多模电磁诱导透明理论及其应用研究
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摘要
最近十几年里,电磁诱导透明(electromagnetically induced transparency,简称EIT)及其应用的研究成为了理论物理、实验物理以及基础应用物理中的重要课题。EIT是一项具有重大意义和实用价值的技术,它可以通过相消干涉使得介质对共振探测光的吸收和色散特性发生显著变化,从而可以实现无吸收的大色散。目前,EIT在光速减慢、量子存储、四波混频、电磁诱导光栅、原子激光、光学双稳、光学开关、超慢光孤子、法拉第旋转、光学频率转换、光学诱导波导、光学诱导规范势、稳态脉冲、量子相位门、量子纠缠、原子分子凝聚、高精度光钟、量子成像、甚至天文学等领域都有着广泛的应用。本文主要研究了多模EIT的理论机制及其应用。其中,我们具体研究了多模EIT介质中慢光的传播、光子之间的交叉相位调制、光子-光子非线性相互作用及其在量子计算和量子信息中的应用。本论文可以分为五部分:
第一部分包括第一章和第二章。为了论文的完整性和系统性,论文的第一章介绍EIT的发展历史以及研究现状。第二章介绍了EIT的一些基本理论,包括暗态的基本性质以及基于单原子图像和基于原子系综集体激发图像的EIT处理方法。
第二部分为论文的第三章。主要研究了双模EIT原子介质中线性极化的量子探测光场在非均匀场中的史特恩-盖拉赫效应。推导了准粒子暗态极化子的有效薛定谔方程,然后分别利用基于准粒子的粒子性和基于光脉冲的波动性的处理方法研究了非均匀磁场和非均匀驱动场中慢光的史特恩-盖拉赫效应。
第三部分包括第四章和第五章。第四章中,我们提出了一个基于八能级原子的三模EIT(TEIT)理论模型,利用哈密顿量方法研究了TEIT系统中三束弱探测光的传播,计算了宏观极化率以及三束弱探测光的群速度。分析表明可以在很短的相互作用距离内实现三束弱探测光之间π量级的交叉相移,并且通过调节三束强驱动光场的拉比频率,可以匹配三束探测光的群速度。第五章主要研究了TEIT系统中的光子-光子相互作用以及在量子计算中的应用。我们获得了光子之间的三模交叉克尔型相互作用,并且发现利用光子的三模交叉克尔型相互作用可以直接实现全光的Toffoli门。
第四部分是论文的第六章。我们提出了自由行波光场的W型纠缠相干态的光学制备方案,包括基于两模交叉克尔介质的四模W型纠缠相干态的制备和基于三模交叉克尔介质的三模杂化W型纠缠相干态的制备。在理想情况下,我们的制备方案的成功几率可以达到1。
最后一部分为论文的第七章,是对本文工作的总结和展望。
In the last ten years, much attention has been paid to understandings and applications of systems exhibiting electromagnetically induced transparency (EIT). The EIT method is a powerful technique with significance and practicability that can make the dispersive and absorptive properties of optical medium modified dramatically, i.e., make the medium having large dispersion without the resonant absorption by means of destructive interference. Recently, EIT has been applied extensively in slow light, quantum memory, four-wave mixing, electromagnetically induced grating, atom laser, optical bistability, optical switching, ultraslow optical solitons, Faraday rotation, optical frequency conversion, stationary pulses, quantum phase gate, atom-molecule dark state, high-accuracy optical clock, quantum imaging, and even astronomy. In this thesis, we study the theory of multi-mode EIT and its applications, including the propagation of slow light pulses, cross-phase modulation of photons, the photon-photon nonlinear interaction and its applications in quantum computation and quantum information. This thesis is divided into five parts:
The first part includes chapter 1 and chapter 2. In chapter 1, the background and the main research results of EIT are introduced. In the chapter2, we introduce the basic theory of EIT, including the characters of the dark state and the theoretical methods given to deal with the EIT system based on single-atom and collective atomic excitation of atomic ensemble.
The second part includes chapter 3. Here we study the generalized Stern-Gerlach effect of the quantized linear-polarized light in a magneto-optically manipulated atomic ensemble. We derive an effective Shr(o|¨)dinger equation for the spatial motion of two dark-state polaritions (DSPs), which behave as a quasi-particle with an effective magnetic moment. We investigate the Stern- Gerlach effect of light in an nonuniform magnetic field and an inhomogeneous coupling field, respectively, via the methods based on the particle feature of the DSPs and the wave feature of light pulses.
The third part includes chapter 4 and chapter 5. In chapter 4, we propose a scheme to generate triple EIT (TEIT) where EIT is induced imultaneously for three weak slow light pulses. We calculate the complex polarizibilities and group velocities of the three slow light pulses in the weak field limit by means of the full Hamiltonian approach. It is shown that strong cross-phase modulation can be realized and large cross-phase shifts on the order ofπcan be generated for three slow weak pulses in very short interaction distance. It is indicated that the three slow weak pulses can reach matching of group velocities through adjusting the Rabi frequency of the control fields. In chapter 5, we study the photon-photon interaction in the TEIT system and its applications in quantum computation. We find that we can obtain a three-mode cross-Kerr-like interation of photons in the TEIT system and we can implement an all-optical Toffoli gate directly via the three-mode cross-Kerr-like interaction.
