量子干涉效应与量子态测量的理论研究
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摘要
基于量子干涉的各类物理效应的发现与应用是量子光学最令人瞩目的进展,如果能以量化描述方式将量子干涉描述出来,这不仅有利于我们理解难以捉摸的量子效应,更有利于我们有效地控制这些效应。同时由于几何相位在量子计算方面的独特优势,使得被忽略很久的几率波函数中的相位问题又重新成为研究热点之一,因此量子态的测量作为一个基本问题又引起了我们的重视。
本文基于以上的研究背景首先研究了由高斯脉冲场所制备的量子体系。当以弱场探测该体系的量子态时会产生量子干涉,文中对不同物理机制的量子干涉效应进行了分类研究和量化描述,细致地讨论了不同的量子干涉对终态布居数的影响。然后本文从理论上提出并研究了两种基于量子干涉效应的量子态精细测量方案:其一是利用终态布居数在频域的干涉条纹实现对由高斯脉冲制备的量子态的几何相位测量;其二是利用延时非相干光脉冲实现对A-T分裂裂距在时域的高分辨率测量。全文分为四个部分:
1.第一部分主要研究了由高斯脉冲场驱动的原子体系在弱场探测时产生的量子干涉效应,并提出了在频域测量量子相位的方案。文中首先研究了高斯脉冲场所制备的量子体系,发现对处于非本征态的量子体系而言,在满足近似绝热条件时,体系中微弱的透热演化对量子相位的影响不可忽略。在共振驱动体系中,高斯脉冲起始时段由于能级简并给两本征态间累积了恒定的非绝热相差。而在离共振的驱动体系中,虽然能级简并被消除,但是微弱的透热演化依然会给体系累积非绝热相差。而在高斯脉冲作用的体系中,脉冲前沿的任意时刻体系都将在后沿找到复归点,从而形成了可以观测的几何相位。研究发现非绝热演化相与几何相都是与动力学过程无关的状态参量。其次,文中对高斯脉冲所制备的量子体系中各种可能产生的量子干涉效应进行了分类研究,通过对干涉效应的解析量化描述细致地讨论了各类干涉间的差别,并利用数值仿真模拟验证了解析解的正确性。量子干涉与光学干涉的类比发现量子波包具有与经典电磁波类似的演化特点。最后,基于量子干涉效应的特点,本文从理论上提出了在频域利用干涉条纹实现几何相位测量的方案,为了避免探测脉冲脉宽对干涉条纹的剪裁效应,应该使探测脉冲宽度略长于驱动场脉宽。利用第Ⅰ类量子干涉可以将非绝热相位提取出来并在频域实现测量。利用第Ⅱ类量子干涉可以将几何相位提取出来并在频域实现测量。对带有线性啁啾的高斯脉冲驱动体系的研究发现,由于啁啾脉冲会使粒子在瞬时量子态上进行选择性的布居,所以大大抑制了第Ⅰ类量子干涉效应的出现。本文提出的测量方案突破了以往的几何相测量方法中要求驱动脉冲必须与体系严格共振的限制,本方案可以用于离共振驱动体系的几何相位测量,甚至是在啁啾脉冲驱动的体系亦可实现相位测量。同时本方案能够在频域干涉条纹中直接得到几何相位的信息,不需要光子回波方法中复杂的信号检测技术,大大简化了实验方法。
2.第二部分主要阐述了量子态波函数在时域的衍射效应。文中首先利用一阶微扰理论研究了带有线性啁啾的弱高斯脉冲作用于二能级体系所产生的布居儿率波函数在时域演化的直边衍射效应,利用直边衍射理论对各参数的物理意义给出了明确的表述。然后将时域直边衍射理论推广至由无啁啾强高斯脉冲作用的二能级体系,利用弱场对该体系进行探测同样可以得到类似的终态布居在时域的直边衍射解,只是布居还会受到量子干涉的影响。第Ⅰ类量子干涉会改变终态布居几率的相位,使衍射振荡变密集,但对振幅没有影响。而第Ⅱ类干涉会使终态布居受共振时刻脉冲面积的调制,对布居几率产生显著的影响。结合对布居几率在频域变化的研究发现,弱探测激发的几率波具有类似于经典电磁波的干涉与衍射性质,在频域展现干涉条纹,而在时域展现直边衍射图样。
3.第三部分主要阐述了利用延时非相干光双脉冲实现对A-T分裂裂距的时域高分辨率测量的方案。当强驱动场激发原子体系时原子能态会产生A-T分裂,形成新的量子态。若采用延时双脉冲非相干光探测系统,激发态分裂的两个量子态向终态的跃迁间会产生量子干涉效应,通过对脉冲延时的控制可以实现控制和影响终态粒子布居的演化过程。文中给出了此物理模型中整个探测过程的解析表示,从而细致地揭示出系统的动力学演化过程。结果中包含了探测场自相关项和量子干涉项,在量子干涉项中既包含了所要测量的量子态的重要信息,同时也包含了探测场的影响形式。通过对布居数在时域演化的测量既可得到A-T能级分裂的间距,也可测量到量子态的相干驰豫速率。同时从解析表示中还可以推演出在频域测量量子态的物理机理。比较两种方法发现,利用非相干光的时域测量有着明显的优势,其特点是测量方便,精度高,是可以全面揭示量子态演化信息的有效测量方法。本方案的优势首先在于测量不再受制于激光线宽,对分裂裂距比激光线宽窄的精细能级分裂能够实现准确测量,对探测光的要求大大降低。其次本方案兼具了可测量超快过程的优点,即使是对发生在原子内部的比激光脉冲持续时间更短的瞬态过程也能实现准确测量。
4.第四部分主要阐述了在简并二能级体系中实现量子态探测的方案,着重研究了量子干涉对探测脉冲传播特性的影响。本章中将一强一弱两偏振方向互相垂直的脉冲光场作用于由ns,np态组成的简并二能级原子体系,原子态在强场作用下发生Stark位移形成原子预置态,而弱场激发不同预置量子态间的交叉跃迁。研究发现对于S_(1/2)→P_(1/2)体系,量子干涉会显著影响弱场在介质中的传播,当Cos[2θ(t′)]＜0时探测光被放大,当Cos[2θ(t′)]＞0时探测光被减弱。而对于S_(12)→P_(32)体系,量子干涉的影响是放大探测光。本方案是一种更易于实际操作的实验方案,由于两场激发的偶极跃迁偏振方向不同,所以作为探测场的弱场在介质中的传播效应更易于与强场作用相分离,同时对强场作用形成的原子预置态的影响也更小,而且此方案更利于保持两脉冲的同步性,因为同步性是影响频域干涉条纹对比度的重要因素。
