腔光机械系统中电磁诱导透明及其相关现象的理论研究
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摘要
由于在精密测量和高灵敏传感器方面具有重要的应用前景，近十几年来人们对各种腔光机械系统展开了广泛的研究，比如Casimir力的测量、冷却机械振子到其量子基态、实现机械振子与腔场的强耦合控制等。此外，由于机械元件的尺度和质量均分布在从纳米到微观再到宏观的过渡范围内，因此这种系统也可以用来验证和调控宏观物体的量子性质，从而加深人们对量子力学基本规律的理解和应用，如制备机械振子的压缩态和宏观量子叠加态、实现机械元件与腔场之间的纠缠等。在本论文中我们主要研究腔光机械系统中的部分非线性量子光学效应，特别是与电磁诱导透明有关的现象。其实现途径主要是通过各种不同跃迁通道之间的干涉来得到显著的共振增强的非线性效应。主要的工作包括以下几个方面：
一、我们通过概率幅方程和Heisenberg-Langevin方程以及微扰法等介绍和总结了Λ型三能级原子介质、线性耦合薄膜腔光机械系统和平方耦合薄膜腔光机械系统三种媒介中的电磁诱导透明效应，并从缀饰态理论、暗态理论和反斯托克斯散射等方面对这些系统中的电磁诱导透明现象进行了物理解释。此外，我们还对这三种电磁诱导透明现象进行了比较分析，在发生条件、物理机制和图形特征三个方面总结了它们之间的异同之处。
二、我们在大原子数极限和原子能级低激发的条件下探索了二能级原子系综对平方耦合薄膜腔光机械系统中电磁诱导透明现象的影响。通过求解系统Heisenberg-Langevin方程的稳态解和输入输出关系得出探测场的透射系数。再通过解析方法找到影响电磁诱导透明现象的四个参量的变化趋势。最后由数值结果确认其中起主导作用的参量从而发现原子介质对系统电磁诱导透明现象的主要影响。
三、我们从理论上研究了在平方耦合薄膜腔光机械系统中通过电磁诱导透明来实现慢光现象。我们计算了由系统电磁诱导透明效应中的相位色散导致的探测脉冲的透射群延迟。并通过解析分析和数值模拟得出通过平方光机械耦合产生的慢光与线性耦合情况有很大差别，其潜在的物理过程涉及到双声子过程。我们还证明了该系统中的声子能量几乎全部来自于由环境温度引起的薄膜的热振动，且耦合场功率和环境温度构成了系统非线性相干的两个必不可少的元素。因此在平方耦合腔光机械系统中慢光不仅能通过耦合场功率来调节，而且也能够被环境温度所控制。且慢光能够在一个非常广泛的参数范围内来实现，甚至在高温下，例如200K。
总之，本论文的研究加深了对宏观物体的量子属性的认识，有助于进一步了解混合系统中的各种非线性量子光学效应。这些研究对量子光学、非线性光学和精密测量等方面的研究和应用具有一定的参考价值。
In the past decades, lots of researches based on cavity optomechanical sys-tems have arisen due to their important applications on precision measurement andhigh-precision sensors, for example, Casimir force measurement, cooling mechan-ical resonators to their ground state of motion, strong coupling regime betweenmechanical resonators and cavity fields and so on. Besides, because the sizes andmass of mechanical elements are in transition range from nanometer to micro-scope even macro-scope, cavity optomechanical systems have also been exploit-ed as a tool to test and control quantum properties of macroscopic objects, andpromote the understanding of fundamental principle of quantum mechanics, e.g.,preparing mechanical squeezed states and macroscopic superposition states, creat-ing optomechanical entanglement between mechanical resonators and cavity fieldsand so on. In this thesis, we mainly study some quantum nonlinear effects in cavityoptomechanical systems, especially electromagnetically induced transparency andrelated phenomena. These phenomena can be realized by prominently enhancedresonant nonlinearity from quantum interference between different transition path-s. The main content is as follows:
1. We introduce and summarize three different effects of electromagneticallyinduced transparency in Λ-type atomic media, linearly coupled cavity optomechan-ical systems and quadratically coupled cavity optomechanical systems via someanalytical methods such as probability amplitude equations, Heisenberg-Langevinequations and tiny-disturbance method, etc. We also make corresponding physicalinterpretation for these three effects in dressed state theory, dark state theory andanti-Stokes scattering. In addition, we do compare between them and find out thedifferences in initial conditions, physical reasons and graphical characteristics, etc.
2. We study the effect of a two-level atomic ensemble on electromagneticallyinduced transparency in a quadratically coupled optomechanical system under theconditions of large atom-number limit and low-excitation case. We firstly acquireprobe-field transmission by solving system’s Heisenberg-Langevin equations insteady-state case and input-output relation. Then we find variation tendency offour parameters relative to electromagnetically induced transparency by analyticalexpression with an atomic medium being, and find out the dominant parameter vianumerical methods, and consequently we discover main effects of atomic mediaon electromagnetically induced transparency in this system.
3. We theoretically investigate the slow-light phenomenon in a quadraticallycoupled cavity optomechanical system. We work out transmission group delay ofprobe field which is generated due to rapid phase dispersion induced by electro-magnetically induced transparency effect. By analysis and numerical examinationwe find the slow light via quadratic coupling has many differences from linear cou-pling cases, and its underlying physical process involves a two-phonon process.We also prove that in quadratically coupled optomechanical systems, almost allphonon energy are from membrane’s oscillation caused by environment tempera-ture, and environment temperature and coupling field power are two indispensableelements in nonlinear coherence. So the slow light can also be tuned by environ-ment temperature besides coupling field power in this system. In addition, the slowlight can be realized in an extensive range of parameters even at high temperature,e.g.,200K.
