两体系统几何相位和纠缠性质的理论研究
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摘要
随着量子信息和量子计算的快速发展,量子理论被当作一种重要的物理资源引起越来越多的关注。量子纠缠,几何相位和量子反馈控制不仅从理论上在量子信息理论中得到广泛研究,并且相应的实验研究已经深入到物理学的各个领域。本文主要通过研究两体系统中几何相以及量子纠缠的物理性质,有助我们理解几何相和量子纠缠的物理涵义,并思考如何将之应用到量子信息处理过程中,具有积极的意义。论文共包括六章,其中我们的工作主要是第三章至第六章。
第一章和第二章简单介绍了本文的研究背景,研究的重要性,回顾了量子纠缠,几何相以及开放体系反馈控制的研究现状。详细介绍了几何相在非绝热,非循环,非幺正条件下的定义。
第三章首先介绍了处于经典场中的粒子与自由粒子相互耦合构成的复合体系几何相的性质,而后分别考虑两个粒子各自构成的子体系几何相的性质。通过比较子体系与复合体系的几何相,我们发现,二者在几何相变化趋势上有相同之处。另外我们又计算了不同种几何相位定义对子体系几何相位的影响,这给我们提供了通过经典场控制体系几何相的理论基础。
第四章研究了Bose-Einstein凝聚体(BECs)体系与经典粒子组成的双粒子体系的纠缠性质,利用并发度von-Neumann熵作为纠缠度量给出纠缠度与表征BECs体系参量——非线性系数之间的函数关系。在非线性系数与能级差系数成一定比例关系时,纠缠度发生突变,由有序的周期性振荡变成混乱无序的。该性质提供了一种通过经典粒子诱导BECs粒子在双势阱中隧穿的实验方法。
第五章我们提出利用量子反馈控制控制二能级开放体系几何相位,结果表明体系即使在不能从任意初始态演化到另一个任意态情况下,我们也可以构造适当的反馈控制来调节开放体系的几何相。当开放体系的衰减率相对磁场强度很大或者很小的时候,几何相都是反馈系数的周期性函数。然后我们又给出了反馈效率对体系几何相的影响,这在实验上是需要考虑的因素。这个结果为研究如何控制开放体系提供了新的方法。
第六章介绍单个二能级原子束缚于腔壁作周期性运动的微腔中,腔壁的快速振荡导致原子和腔场的非线性耦合。通过分析原子内部自由度随时间的变化,反映动壁腔效应对原子的影响。另一方面,由于场和原子相互作用在不断变化,对原子的质心运动和腔壁振动产生了一个额外的势,导致了腔与原予的纠缠。我们利用数值模拟计算出体系的von-Neumann熵,发现纠缠不受耦合参量变化的影响,纠缠随时间的演化是无序的,只有在特殊情况下纠缠随时间的演化呈现周期性变化规律。最后为全文的总结与展望。
With the rapid development of quantum information and quantum computation,the quantum theory has attracted more and more attention as an important physical resource. Quantum entanglement,geometric phase and quantum feedback control have been studied extensively in theory.Furthermore,their wide applications were rediscovered as a new resource to manipulate the quantum system in various physical research field.In this thesis, the geometric phase and entanglement properties in a bipartite system have been discussed, respectively.This discussions lead to some interesting results,which shed light on understanding the physical implications of geometric phase and quantum entanglement,it also inspires us how they can be applied in quantum information experiment.The dissertation consists of seven chapters,and the main contents are given in Chapters 3 through 6.
In Chapter 1 and Chapter 2,the background of our study and the importance of the investigation are introduced,the general situation of quantification of quantum information theory,entanglement,geometric phase,as well as quantum feedback control are briefly described. The geometric phase in a nonunitary,nonadiabatic,noncyclic system are described in detail.
In Chapter 3,a detailed investigation on the Berry phase in a bipartite system which consists of two coupled spin-1/2 particles with an X-X-Z term coupling is introduced.The Berry phase acquired by the bipartite system as well as the geometric phase gained by each subsystem are calculated.The results show that the Berry phase of the bipartite system is a weighted sum of the geometric phases of the subsystems.And with the coupling constants tend to infinity the phases go to zero,this confirms the prediction given by Yi previously (Phys.Rev.Lett.92,150406(2004)) with a specific subsystem-subsystem coupling.
In Chapter 4,a few features of entanglement of two types of particles coupled through a nonlinear interaction are presented.It is shown that the entanglement created by the nonlinear interaction can reflect nonlinearity of the system.Possible observation of our prediction in a double-well trapped Bose-Einstein condensates is discussed.
In Chapter 5,the effect of feedback control on geometric phase in a two-level dissipative system is studied.The dependence of the phase on the feed-back parameters are calculated and discussed.The results suggested that we can manipulate the phase by a properly designed feedback control.For small and large atomic dissipative rates with respect to the amplitude of the driving magnetic fieldμB_0,the geometric phase is a periodic function of the feedback parameters,the physics behind these features is also presented.
