腔QED系统中的量子模拟以及量子控制
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摘要
光与物质之间的相互作用是量子光学的重要内容。近些年来量子信息得到了飞速的发展。利用量子光学手段实现量子信息过程是很热门的话题。腔QED(cavity quantum electrodynamics)研究腔中的物质与腔场作用的动力学,是非常有前景的量子器件。人们做了很多优秀的工作研究腔QED系统中的量子信息过程,这些工作对于腔QED系统的量子器件地位的确立起着非常重要的作用。本文研究了由多个腔QED系统耦合组成的耦合腔列模型以及由腔QED系统与波导管耦合组成的模型,旨在为量子信息服务。本论文主要分为七章,从第三章开始介绍我们的工作,具体内容的安排如下：
第一章首先介绍了量子信息和量子光学之间的关系以及腔QED的发展。然后对耦合腔列中自旋链的模型的意义以及研究现状做了介绍,也对腔QED与波导管耦合系统做了简单介绍。最后给出了本论文的研究内容和结构安排。
第二章中给出了本论文中需要用到的理论知识。首先介绍了电磁场是如何量子化的,接下来给出了光场与物质相互作用的量子理论。然后对绝热消除法、缀饰态理论、信息熵度量纠缠以及光子之间的相干做了介绍。
第三章研究了如何在耦合腔列中实现自旋为1的海森堡模型。我们考虑由N个全同腔组成的耦合腔列系统,其中每个腔包含一个五能级原子。结果显示,在一定条件下通过相邻腔之间交换虚光子,我们模型可以有效地等价为自旋为1的海森堡模型。可以通过调节外加激光场来控制有效哈密顿量中的参量。
第四章中我们利用耦合腔列的模型模拟了各向异性的XYZ自旋链。在我们的模型中每个腔中有一个五能级原子。有效各向异性自旋链哈密顿量中的各向异性参量可以通过控制外加激光场来调节。我们通过数值模拟的方法验证了在计算过程中所取的近似的有效性,最后对系统的退相干进行了讨论,发现我们的系统是可以克服退相干效应的。
第五章我们利用polariton理论研究了V型原子系综与场相互作用的系统。polariton方法在强耦合机制下的腔QED系统中是一个非常有效的方法。我们分析了连续场跟物质相互作用情况下的polariton(?)理论。利用polariton理论研究了系统中双模光子之间的转换效率和纠缠。我们研究了光场与原子能级之间的失谐量对频率上转换的影响。结果显示当入射光子与原子非共振时,调节探测场的频率同样可以得到很大的转换效率。另外我们还分析了原子能级的自发辐射对双模光子之间转换效率的影响。
第六章中我们研究了非线性腔系统与波导管耦合的模型中光子的传输。波导管中光子的传播可以通过操作非线性腔系统中的原子来控制。我们利用polariton理论进行分析。在单光子情况下,我们的模型等价为一个波导管与一个二能级系统耦合。通过解薛定谔方程,我们发现可以通过控制外加经典场的拉比频率来实现光子的开关。在双光子情况下,系统等价为波导管与一个级联三能级系统耦合,光子的二阶相干度可以通过调节经典场的拉比频率来控制。
第七章中我们研究了腔QED系统与波导管耦合模型中的双光子传输问题。腔QED系统由一个线性腔以及腔中的四能级原子组成。我们在缀饰态表象下进行分析,发现原子和腔组成的系统会导致非线性效应。可以通过调节外加经典场的拉比频率来控制关联光子对的透射和反射。
最后,我们给出了总结和展望。
The interaction between light and matter is an important element of quantum optics. Quantum information has rapidly developed in recent years. The realization of quantum information processing taking advantage of the tool of quantum optics is a very hot topic. Cavity QED (cavity quantum electrodynamics) is the study of the interaction between cavity field and material in the cavity. People has done a large mount of excellent work studying cavity QED system in quantum information processing, these work plays an important role on establishing the status of the cavity QED system as Quantum Devices. This paper studies the coupled cavities composed of cavity QED system, as well as the cavity QED system coupled with waveguide, for the purpose of serving for the quantum information processing. This paper is divided into seven chapters, with our work included in the chapters from chapter3to chapter7. The structure of this paper is organized as follows:
In chapter1, We introduce relationship between quantum information and quantum optics and the development of cavity QED, then give the significance of the study of the spin chain model in the coupled cavities. We also give a brief introduction of the Cavity QED system coupled with the waveguide. Finally, we give the structure of this paper.
