[论文解读] Reply to Comment on "Properties and dynamics of generalized squeezed states"

Sahel Ashhab, Mohammad Ayyash|arXiv (Cornell University)|Jan 12, 2026

Statistical Mechanics and Entropy被引用 0

一句话总结

本回复捍卫广义挤压中的振荡动力学的存在，强调偶奇奇偶性依赖，并论证只有在获得额外物理信息或使用量子泵模型时，动力学才是良定义的。

ABSTRACT

In our paper [1], our numerical simulations showed that, unlike displacement and conventional squeezing, higher-order squeezing exhibits oscillatory dynamics. Subsequently, Gordillo and Puebla pointed out that simulation results depend on whether the size of the state space in the simulations is even or odd [2]. Using additional derivations, they argued that the oscillatory dynamics is unphysical and that the photon number must increase monotonically as a function of the squeezing parameter $r$. We agree with the observation of an even-odd parity dependence in the simulations. We independently noticed the same feature in our simulations after the publication of Ref. [1]. This observation led us to perform a more detailed investigation of the numerical simulation and mathematical aspects of the generalized squeezing problem. Our new findings were reported in Ref. [3]. Further analysis was reported in Ref. [4]. Our conclusion is that the generalized squeezing operator is physically not well defined but can be made well defined when combined with additional information about the physical system under study. We demonstrated this point in the case where we include an additional nonlinear interaction term in the Hamiltonian. We disagree with the claim that the photon number must be a monotonically increasing function of $r$. This claim contradicts the mathematically rigorous results of Ref. [4]. Furthermore, we show that the oscillatory behaviour persists in two closely related, well-behaved models.

研究动机与目标

• 研究广义挤压中振荡动力学的起源。
• 分析数值模拟中奇偶性（偶数与奇数）在结果中的作用。
• 检查广义挤压算符的数学良定义性和自伴性。
• 展示包含高阶非线性项或量子泵模型如何影响结果。
• 阐明经典泵模型和在此情境下的发散级数的局限性。

提出的方法

• 对各种参数进行广义挤压的数值模拟。
• 分析偶数与奇数有限状态截断对结果的影响。
• 引入 Kerr（非线性）项以获得正则化、收敛的动力学。
• 引入带辅助模的量子泵模型以定义有效挤压参数。
• 比较经典泵与量子泵公式下的结果以评估物理相关性。

实验结果

研究问题

• RQ1 在良定义的数学公式下，振荡在广义挤压动力学中是否仍然存在？
• RQ2 观察到的奇偶性依赖（偶数与奇数状态空间大小）是截断的伪影还是物理特征？
• RQ3 通过自伴扩展或额外物理项，是否可以使广义挤压问题良定义？
• RQ4 量子泵模型是否消除数学病态并产生与截断无关的泵数相关动力学？
• RQ5 高阶非线性项如何影响收敛性和动力行为？

主要发现

• 在良好行为、正则化模型中振荡动力学仍然存在。
• 奇偶性依赖（偶数与奇数）对仿真结果有强烈影响。
• 有限截断表现出非收敛的渐近行为，表明需要自伴扩展或物理约束。
• 加入 Kerr 项可获得收敛的动力学并保持振荡。
• 量子泵模型自然正则化问题并再现振荡行为及奇偶性效应。
• 幂级数方法可能不收敛，且可能误导关于光子数增长的结论。