光子系统的量子操纵与物理模拟
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摘要
量子信息的核心旨在巧妙地利用量子相干性(对多粒子系统表现为量子纠缠)对信息的新型载体-量子比特进行操纵控制,以非常规的方式进行信息的编码、存储和传递。量子信息处理技术本质上就是对量子态的操控技术。量子相干操纵的目标是在适当的物理系统中实现对其相干动力学的控制和操作。要实现相干操纵,最关键的问题是找到一个相干性好的物理系统。由于具有最快的传播速度,很强的稳定性及良好的抗环境干扰能力,光子系统早已成为实现量子信息处理的最理想和最热门的物理系统之一。为了利用光子系统来进行量子计算和量子信息的传输,对光子态的相干操作是必须的。本文的工作首先是利用原子来控制量子光在空间中的传输,这里的研究主要是从在大N和低激发条件下原子系综的激发可以简化为一个玻色子模式出发的。具体来说包括基于相干原子介质传播空间的相干操纵、单光子水平的量子操纵方案.随后讨论利用光学系统模拟量子信息处理。主要是利用光学被动光学元件,如分束器,极化分束器,波片等线性光学元件区分相互独立但却不正交的量子态,以及模拟二人囚徒困境量子博弈。本论文的结构分为五部分:
论文的第一章是绪论,作为整篇论文的铺垫,在这部分中我们介绍量子信息和量子计算的发展历史以及研究现状,并分别从理论和实验的角度重点阐述了光子系统量子性质研究的几个热点问题的研究现状。
第二部分为论文的第二章。基于慢光实验的进展,在这一章中,我们研究非均匀介质中光子态传播与空间控制问题。产生慢光有两种方法,一种基于原子相干振荡,它使用二能级原子系综与探测光和控制光相互作用,另一种方法是利用电磁诱导透明技术,它通常使用∧型三能级与探测光和控制光相互作用。我们首先对由相干布局数振荡所产生的慢光的空间传播问题进行讨论,我们使用了半经典处理,利用绝热近似分别得到了描述探测光的薛定谔方程和描述控制光空间运动的非线性薛定谔方程,并发现控制光在传播过程中形状、幅度和速度都可维持不变.然而控制光的空间分布将使得入射到介质中的探测光束在经过介质后发生偏转现象。随后我们对由电磁诱导透明所产生的慢光的空间传播问题进行讨论。现今实验发现:当探测光束通过处于非均匀磁场中的人型三能级原子介质时,由于磁场依赖于空间位置的变化,探测光束将发生偏转。针对这一现象,并考虑到电磁诱导透明现象在微观上是由于光子和原子集体激发形成了一种激子极化子——暗态极化子,我们使用平均场理论得到了描述暗态空间运动的有效薛定谔方程。随后我们采用特定的波包描述了这种准粒子,从波动的角度考虑了横向分布为二次型或线性的磁场中暗态极化子的运动。我们的处理方法反映了准粒子的波粒二象性。研究也表明,暗态极化子具有有效磁矩。
第三章中,我们将利用原子系综与光的相互作用来操作光子以及将光子限制在高品质因子的共振腔阵列中这两种操纵光子的方法相结合,并使用一维的离散坐标量子散射理论进行计算。我们发现由于原子系综的嵌入破坏了耦合腔阵列的平移不变性,使得入射到腔阵列中的光子会被囚禁在嵌入原子系综的腔附近,而不会在阵列中游走。另一方面,对于在阵列中游走的光子,原子与腔场的强耦合改变了阵列中特定腔场的能级分布,从而使得光子共振遂穿几率发生了改变,因此我们可以通过调节原子的跃迁频率来控制光子的传输。从而在理论上提出了一种实现量子网络中不同网络之间连接的方法。
在论文的第四章主要是利用光学系统模拟量子信息处理,这里我们利用了光子的两个自由度,光子空间路径是一个自由度,另一个自由度是光子的极化。首先,对于相互独立但却不正交的量子态,我们提出在直积空间利用偏振分束器、波片、偏振片和单光子探测器来实现它们的最佳无错鉴别。在模拟二人囚徒困境量子博弈方面,量子博弈中所需的两个量子比特分别由光子的两条路径和光子的两个极化方向提供。我们利用分束器和相移器实现其中一个参与人的量子对策,另一参与人的量子对策通过1/4波片和半波片的组合实现,使参与人拥有了实施操纵的物理仪器。
最后一部分为论文的第五章,是对本文工作的总结和展望。
The use of quantum physics has revolutionized the way we communicate and process information.Quantum coherence and decoherence are at the heart of both foundations and applications of quantum physics.When there is no decoherence,any physical system should offer the possibility to implement a large number of quantum gates and transfer information.A photon is an element particle of electromagnetic radiation with a well-defined energy,due to its high speed,strong stability and low dissipation,photon has been an ideal carrier of quantum information as well as the experimental implementation of quantum information processing.The current explosion in information technology has been derived from our ability to control the flow of photons in the most intricate ways,specially,the experiment on slow light.This dissertation theoretical study on the following two problems:one is on how to control the flow of photons by means of the atomic ensemble system,which includes the propagation of slow light in a rectangle atomic medium and the scattering process of photons confined in a one dimensional optical waveguide.The other is on simulation the quantum information processing in optical system,which includes realizing error-free discriminations of quantum states and the quantum game of the two-player quantum prisoner's dilemma by using linear optical elements.This dissertation includes five part.It is organized as follows:
The first part is introduction,which paves the way for the dissertation. In this part,we introduce the history of the development of the quantum information and quantum computation,as well as its status of current research.
The second part is the second chapter of this dissertation.Here we mainly concerns on how to coherently control the propagation of slow light by a rectangle atomic medium.Currently there are two ways to get the slow light:coher- ent population oscillation and electromagnetical induced transparency.First, we theoretically predicted a phenomenon of the enhanced light deflection by an atomic ensemble through coherent population oscillation mechanism,which is realized by a two-level atomic ensemble interacting with a control field and a much weaker probe field.Here both optical fields are treated classical.Then, for the light deflection by a A-type atomic ensemble,we systematically develop a quantum theory describing the spatial motion of polaritons in inhomogeneous magnetic fields.Our treatment is based on the mean field theory.
The third part is the third chapter of this dissertation.Here,we study the coherent transport of photons,which propagate in a one-dimensional coupled-resonator waveguide(CRW) and are scattered by an atomic ensemble localized in one of the CRW.The coherent control can be realized by adjusting the detuning between the single photon frequency and the energylevel-spacings of the atoms.There also exist bound states which trap the single photon in the CRW.
The forth part is the forth chapter of this dissertation.We propose a linear optical scheme for optimal unambiguous discrimination among nonorthogonal quantum states,and also simulation the quantum game of the two-player quantum prisoner's dilemma.Here,both spatial anb polarization degree of freedom of single photon are used.
A summary of the work and an outlook of this thesis are given in the last part.
论文的第一章是绪论,作为整篇论文的铺垫,在这部分中我们介绍量子信息和量子计算的发展历史以及研究现状,并分别从理论和实验的角度重点阐述了光子系统量子性质研究的几个热点问题的研究现状。
第二部分为论文的第二章。基于慢光实验的进展,在这一章中,我们研究非均匀介质中光子态传播与空间控制问题。产生慢光有两种方法,一种基于原子相干振荡,它使用二能级原子系综与探测光和控制光相互作用,另一种方法是利用电磁诱导透明技术,它通常使用∧型三能级与探测光和控制光相互作用。我们首先对由相干布局数振荡所产生的慢光的空间传播问题进行讨论,我们使用了半经典处理,利用绝热近似分别得到了描述探测光的薛定谔方程和描述控制光空间运动的非线性薛定谔方程,并发现控制光在传播过程中形状、幅度和速度都可维持不变.然而控制光的空间分布将使得入射到介质中的探测光束在经过介质后发生偏转现象。随后我们对由电磁诱导透明所产生的慢光的空间传播问题进行讨论。现今实验发现:当探测光束通过处于非均匀磁场中的人型三能级原子介质时,由于磁场依赖于空间位置的变化,探测光束将发生偏转。针对这一现象,并考虑到电磁诱导透明现象在微观上是由于光子和原子集体激发形成了一种激子极化子——暗态极化子,我们使用平均场理论得到了描述暗态空间运动的有效薛定谔方程。随后我们采用特定的波包描述了这种准粒子,从波动的角度考虑了横向分布为二次型或线性的磁场中暗态极化子的运动。我们的处理方法反映了准粒子的波粒二象性。研究也表明,暗态极化子具有有效磁矩。
第三章中,我们将利用原子系综与光的相互作用来操作光子以及将光子限制在高品质因子的共振腔阵列中这两种操纵光子的方法相结合,并使用一维的离散坐标量子散射理论进行计算。我们发现由于原子系综的嵌入破坏了耦合腔阵列的平移不变性,使得入射到腔阵列中的光子会被囚禁在嵌入原子系综的腔附近,而不会在阵列中游走。另一方面,对于在阵列中游走的光子,原子与腔场的强耦合改变了阵列中特定腔场的能级分布,从而使得光子共振遂穿几率发生了改变,因此我们可以通过调节原子的跃迁频率来控制光子的传输。从而在理论上提出了一种实现量子网络中不同网络之间连接的方法。
在论文的第四章主要是利用光学系统模拟量子信息处理,这里我们利用了光子的两个自由度,光子空间路径是一个自由度,另一个自由度是光子的极化。首先,对于相互独立但却不正交的量子态,我们提出在直积空间利用偏振分束器、波片、偏振片和单光子探测器来实现它们的最佳无错鉴别。在模拟二人囚徒困境量子博弈方面,量子博弈中所需的两个量子比特分别由光子的两条路径和光子的两个极化方向提供。我们利用分束器和相移器实现其中一个参与人的量子对策,另一参与人的量子对策通过1/4波片和半波片的组合实现,使参与人拥有了实施操纵的物理仪器。
最后一部分为论文的第五章,是对本文工作的总结和展望。