Three quantum interferences based on different physical mechanism,which derives from a weak field probing on the quantum states prepared by a Gaussian pulse,were demonstrated in this paper.Two projects about quantum state measurement were also presented.One is to measure the geometric phase of quantum state prepared by Gaussian pulse with interference fringes in the spectral domain,and the other is to measure the energy spacing of A-T splitting with incoherent light.The paper is divided into four parts:
Part one:
The quantum system prepared by Gaussian pulse was investigated firstly.It was found that the quantum phase cumulated during the weak nonadiabatic evolution cannot be neglected when the system stays in a non-eigenstate.In a resonant system,the constant phase difference between two eigenstates was cumulated because the degeneration of two quantum states at the start of the Gaussian pulse.In a nonresonant system,the subtle nonadiabatic evolution can also cumulate the phase difference.The cyclic point can be found in a quantum system driven by a Gaussian pulse and the geometric phase can be observed in this system.Secondly,By simulating numerically with density matrix motion equation and discerning the physical process with analytical expression,we found that the quantum phases are sensitive to the different quantum interference effects and the geometric phase plays an important role in the type-Ⅱquantum interference.In particular, the period of the signal for the different type quantum interferences is predicted correctly by our explicit formulation of various interference.Finally,based on the quantum interferences,a novel project to measure the geometric phase with fringes in spectral domain was present in this paper.To avoiding the tailor effect of the probe field,the probe pulse should be longer than the pump pulse.The nonadiabatic phase can be picked up by the typeⅠinterference and measured in spectral domain.The Geometric phase can be picked up by the typeⅡinterference and measured in spectral domain.The geometric phase in a nonresonant system can also be measured by this method.The typeⅠquantum interference will be depressed in a system driven by a linear chirp Gaussian pulse because of the selective population.