In summary, this thesis may be helpful to deepen understanding of quantumproperties of macroscopic objects and know some quantum nonlinear effects inhybrid systems. These studies also may be with some reference value for theresearches and applications of quantum optics, nonlinear optics and precision
一、我们通过概率幅方程和Heisenberg-Langevin方程以及微扰法等介绍和总结了Λ型三能级原子介质、线性耦合薄膜腔光机械系统和平方耦合薄膜腔光机械系统三种媒介中的电磁诱导透明效应，并从缀饰态理论、暗态理论和反斯托克斯散射等方面对这些系统中的电磁诱导透明现象进行了物理解释。此外，我们还对这三种电磁诱导透明现象进行了比较分析，在发生条件、物理机制和图形特征三个方面总结了它们之间的异同之处。
二、我们在大原子数极限和原子能级低激发的条件下探索了二能级原子系综对平方耦合薄膜腔光机械系统中电磁诱导透明现象的影响。通过求解系统Heisenberg-Langevin方程的稳态解和输入输出关系得出探测场的透射系数。再通过解析方法找到影响电磁诱导透明现象的四个参量的变化趋势。最后由数值结果确认其中起主导作用的参量从而发现原子介质对系统电磁诱导透明现象的主要影响。
三、我们从理论上研究了在平方耦合薄膜腔光机械系统中通过电磁诱导透明来实现慢光现象。我们计算了由系统电磁诱导透明效应中的相位色散导致的探测脉冲的透射群延迟。并通过解析分析和数值模拟得出通过平方光机械耦合产生的慢光与线性耦合情况有很大差别，其潜在的物理过程涉及到双声子过程。我们还证明了该系统中的声子能量几乎全部来自于由环境温度引起的薄膜的热振动，且耦合场功率和环境温度构成了系统非线性相干的两个必不可少的元素。因此在平方耦合腔光机械系统中慢光不仅能通过耦合场功率来调节，而且也能够被环境温度所控制。且慢光能够在一个非常广泛的参数范围内来实现，甚至在高温下，例如200K。
总之，本论文的研究加深了对宏观物体的量子属性的认识，有助于进一步了解混合系统中的各种非线性量子光学效应。这些研究对量子光学、非线性光学和精密测量等方面的研究和应用具有一定的参考价值。
In the past decades, lots of researches based on cavity optomechanical sys-tems have arisen due to their important applications on precision measurement andhigh-precision sensors, for example, Casimir force measurement, cooling mechan-ical resonators to their ground state of motion, strong coupling regime betweenmechanical resonators and cavity fields and so on. Besides, because the sizes andmass of mechanical elements are in transition range from nanometer to micro-scope even macro-scope, cavity optomechanical systems have also been exploit-ed as a tool to test and control quantum properties of macroscopic objects, andpromote the understanding of fundamental principle of quantum mechanics, e.g.,preparing mechanical squeezed states and macroscopic superposition states, creat-ing optomechanical entanglement between mechanical resonators and cavity fieldsand so on. In this thesis, we mainly study some quantum nonlinear effects in cavityoptomechanical systems, especially electromagnetically induced transparency andrelated phenomena. These phenomena can be realized by prominently enhancedresonant nonlinearity from quantum interference between different transition path-s. The main content is as follows:
1. We introduce and summarize three different effects of electromagneticallyinduced transparency in Λ-type atomic media, linearly coupled cavity optomechan-ical systems and quadratically coupled cavity optomechanical systems via someanalytical methods such as probability amplitude equations, Heisenberg-Langevinequations and tiny-disturbance method, etc. We also make corresponding physicalinterpretation for these three effects in dressed state theory, dark state theory andanti-Stokes scattering. In addition, we do compare between them and find out thedifferences in initial conditions, physical reasons and graphical characteristics, etc.
2. We study the effect of a two-level atomic ensemble on electromagneticallyinduced transparency in a quadratically coupled optomechanical system under theconditions of large atom-number limit and low-excitation case. We firstly acquireprobe-field transmission by solving system’s Heisenberg-Langevin equations insteady-state case and input-output relation. Then we find variation tendency offour parameters relative to electromagnetically induced transparency by analyticalexpression with an atomic medium being, and find out the dominant parameter vianumerical methods, and consequently we discover main effects of atomic mediaon electromagnetically induced transparency in this system.
3. We theoretically investigate the slow-light phenomenon in a quadraticallycoupled cavity optomechanical system. We work out transmission group delay ofprobe field which is generated due to rapid phase dispersion induced by electro-magnetically induced transparency effect. By analysis and numerical examinationwe find the slow light via quadratic coupling has many differences from linear cou-pling cases, and its underlying physical process involves a two-phonon process.We also prove that in quadratically coupled optomechanical systems, almost allphonon energy are from membrane’s oscillation caused by environment tempera-ture, and environment temperature and coupling field power are two indispensableelements in nonlinear coherence. So the slow light can also be tuned by environ-ment temperature besides coupling field power in this system. In addition, the slowlight can be realized in an extensive range of parameters even at high temperature,e.g.,200K.
In summary, this thesis may be helpful to deepen understanding of quantumproperties of macroscopic objects and know some quantum nonlinear effects inhybrid systems. These studies also may be with some reference value for theresearches and applications of quantum optics, nonlinear optics and precision
引文
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