The use of quantum physics has revolutionized the way we communicate and process information.Quantum coherence and decoherence are at the heart of both foundations and applications of quantum physics.When there is no decoherence,any physical system should offer the possibility to implement a large number of quantum gates and transfer information.A photon is an element particle of electromagnetic radiation with a well-defined energy,due to its high speed,strong stability and low dissipation,photon has been an ideal carrier of quantum information as well as the experimental implementation of quantum information processing.The current explosion in information technology has been derived from our ability to control the flow of photons in the most intricate ways,specially,the experiment on slow light.This dissertation theoretical study on the following two problems:one is on how to control the flow of photons by means of the atomic ensemble system,which includes the propagation of slow light in a rectangle atomic medium and the scattering process of photons confined in a one dimensional optical waveguide.The other is on simulation the quantum information processing in optical system,which includes realizing error-free discriminations of quantum states and the quantum game of the two-player quantum prisoner's dilemma by using linear optical elements.This dissertation includes five part.It is organized as follows:
The first part is introduction,which paves the way for the dissertation. In this part,we introduce the history of the development of the quantum information and quantum computation,as well as its status of current research.
The second part is the second chapter of this dissertation.Here we mainly concerns on how to coherently control the propagation of slow light by a rectangle atomic medium.Currently there are two ways to get the slow light:coher- ent population oscillation and electromagnetical induced transparency.First, we theoretically predicted a phenomenon of the enhanced light deflection by an atomic ensemble through coherent population oscillation mechanism,which is realized by a two-level atomic ensemble interacting with a control field and a much weaker probe field.Here both optical fields are treated classical.Then, for the light deflection by a A-type atomic ensemble,we systematically develop a quantum theory describing the spatial motion of polaritons in inhomogeneous magnetic fields.Our treatment is based on the mean field theory.
The third part is the third chapter of this dissertation.Here,we study the coherent transport of photons,which propagate in a one-dimensional coupled-resonator waveguide(CRW) and are scattered by an atomic ensemble localized in one of the CRW.The coherent control can be realized by adjusting the detuning between the single photon frequency and the energylevel-spacings of the atoms.There also exist bound states which trap the single photon in the CRW.
The forth part is the forth chapter of this dissertation.We propose a linear optical scheme for optimal unambiguous discrimination among nonorthogonal quantum states,and also simulation the quantum game of the two-player quantum prisoner's dilemma.Here,both spatial anb polarization degree of freedom of single photon are used.
A summary of the work and an outlook of this thesis are given in the last part.
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