量子非线性光学腔的正则化线性化：在简并光学参量振荡器中的应用
Regularized linearization for quantum nonlinear optical cavities: Application to Degenerate Optical Parametric Oscillators
摘要：
非线性光学腔在经典光学和量子光学中都是至关重要的;特别是，如今光学参量振荡器是最通用和可调谐的相干光源之一，也是连续可变区中最高质量量子相关光源。作为非线性系统，它们可以被驱动通过临界点，在临界点处，一个解决方案不再存在，而有利于一个新的解决方案，并且它靠近量子相关性最强的这些点。对这类系统最简单的描述是将量子场写成经典部分加上一些量子涨落，然后相对于后者线性化动力学方程;然而，这种方法在接近临界点时就失效了，在那里它提供了非物理的预测，例如无限光子数。另一方面，超越简单线性描述的技术变得过于复杂，特别是关于两次衰减器的评估，这对于计算腔外的观测量至关重要。本文以简并光学参量振荡器为例，给出了非线性腔的正则化线性描述，即产生物理结果的线性化过程。该方法，我们称之为自洽线性化，被证明是等价于一个一般的高斯anastomic系统的状态，我们比较其预测与可用的精确（或准精确）的方法。
英文摘要：
Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest quality quantum-correlated light in the continuous variable regime. Being nonlinear systems, they can be driven through critical points in which a solution ceases to exist in favour of a new one, and it is close to these points where quantum correlations are the strongest. The simplest description of such systems consists in writing the quantum fields as the classical part plus some quantum fluctuations, linearizing then the dynamical equations with respect to the latter; however, such an approach breaks down close to critical points, where it provides unphysical predictions such as infinite photon numbers. On the other hand, techniques going beyond the simple linear description become too complicated especially regarding the evaluation of two-time correlators, which are of major importance to compute observables outside the cavity. In this article we provide a regularized linear description of nonlinear cavities, that is, a linearization procedure yielding physical results, taking the degenerate optical parametric oscillator as the guiding example. The method, which we call self-consistent linearization, is shown to be equivalent to a general Gaussian ansatz for the state of the system, and we compare its predictions with those obtained with available exact (or quasi-exact) methods.
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