In Chapter 6,the dynamics and entanglement of a two-level atom trapped in a cavity with a movable mirror is studied.The fast vibrating mirror induces nonlinear couplings between the cavity field and the atom.This optical effect by showing the population of the atom in its internal degrees of freedom as a function of time is studied.On the other side,fast atom-field variables result in an additional potential for the atomic center-of-mass motion and the mirror vibration,leading to entanglement in the motion and the vibration. The entanglement has been numerically simulated and discussed.
Finally,the conclusions and discussions are presented.
第一章和第二章简单介绍了本文的研究背景,研究的重要性,回顾了量子纠缠,几何相以及开放体系反馈控制的研究现状。详细介绍了几何相在非绝热,非循环,非幺正条件下的定义。
第三章首先介绍了处于经典场中的粒子与自由粒子相互耦合构成的复合体系几何相的性质,而后分别考虑两个粒子各自构成的子体系几何相的性质。通过比较子体系与复合体系的几何相,我们发现,二者在几何相变化趋势上有相同之处。另外我们又计算了不同种几何相位定义对子体系几何相位的影响,这给我们提供了通过经典场控制体系几何相的理论基础。
第四章研究了Bose-Einstein凝聚体(BECs)体系与经典粒子组成的双粒子体系的纠缠性质,利用并发度von-Neumann熵作为纠缠度量给出纠缠度与表征BECs体系参量——非线性系数之间的函数关系。在非线性系数与能级差系数成一定比例关系时,纠缠度发生突变,由有序的周期性振荡变成混乱无序的。该性质提供了一种通过经典粒子诱导BECs粒子在双势阱中隧穿的实验方法。
第五章我们提出利用量子反馈控制控制二能级开放体系几何相位,结果表明体系即使在不能从任意初始态演化到另一个任意态情况下,我们也可以构造适当的反馈控制来调节开放体系的几何相。当开放体系的衰减率相对磁场强度很大或者很小的时候,几何相都是反馈系数的周期性函数。然后我们又给出了反馈效率对体系几何相的影响,这在实验上是需要考虑的因素。这个结果为研究如何控制开放体系提供了新的方法。
第六章介绍单个二能级原子束缚于腔壁作周期性运动的微腔中,腔壁的快速振荡导致原子和腔场的非线性耦合。通过分析原子内部自由度随时间的变化,反映动壁腔效应对原子的影响。另一方面,由于场和原子相互作用在不断变化,对原子的质心运动和腔壁振动产生了一个额外的势,导致了腔与原予的纠缠。我们利用数值模拟计算出体系的von-Neumann熵,发现纠缠不受耦合参量变化的影响,纠缠随时间的演化是无序的,只有在特殊情况下纠缠随时间的演化呈现周期性变化规律。最后为全文的总结与展望。
With the rapid development of quantum information and quantum computation,the quantum theory has attracted more and more attention as an important physical resource. Quantum entanglement,geometric phase and quantum feedback control have been studied extensively in theory.Furthermore,their wide applications were rediscovered as a new resource to manipulate the quantum system in various physical research field.In this thesis, the geometric phase and entanglement properties in a bipartite system have been discussed, respectively.This discussions lead to some interesting results,which shed light on understanding the physical implications of geometric phase and quantum entanglement,it also inspires us how they can be applied in quantum information experiment.The dissertation consists of seven chapters,and the main contents are given in Chapters 3 through 6.
In Chapter 1 and Chapter 2,the background of our study and the importance of the investigation are introduced,the general situation of quantification of quantum information theory,entanglement,geometric phase,as well as quantum feedback control are briefly described. The geometric phase in a nonunitary,nonadiabatic,noncyclic system are described in detail.
In Chapter 3,a detailed investigation on the Berry phase in a bipartite system which consists of two coupled spin-1/2 particles with an X-X-Z term coupling is introduced.The Berry phase acquired by the bipartite system as well as the geometric phase gained by each subsystem are calculated.The results show that the Berry phase of the bipartite system is a weighted sum of the geometric phases of the subsystems.And with the coupling constants tend to infinity the phases go to zero,this confirms the prediction given by Yi previously (Phys.Rev.Lett.92,150406(2004)) with a specific subsystem-subsystem coupling.
In Chapter 4,a few features of entanglement of two types of particles coupled through a nonlinear interaction are presented.It is shown that the entanglement created by the nonlinear interaction can reflect nonlinearity of the system.Possible observation of our prediction in a double-well trapped Bose-Einstein condensates is discussed.
In Chapter 5,the effect of feedback control on geometric phase in a two-level dissipative system is studied.The dependence of the phase on the feed-back parameters are calculated and discussed.The results suggested that we can manipulate the phase by a properly designed feedback control.For small and large atomic dissipative rates with respect to the amplitude of the driving magnetic fieldμB_0,the geometric phase is a periodic function of the feedback parameters,the physics behind these features is also presented.
In Chapter 6,the dynamics and entanglement of a two-level atom trapped in a cavity with a movable mirror is studied.The fast vibrating mirror induces nonlinear couplings between the cavity field and the atom.This optical effect by showing the population of the atom in its internal degrees of freedom as a function of time is studied.On the other side,fast atom-field variables result in an additional potential for the atomic center-of-mass motion and the mirror vibration,leading to entanglement in the motion and the vibration. The entanglement has been numerically simulated and discussed.
Finally,the conclusions and discussions are presented.
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