The second chapter gives the theoretical knowledge which will be needed in this paper. We introduced the quantization of electromagnetic field, the theory of the interaction between the matter and field. Then we briefly introduce adiabatic elimination method theory, dressed states theory, information entropy and entanglement measurement and the theory of photon coherent.
In chapter3, a coupled array of N identical cavities, each of which contains a five-level atom, is investigated. The results show that the atoms, via the exchange of virtual photons, can be effectively equal to a spin-1Heisenberg model under certain conditions. By tuning the laser fields, the parameters of the effective Hamiltonian can be controlled.
In chapter4, we simulated anisotropic XYZ-spin chain with an array of coupled cavities, each of which contains one four-level atom. The anisotropic parameters of the effective Hamilton can be tuned by controlling the external lasers. The validity of our approximations are confirmed via a numerical simulation. The decoherence can be neglected under current experimental condition. Finally, the conclusions and discussion are given.
In chapter5. We introduce the polaritom theory, which is a effective method for the realization of cavity QED system when the cavity QED system works in strong coupled regime. We investigate frequency conversion and entanglement via polariton technique. We analyze the effect of detuning on the efficiency of frequency conversion (EFC). The results show that by adjusting the second mode frequency, the EFC still can be achieved perfectly when the incoming photon is off-resonant. The effect of the spontaneous emission of the atoms on EFC is included.
In chapter6, we study the system consisting of a one-dimension waveguide side-coupled with a nonlinear cavity with a lambda-type atom and investigate the controlling of photons transport in one-dimension waveguide through manipulating the atom contained in the cavity. Employing the polariton technique, we show that in the single-photon case, the system can behave as a waveguide coupled to a two-level system. By solving the Schrodinger equation, we show that single photon switch by tuning the Rabi frequency of the classical field. In the two-photon case, the system can behaves like a waveguide coupled to a cascade three-level system. Two-photon quantum correlation in the position variation can be controlled by adjusting the Rabi frequency.
In chapter7, we investigate the two-photon transport properties inside one-dimensional waveguide side-coupled to a cavity. The cavity is doped with a four level atom. By employing dressed state basis, we show that the atom-cavity molecule produces a nonlinear interaction. The bunching and antibunching of the transmitted and reflected photons can be observed due to the nonlinearity. By tuning the Rabi frequency of the classical field. the transmission and reflection of the correlated photons can be controlled.
第一章首先介绍了量子信息和量子光学之间的关系以及腔QED的发展。然后对耦合腔列中自旋链的模型的意义以及研究现状做了介绍,也对腔QED与波导管耦合系统做了简单介绍。最后给出了本论文的研究内容和结构安排。
第二章中给出了本论文中需要用到的理论知识。首先介绍了电磁场是如何量子化的,接下来给出了光场与物质相互作用的量子理论。然后对绝热消除法、缀饰态理论、信息熵度量纠缠以及光子之间的相干做了介绍。
第三章研究了如何在耦合腔列中实现自旋为1的海森堡模型。我们考虑由N个全同腔组成的耦合腔列系统,其中每个腔包含一个五能级原子。结果显示,在一定条件下通过相邻腔之间交换虚光子,我们模型可以有效地等价为自旋为1的海森堡模型。可以通过调节外加激光场来控制有效哈密顿量中的参量。
第四章中我们利用耦合腔列的模型模拟了各向异性的XYZ自旋链。在我们的模型中每个腔中有一个五能级原子。有效各向异性自旋链哈密顿量中的各向异性参量可以通过控制外加激光场来调节。我们通过数值模拟的方法验证了在计算过程中所取的近似的有效性,最后对系统的退相干进行了讨论,发现我们的系统是可以克服退相干效应的。
第五章我们利用polariton理论研究了V型原子系综与场相互作用的系统。polariton方法在强耦合机制下的腔QED系统中是一个非常有效的方法。我们分析了连续场跟物质相互作用情况下的polariton(?)理论。利用polariton理论研究了系统中双模光子之间的转换效率和纠缠。我们研究了光场与原子能级之间的失谐量对频率上转换的影响。结果显示当入射光子与原子非共振时,调节探测场的频率同样可以得到很大的转换效率。另外我们还分析了原子能级的自发辐射对双模光子之间转换效率的影响。
第六章中我们研究了非线性腔系统与波导管耦合的模型中光子的传输。波导管中光子的传播可以通过操作非线性腔系统中的原子来控制。我们利用polariton理论进行分析。在单光子情况下,我们的模型等价为一个波导管与一个二能级系统耦合。通过解薛定谔方程,我们发现可以通过控制外加经典场的拉比频率来实现光子的开关。在双光子情况下,系统等价为波导管与一个级联三能级系统耦合,光子的二阶相干度可以通过调节经典场的拉比频率来控制。
第七章中我们研究了腔QED系统与波导管耦合模型中的双光子传输问题。腔QED系统由一个线性腔以及腔中的四能级原子组成。我们在缀饰态表象下进行分析,发现原子和腔组成的系统会导致非线性效应。可以通过调节外加经典场的拉比频率来控制关联光子对的透射和反射。
最后,我们给出了总结和展望。
