1.Institute for Interdisciplinary Quantum Information Technology, Jilin Engineering Normal University, Changchun 130052, China 2.Jilin Engineering Laboratory for Quantum Information Technology, Changchun 130052, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 11347013), the Scientific Research Foundation of the Education Department of Jilin Province, China (Grant No. JJKH20190764KJ), the Specialized Fund for the Doctoral Research of Jilin Engineering Normal University, China (Grant No. BSKJ201825), and the General Program of of Jilin Engineering Normal University, China (Grant No. XYB201820).
Received Date:27 January 2019
Accepted Date:04 April 2019
Available Online:01 June 2019
Published Online:20 June 2019
Abstract:In this paper, we present a scheme to realize an unconventional photon blockade effect in a Fabry-Perot cavity and optical parametric amplifier (OPA) composite system. The system includes a tunable phase of complex driving strength, the second-order correlation function is used to describe the photon statistical properties. The numerical simulation of the photon blockade effect is conducted with different parameters. Our calculations show that the unconventional photon blockade effect can be controlled by the tunable phase of complex driving strength. Under the weak driving condition, the exact optimal conditions for strong photon anti-bunching are analytically derived (i.e. the optimal nonlinear gain of optical parametric amplifier and the phase of the field driving for the strong photon anti-bunching are obtained), and obtain the analytic calculations of the second-order correlation function. Under the optimal conditions, we perform a numerical simulation with different parameters. The optimal conditions for strong photon anti-bunching are found by analytic calculations, which are in good agreement with the numerical results. The results provide a platform for coherently operating the photon blockade and have potential applications in quantum information processing and quantum optical devices. Keywords:unconventional photon blockade/ Fabry-Perot cavity/ second-order correlation functions
其中${\varDelta _a} = {\omega _a} - {\omega _{\rm{l}}}$表示腔的失谐量. 在下面的研究中, 主要探索相位$\phi $对光子阻塞的影响. 图 1 (a) 用激光抽运OPA, 在腔内产生参量放大的腔结构示意图; (b) 量子干涉系统的跃迁路径 Figure1. (a) Schematic diagram of the cavity setup with an OPA which is pumped by a laser to produce parametric amplification in the cavity; (b) transition paths of the system for quantum interference.
3.数值结果本文所有计算结果都是基于弱驱动条件, 令${\varOmega / {\kappa = 0.01}}$, 数值模拟结果如图2和图3所示. 为方便起见, 将耗散率$\kappa $归一化. 在图2中, 展示了关联函数数值计算结果随相位$\phi $和$G$的变化, 结果表明对于不同的$G$存在光子反聚束效应. 相位$\phi $分别取0.5, 0.8和1.2 rad, 数值结果表明$\phi = 0.5\;{\rm{rad}}$时对应优化的强反聚束效应. 为了得到对应反聚束效应的优化参数, 图3展示了$\lg \left[ {{g^{\left(2\right)}}\left(0\right)} \right]$随OPA非线性增益$G$和相位$\theta $的等高线图, 其他参数为$\phi = 0.5\;{\rm{rad}}$, ${\varDelta _a} = 1$. 由图3可见, 在一小区域内${g^{\left(2\right)}}(0)\ll 1$, 这区域内选定参数可实现强的反聚束效应. 图 3 等时二阶关联函数$\lg \left[ {{g^{\left(2\right)}}\left(0\right)} \right]$数值结果随OPA非线性增益G和相位$\theta $的等高线图${\varOmega / {\kappa = 0.01}}$, ${\varDelta _a} = 1$, $\phi = 0.5\;{\rm{rad}}$ Figure3. Contour plot of the second-order correlation functions $\lg \left[ {{g^{\left(2\right)}}\left(0\right)} \right]$ vs. the nonlinear gain G of the OPA and phase $\theta $. Other parameters are ${\varOmega / {\kappa = 0.01}}$, ${\varDelta _a} = 1$, $\phi = 0.5\;{\rm{rad}}$.
图 2 等时二阶关联函数${g^{\left(2\right)}}(0)$随OPA非线性增益G的变化${\varOmega / {\kappa = 0.01}}$, $\theta = - 0.0341{\text{π}}$, ${\varDelta _a} = 1$ Figure2. Variation curves of the zero-time-delay second-order correlation function ${g^{\left(2\right)}}(0)$ with the nonlinear gain G of the OPA. Other parameters are ${\varOmega / {\kappa = 0.01}}$, $\theta = - 0.0341{\text{π}}$, ${\varDelta _a} = 1$.