Part two:
Firstly,we study the oscillating of the transition in the two-state system driven by a linearly weak chirped pulse.The analytical expression of the wave function of the excited state is similar to the Fresnel diffraction by an edge.We show that the population oscillation results from the quantum diffraction of the wave function in time domain.Then in a system driven by the strong pulse,it was also obtained that the behavior of population on the final state is similar to the Fresnel diffraction by an edge.Moreover,the typeⅠquantum interference will change the phase of the probability function,and lead to a higher numbers of oscillation.The typeⅡquantum interference will affect the population prominently and lead to the population be modulated by the pulse area.
Part three:
A novel and high resolution method for measuring quantum states with incoherent light in the time-domain is presented.Taking Autler-Townes as an example,the physics process and the evolutive rule during measuring are discussed by an explicit and analytical formulation in detail;and the influence of measuring process on the quantum state is disclosed.With this method,the very small splitting of the energy-level and large energy-level space can be measured availably at the same time,while the transverse relaxation rate of the system can be obtained directly by testing the decay time of the signal.Comparing with the characteristics of the measuring methods between the time-domain and frequency-domain,we found that the measuring quantum states with incoherent light in the times-domain is robust and valid for disclosing information of the quantum stare entirely.
Part four:
A degenerate two-level atomic system was considered where a strong pulse prepared the quantum state,and a weak pulse with perpendicular polarization probed the quantum system.The strong pulse drives the parallel transition and the weak pulse connects the cross transition.It was found that in the system S_(1/2)→P_(1/2),the quantum interference affects the propagation of the weak pulse prominently.The probe field will be amplified where Cos[2θ(t′)]＜0 and absorbed where Cos[2θ(t′)]＞0.But in the system S_(1/2)→P_(3/2),the probe field will always be amplified.