The interaction between light and matter is an important element of quantum optics. Quantum information has rapidly developed in recent years. The realization of quantum information processing taking advantage of the tool of quantum optics is a very hot topic. Cavity QED (cavity quantum electrodynamics) is the study of the interaction between cavity field and material in the cavity. People has done a large mount of excellent work studying cavity QED system in quantum information processing, these work plays an important role on establishing the status of the cavity QED system as Quantum Devices. This paper studies the coupled cavities composed of cavity QED system, as well as the cavity QED system coupled with waveguide, for the purpose of serving for the quantum information processing. This paper is divided into seven chapters, with our work included in the chapters from chapter3to chapter7. The structure of this paper is organized as follows:
In chapter1, We introduce relationship between quantum information and quantum optics and the development of cavity QED, then give the significance of the study of the spin chain model in the coupled cavities. We also give a brief introduction of the Cavity QED system coupled with the waveguide. Finally, we give the structure of this paper.
The second chapter gives the theoretical knowledge which will be needed in this paper. We introduced the quantization of electromagnetic field, the theory of the interaction between the matter and field. Then we briefly introduce adiabatic elimination method theory, dressed states theory, information entropy and entanglement measurement and the theory of photon coherent.
In chapter3, a coupled array of N identical cavities, each of which contains a five-level atom, is investigated. The results show that the atoms, via the exchange of virtual photons, can be effectively equal to a spin-1Heisenberg model under certain conditions. By tuning the laser fields, the parameters of the effective Hamiltonian can be controlled.
In chapter4, we simulated anisotropic XYZ-spin chain with an array of coupled cavities, each of which contains one four-level atom. The anisotropic parameters of the effective Hamilton can be tuned by controlling the external lasers. The validity of our approximations are confirmed via a numerical simulation. The decoherence can be neglected under current experimental condition. Finally, the conclusions and discussion are given.
In chapter5. We introduce the polaritom theory, which is a effective method for the realization of cavity QED system when the cavity QED system works in strong coupled regime. We investigate frequency conversion and entanglement via polariton technique. We analyze the effect of detuning on the efficiency of frequency conversion (EFC). The results show that by adjusting the second mode frequency, the EFC still can be achieved perfectly when the incoming photon is off-resonant. The effect of the spontaneous emission of the atoms on EFC is included.
In chapter6, we study the system consisting of a one-dimension waveguide side-coupled with a nonlinear cavity with a lambda-type atom and investigate the controlling of photons transport in one-dimension waveguide through manipulating the atom contained in the cavity. Employing the polariton technique, we show that in the single-photon case, the system can behave as a waveguide coupled to a two-level system. By solving the Schrodinger equation, we show that single photon switch by tuning the Rabi frequency of the classical field. In the two-photon case, the system can behaves like a waveguide coupled to a cascade three-level system. Two-photon quantum correlation in the position variation can be controlled by adjusting the Rabi frequency.
In chapter7, we investigate the two-photon transport properties inside one-dimensional waveguide side-coupled to a cavity. The cavity is doped with a four level atom. By employing dressed state basis, we show that the atom-cavity molecule produces a nonlinear interaction. The bunching and antibunching of the transmitted and reflected photons can be observed due to the nonlinearity. By tuning the Rabi frequency of the classical field. the transmission and reflection of the correlated photons can be controlled.
引文
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