The fourth part includes chapter 6. We propose optical schemes to generate W-type entangled coherent states in free travelling optical fields, including the generation of four-mode W-type entangled coherent states based on two-mode cross-Kerr media and the generation of three-mode hybrid W-type entangled coherent states based on three-mode cross-Kerr media. In the ideal conditions, the success probabilities of our schemes are unity.
A summary of the work and an outlook of this thesis are given in the last part.
第一部分包括第一章和第二章。为了论文的完整性和系统性,论文的第一章介绍EIT的发展历史以及研究现状。第二章介绍了EIT的一些基本理论,包括暗态的基本性质以及基于单原子图像和基于原子系综集体激发图像的EIT处理方法。
第二部分为论文的第三章。主要研究了双模EIT原子介质中线性极化的量子探测光场在非均匀场中的史特恩-盖拉赫效应。推导了准粒子暗态极化子的有效薛定谔方程,然后分别利用基于准粒子的粒子性和基于光脉冲的波动性的处理方法研究了非均匀磁场和非均匀驱动场中慢光的史特恩-盖拉赫效应。
第三部分包括第四章和第五章。第四章中,我们提出了一个基于八能级原子的三模EIT(TEIT)理论模型,利用哈密顿量方法研究了TEIT系统中三束弱探测光的传播,计算了宏观极化率以及三束弱探测光的群速度。分析表明可以在很短的相互作用距离内实现三束弱探测光之间π量级的交叉相移,并且通过调节三束强驱动光场的拉比频率,可以匹配三束探测光的群速度。第五章主要研究了TEIT系统中的光子-光子相互作用以及在量子计算中的应用。我们获得了光子之间的三模交叉克尔型相互作用,并且发现利用光子的三模交叉克尔型相互作用可以直接实现全光的Toffoli门。
第四部分是论文的第六章。我们提出了自由行波光场的W型纠缠相干态的光学制备方案,包括基于两模交叉克尔介质的四模W型纠缠相干态的制备和基于三模交叉克尔介质的三模杂化W型纠缠相干态的制备。在理想情况下,我们的制备方案的成功几率可以达到1。
最后一部分为论文的第七章,是对本文工作的总结和展望。
In the last ten years, much attention has been paid to understandings and applications of systems exhibiting electromagnetically induced transparency (EIT). The EIT method is a powerful technique with significance and practicability that can make the dispersive and absorptive properties of optical medium modified dramatically, i.e., make the medium having large dispersion without the resonant absorption by means of destructive interference. Recently, EIT has been applied extensively in slow light, quantum memory, four-wave mixing, electromagnetically induced grating, atom laser, optical bistability, optical switching, ultraslow optical solitons, Faraday rotation, optical frequency conversion, stationary pulses, quantum phase gate, atom-molecule dark state, high-accuracy optical clock, quantum imaging, and even astronomy. In this thesis, we study the theory of multi-mode EIT and its applications, including the propagation of slow light pulses, cross-phase modulation of photons, the photon-photon nonlinear interaction and its applications in quantum computation and quantum information. This thesis is divided into five parts:
The first part includes chapter 1 and chapter 2. In chapter 1, the background and the main research results of EIT are introduced. In the chapter2, we introduce the basic theory of EIT, including the characters of the dark state and the theoretical methods given to deal with the EIT system based on single-atom and collective atomic excitation of atomic ensemble.
The second part includes chapter 3. Here we study the generalized Stern-Gerlach effect of the quantized linear-polarized light in a magneto-optically manipulated atomic ensemble. We derive an effective Shr(o|¨)dinger equation for the spatial motion of two dark-state polaritions (DSPs), which behave as a quasi-particle with an effective magnetic moment. We investigate the Stern- Gerlach effect of light in an nonuniform magnetic field and an inhomogeneous coupling field, respectively, via the methods based on the particle feature of the DSPs and the wave feature of light pulses.
The third part includes chapter 4 and chapter 5. In chapter 4, we propose a scheme to generate triple EIT (TEIT) where EIT is induced imultaneously for three weak slow light pulses. We calculate the complex polarizibilities and group velocities of the three slow light pulses in the weak field limit by means of the full Hamiltonian approach. It is shown that strong cross-phase modulation can be realized and large cross-phase shifts on the order ofπcan be generated for three slow weak pulses in very short interaction distance. It is indicated that the three slow weak pulses can reach matching of group velocities through adjusting the Rabi frequency of the control fields. In chapter 5, we study the photon-photon interaction in the TEIT system and its applications in quantum computation. We find that we can obtain a three-mode cross-Kerr-like interation of photons in the TEIT system and we can implement an all-optical Toffoli gate directly via the three-mode cross-Kerr-like interaction.
The fourth part includes chapter 6. We propose optical schemes to generate W-type entangled coherent states in free travelling optical fields, including the generation of four-mode W-type entangled coherent states based on two-mode cross-Kerr media and the generation of three-mode hybrid W-type entangled coherent states based on three-mode cross-Kerr media. In the ideal conditions, the success probabilities of our schemes are unity.
A summary of the work and an outlook of this thesis are given in the last part.
引文
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