Applications of the Fokker-Planck equation in circuit quantum electrodynamics
Applications of the Fokker-Planck equation in circuit quantum electrodynamics
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DOI：
10.1103/physreva.94.043840
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发表时间：
2016-10-21
影响因子：
2.9
通讯作者：
Ginossar, Eran
中科院分区：
文献类型：
--
作者：
Elliott, Matthew;Ginossar, Eran
本文研究了几个可应用于电路量子电动力学领域的非线性开放量子系统稳态行为的精确解。利用广义P表象中的Fokker-Planck方程，研究了两个基本模型的解析解.首先，我们解决了一个线性腔，耦合到一个近似的transmon量子比特的稳态响应，并使用此解决方案来研究弱和强驱动制度，使用腔和transmon场的矩的解析表达式，沿着与transmon的Husimi Q函数。其次，我们修正了量子Duffing振子的精确解，该振子是相干和参数驱动的，同时也经历了单光子和光子对的损失引起的退相干。我们利用这个解讨论了薛定谔猫态的稳定化和参量放大器中压缩态的产生，以及量子系统不同相位的Q函数。超导电路领域具有很强的非线性和耦合性，提供了进入参数体系的途径，其中返回到这些精确的量子光学方法可以提供有价值的见解。
We study exact solutions of the steady-state behavior of several nonlinear open quantum systems which can be applied to the field of circuit quantum electrodynamics. Using Fokker-Planck equations in the generalized P representation, we investigate the analytical solutions of two fundamental models. First, we solve for the steady-state response of a linear cavity that is coupled to an approximate transmon qubit and use this solution to study both the weak and strong driving regimes, using analytical expressions for the moments of both cavity and transmon fields, along with the Husimi Q function for the transmon. Second, we revist exact solutions of a quantum Duffing oscillator, which is driven both coherently and parametrically while also experiencing decoherence by the loss of single photons and pairs of photons. We use this solution to discuss both stabilization of Schrodinger cat states and the generation of squeezed states in parametric amplifiers, in addition to studying the Q functions of the different phases of the quantum system. The field of superconducting circuits, with its strong nonlinearities and couplings, has provided access to parameter regimes in which returning to these exact quantum optics methods can provide valuable insights.