定位和定向最快的压缩。这些操作将感兴趣的相空间点转换为具有相反主曲率的鞍点。对于布洛赫球相空间和自旋压缩也得到了类似的结果。通过几个模型例子说明了一般公式的应用,包括参量下转换,克尔非线性,Jaynes-Cummings相互作用,以及单轴扭转和双轴反扭转的自旋压缩。

英文摘要:

A simple formula is derived for the maximum squeezing rate which occurs at the initial stages of the squeezing process: the rate only depends on the second partial derivatives of a classical Hamiltonian. Rules for optimum rotation of the phase space are found to keep the state optimally located and oriented for fastest squeezing. These operations transform the phase-space point of interest into a saddle point with opposite principal curvatures. Similar results are found for the Bloch-sphere phase space and spin squeezing. Application of the general formulas is illustrated by several model examples including parametric downconversion, Kerr nonlinearity, Jaynes-Cummings interaction, and spin squeezing by one-axis twisting and two-axis countertwisting.

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