1.College of Electronic Science, Northeast Petroleum University, Daqing 163318, China 2.College of Automation, Harbin Engineering University, Harbin 150001, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 41472126, 11804066), the China Postdoctoral Science Foundation (Grant No. 2018M630337), the Fundamental Research Fund for the Central Universities, China (Grant No. 3072019CFM0405), the Natural Science Foundation of Heilongjiang Province, China (Grant No. LH2019A005), and the Heilongjiang Postdoctoral Sustentation Fund, China (Grant No. LBH-Z18062).
Received Date:16 February 2019
Accepted Date:19 May 2019
Available Online:01 September 2019
Published Online:05 September 2019
Abstract:Radiation pressure in an optomechanical system can be used to generate various quantum phenomena. Recently, one paid more attention to the study of optical nonreciprocity in an optomechanical system, and nonreciprocal devices are indispensable for building quantum networks and ubiquitous in modern communication technology. Here in this work, we study how to realize the perfect optical nonreciprocity in a two-cavity optomechanical system with blue-detuned driving. Our calculations show that the optical nonreciprocity comes from the quantum interference of signal transmission between two possible paths corresponding to the two interactions in this system, i.e. optomechanical interaction and linearly-coupled interaction. According to the standard input-output relation of optical field in cavity optomechanics, we obtain the expression of output optical field, from which we can derive the essential conditions to achieve the perfect optical nonreciprocity, and find there are two sets of coupling strengths both of which can realize the perfect optical nonreciprocal transmission. Because the system is driven by blue-detuned driving, the system is stable only under some conditions which we can obtain according to the Routh-Hurwitz criterion. Due to the blue-detuned driving, there will be transmission gain (transmission amplitude is greater than 1) in the nonreciprocal transmission spectrum. We also find that the bandwidth of nonreciprocal transmission spectrum is in proportion to mechanical decay rate if mechanical decay rate is much less than the cavity decay rate. In other words, in a realistic optomechanical parameter regime, where mechanical decay rate is much less than cavity decay rate, the bandwidth of nonreciprocal transmission spectrum is very narrow. Our results can also be applied to other parametrically coupled three-mode bosonic systems and may be used to realize the state transfer process and optical nonreciprocal transmission in an optomechanical system. Keywords:cavity optomechanics/ optical nonreciprocity/ optical isolator
全文HTML
--> --> --> 1.引 言非互易光学器件在光源和接收器调换位置后可以使光信号表现出不同的传输特性. 由于其可以抑制多余的信号, 因此在量子信号处理和量子通信中有着重要的应用. 例如, 在量子超导电路中它们可以保护信号源不被读取器件发出的噪声干扰[1]. 为实现光学非互易性, 时间反演对称性破缺是必须的. 传统的非互易性光学器件都是依赖 强磁场去实现时间反演对称性破缺[2]. 然而由于需要较强磁场, 这些传统器件体积往往较大, 不便于微型化和集成化. 近年来由于纳米技术的进步, 使微纳系统中光学现象得到广泛研究[3-7]. 腔光力学系统中的光辐射压力可以使系统呈现出各种有趣的量子现象. 例如, 腔光力学系统中的量子纠缠[8-16], 力学振子的基态冷却[17-21], 光力诱导透明[22-26]以及非线性效应[26-33]和声子阻塞[34]等量子现象. 最近, 人们意识到光力耦合相互作用也可以产生光学非互易传输现象. 例如通过光力相互作用可以产生非互易光学反应在理论上被预言[35-37], 并在实验上得到证实[38-42]. 并在理论上指出如果采用适当的驱动场, 以力学模为中介的两个腔模之间的态转换可以是非互易的[43-45], 以及通过光力耦合相互作用可以实现信号非互易放大现象[46-48]. 在文献[49,50]中, 理论上给出了通过光力相互作用可以实现非互易光子阻塞效应, 以及在文献[51]中, 作者理论上指出通过光力相互作用可以实现非互易慢光. 另外, 在文献[52,53]中, 作者理论上预言了通过光力耦合可以实现声子环形器和热二极管. 然而在大部分文献当中人们常常采用红失谐的驱动场和$ \pm\dfrac{{\text{π}}}{2} $的非互易相位差去实现光学非互易性. 本文研究了在蓝失谐驱动下, 在双腔光力系统(如图1所示)中如何实现光场的非互易传输. 在此模型中, Li等[48]利用力学驱动机制实现了光的非互易放大, 并在红失谐驱动下, 利用$ \pm\dfrac{{\text{π}}}{2} $的非互易相位差去实现光学非互易性[43]. 实际上, 此系统中的光学非互易性源于光力耦合和腔模线性耦合的共同作用, 使从不同路径传输的光信号之间产生干涉效应. 本文根据此物理机理并由腔光力学中标准的光场输入输出关系, 得到了实现完美的非互易光传输条件. 研究发现, 在系统中各耗散速率一定的情况下, 会有两套耦合强度可以实现光学非互易传输, 并且即使在非互易相位差不为$ \pm\dfrac{{\text{π}}}{2} $时系统依然可以实现完美光学非互易性. 最后根据劳斯-霍尔维茨(Routh-Hurwitz)稳态判据给出了系统在蓝失谐驱动下的稳定条件. 这些研究结果有望能应用于在光力系统中实现光频隔离器、非互易态转换等量子信息处理过程. 图 1 双腔光力学系统示意图, 两光学腔通过光力相互作用与一个力学振子相耦合, 振幅为$\varepsilon_{\rm c}$和 $\varepsilon_{\rm d}$($\varepsilon_{\rm L}$和$\varepsilon_{\rm R}$)的强耦合场 (探测场)分别从左右两侧驱动腔模$c_{1}$和$c_{2}$, 同时两腔模之间存在线性耦合相互作用J Figure1. A two-cavity optomechanical system with a mechanical resonator interacted with two cavities. Two strong coupling fields (probe fields) with amplitudes $\varepsilon_{\rm c}$ and $\varepsilon_{\rm d}$ ($\varepsilon_{\rm L}$ and $\varepsilon _{\rm R}$) are used to drive cavity $c_{1}$ and $c_{2}$ respectively. Meanwhile, the two cavities are linearly coupled to each other with coupling strength J