Parametric gates and processes engineered from the perspective of the static effective Hamiltonian of a driven system are central to quantum technology. However, the perturbative expansions used to derive static effective models may not be able to efficiently capture all the relevant physics of the original system. In this work, we investigate the conditions for the validity of the usual low-order static effective Hamiltonian used to describe a Kerr oscillator under a squeezing drive. This system is of fundamental and technological interest. In particular, it has been used to stabilize Schrödinger cat states, which have applications for quantum computing. We compare the states and energies of the effective static Hamiltonian with the exact Floquet states and quasi-energies of the driven system and determine the parameter regime where the two descriptions agree. Our work brings to light the physics that is left out by ordinary static effective treatments and that can be explored by state-of-the-art experiments.

中文翻译：

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克尔参量振荡器的有效理论与 Floquet 理论

从驱动系统的静态有效哈密顿量的角度设计的参数门和过程是量子技术的核心。然而，用于推导静态有效模型的微扰展开可能无法有效地捕获原始系统的所有相关物理现象。在这项工作中，我们研究了用于描述压缩驱动下克尔振荡器的常用低阶静态有效哈密顿量的有效性条件。该系统具有基础和技术意义。特别是，它已被用于稳定薛定谔猫态，这在量子计算中具有应用。我们将有效静态哈密顿量的状态和能量与驱动系统的精确 Floquet 状态和准能量进行比较，并确定两种描述一致的参数范围。我们的工作揭示了普通静态有效治疗所遗漏的物理原理，并且可以通过最先进的实验来探索。