论文标题
非线性制度中具有光力学系统的量子计量学
Quantum metrology with optomechanical systems in the nonlinear regime
论文作者
论文摘要
本论文重点介绍了非线性腔光系统的数学描述和应用。第一部分涉及解决标准非线性光学机电哈密顿量的动力学，并具有额外的时间依赖于时间的机械位移和单模挤压项。该解决方案基于确定生成系统时间进化的LIE代数，该代数将问题降低到考虑有限的耦合的真实功能的常规微分方程。第二部分将扩展的光力学哈密顿量的溶液应用于非高斯性研究。我们计算光力状态的非高斯特征是哈密顿量中参数的函数，并研究了非高斯性，非线性耦合的强度和单模机械挤压项的强度之间的相互作用。我们发现非线性耦合的强度和形式强烈影响非高斯性，并且其与挤压术语的关系非常复杂。第三部分涉及将非线性光力系统用作量子传感器的使用。鉴于扩展的光学机电哈密顿量，我们得出了量子渔民信息的一般表达，并通过三个具体示例证明了其适用性：估计非线性光耦合的强度，即定制的机械位移的强度，以及单态机械式机械式机械式侵居参数的强度，所有均模块的强度。在论文的最后一章中，我们考虑使用光力学系统估算恒定重力加速度。我们的结果表明，原则上可以将光力学系统用作强大的量子传感器。
This thesis focuses on the mathematical description and application of nonlinear cavity optomechanical systems. The first part is concerned with solving the dynamics of the standard nonlinear optomechanical Hamiltonian with an additional time-dependent mechanical displacement and single-mode squeezing term. The solution is based on identifying a Lie algebra that generates the time-evolution of the system, which reduces the problem to considering a finite set of coupled ordinary differential equations of real functions. The second part applies the solutions of the extended optomechanical Hamiltonian to the study of non-Gaussianity. We compute the non-Gaussian character of an optomechanical state as a function of the parameters in the Hamiltonian, and investigate the interplay between the non-Gaussianity, the strength of the nonlinear coupling and the strength of the single-mode mechanical squeezing term. We find that the strength and form of the nonlinear coupling strongly impacts the non-Gaussianity, and that its relationship with the squeezing term is highly complex. The third part concerns the use of nonlinear optomechanical systems as quantum sensors. We derive a general expression of the quantum Fisher information given the extended optomechanical Hamiltonian and demonstrate its applicability through three concrete examples: estimating the strength of a nonlinear light--matter coupling, the strength of a time-modulated mechanical displacement, and the strength of a single-mode mechanical squeezing parameter, all of which are modulated at resonance. In the last Chapter of the thesis, we consider the estimation of a constant gravitational acceleration with an optomechanical system. Our results suggest that optomechanical systems could, in principle, be used as powerful quantum sensors.
