We investigate superpositions of two-mode squeezed states (TMSSs), which have potential applications in quantum information processing and quantum sensing. We study some properties of these nonclassical states such as the statistics of each mode and the degree of entanglement between the two modes, which can be higher than that of a TMSS with the same degree of squeezing. The states we consider can be prepared by inducing two-mode Jaynes-Cummings and anti-Jaynes-Cummings interactions in a system of two modes and a spin-$\frac{1}{2}$ particle, for instance, in the trapped ion domain, as described here. We show that when two harmonic oscillators are prepared in a superposition of two TMSSs, each reduced single-mode state can be advantageously employed to sense arbitrary displacements of the mode in phase space. The Wigner function of this reduced state exhibits a symmetrical peak centered at the phase-space origin, which has the convenient peculiarity of getting narrower in both quadratures simultaneously as the average photon number increases. This narrow peak can be used as the pointer of our quantum sensor, with its position in phase space indicating the displacement undergone by the oscillator.

中文翻译：

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用于量子信息处理和量子传感的双模压缩态叠加

我们研究了双模压缩态 (TMSS) 的叠加，其在量子信息处理和量子传感中具有潜在的应用。我们研究了这些非经典态的一些特性，例如每种模式的统计数据以及两种模式之间的纠缠度，这可能高于具有相同挤压度的 TMSS。我们考虑的状态可以通过在两个模式和一个自旋的系统中引入双模式 Jaynes-Cummings 和反 Jaynes-Cummings 相互作用来准备$\frac{1}{2}$粒子，例如，在俘获离子域中，如此处所述。我们表明，当在两个 TMSS 的叠加中准备两个谐振子时，可以有利地采用每个减少的单模态来感测相空间中模式的任意位移。这种减少状态的 Wigner 函数表现出以相空间原点为中心的对称峰，它具有随平均光子数增加而同时在两个正交中变窄的便利特性。这个窄峰可以用作我们的量子传感器的指针，它在相空间中的位置表示振荡器所经历的位移。