本文基于以上的研究背景首先研究了由高斯脉冲场所制备的量子体系。当以弱场探测该体系的量子态时会产生量子干涉,文中对不同物理机制的量子干涉效应进行了分类研究和量化描述,细致地讨论了不同的量子干涉对终态布居数的影响。然后本文从理论上提出并研究了两种基于量子干涉效应的量子态精细测量方案:其一是利用终态布居数在频域的干涉条纹实现对由高斯脉冲制备的量子态的几何相位测量;其二是利用延时非相干光脉冲实现对A-T分裂裂距在时域的高分辨率测量。全文分为四个部分:
1.第一部分主要研究了由高斯脉冲场驱动的原子体系在弱场探测时产生的量子干涉效应,并提出了在频域测量量子相位的方案。文中首先研究了高斯脉冲场所制备的量子体系,发现对处于非本征态的量子体系而言,在满足近似绝热条件时,体系中微弱的透热演化对量子相位的影响不可忽略。在共振驱动体系中,高斯脉冲起始时段由于能级简并给两本征态间累积了恒定的非绝热相差。而在离共振的驱动体系中,虽然能级简并被消除,但是微弱的透热演化依然会给体系累积非绝热相差。而在高斯脉冲作用的体系中,脉冲前沿的任意时刻体系都将在后沿找到复归点,从而形成了可以观测的几何相位。研究发现非绝热演化相与几何相都是与动力学过程无关的状态参量。其次,文中对高斯脉冲所制备的量子体系中各种可能产生的量子干涉效应进行了分类研究,通过对干涉效应的解析量化描述细致地讨论了各类干涉间的差别,并利用数值仿真模拟验证了解析解的正确性。量子干涉与光学干涉的类比发现量子波包具有与经典电磁波类似的演化特点。最后,基于量子干涉效应的特点,本文从理论上提出了在频域利用干涉条纹实现几何相位测量的方案,为了避免探测脉冲脉宽对干涉条纹的剪裁效应,应该使探测脉冲宽度略长于驱动场脉宽。利用第Ⅰ类量子干涉可以将非绝热相位提取出来并在频域实现测量。利用第Ⅱ类量子干涉可以将几何相位提取出来并在频域实现测量。对带有线性啁啾的高斯脉冲驱动体系的研究发现,由于啁啾脉冲会使粒子在瞬时量子态上进行选择性的布居,所以大大抑制了第Ⅰ类量子干涉效应的出现。本文提出的测量方案突破了以往的几何相测量方法中要求驱动脉冲必须与体系严格共振的限制,本方案可以用于离共振驱动体系的几何相位测量,甚至是在啁啾脉冲驱动的体系亦可实现相位测量。同时本方案能够在频域干涉条纹中直接得到几何相位的信息,不需要光子回波方法中复杂的信号检测技术,大大简化了实验方法。
2.第二部分主要阐述了量子态波函数在时域的衍射效应。文中首先利用一阶微扰理论研究了带有线性啁啾的弱高斯脉冲作用于二能级体系所产生的布居儿率波函数在时域演化的直边衍射效应,利用直边衍射理论对各参数的物理意义给出了明确的表述。然后将时域直边衍射理论推广至由无啁啾强高斯脉冲作用的二能级体系,利用弱场对该体系进行探测同样可以得到类似的终态布居在时域的直边衍射解,只是布居还会受到量子干涉的影响。第Ⅰ类量子干涉会改变终态布居几率的相位,使衍射振荡变密集,但对振幅没有影响。而第Ⅱ类干涉会使终态布居受共振时刻脉冲面积的调制,对布居几率产生显著的影响。结合对布居几率在频域变化的研究发现,弱探测激发的几率波具有类似于经典电磁波的干涉与衍射性质,在频域展现干涉条纹,而在时域展现直边衍射图样。
3.第三部分主要阐述了利用延时非相干光双脉冲实现对A-T分裂裂距的时域高分辨率测量的方案。当强驱动场激发原子体系时原子能态会产生A-T分裂,形成新的量子态。若采用延时双脉冲非相干光探测系统,激发态分裂的两个量子态向终态的跃迁间会产生量子干涉效应,通过对脉冲延时的控制可以实现控制和影响终态粒子布居的演化过程。文中给出了此物理模型中整个探测过程的解析表示,从而细致地揭示出系统的动力学演化过程。结果中包含了探测场自相关项和量子干涉项,在量子干涉项中既包含了所要测量的量子态的重要信息,同时也包含了探测场的影响形式。通过对布居数在时域演化的测量既可得到A-T能级分裂的间距,也可测量到量子态的相干驰豫速率。同时从解析表示中还可以推演出在频域测量量子态的物理机理。比较两种方法发现,利用非相干光的时域测量有着明显的优势,其特点是测量方便,精度高,是可以全面揭示量子态演化信息的有效测量方法。本方案的优势首先在于测量不再受制于激光线宽,对分裂裂距比激光线宽窄的精细能级分裂能够实现准确测量,对探测光的要求大大降低。其次本方案兼具了可测量超快过程的优点,即使是对发生在原子内部的比激光脉冲持续时间更短的瞬态过程也能实现准确测量。
4.第四部分主要阐述了在简并二能级体系中实现量子态探测的方案,着重研究了量子干涉对探测脉冲传播特性的影响。本章中将一强一弱两偏振方向互相垂直的脉冲光场作用于由ns,np态组成的简并二能级原子体系,原子态在强场作用下发生Stark位移形成原子预置态,而弱场激发不同预置量子态间的交叉跃迁。研究发现对于S_(1/2)→P_(1/2)体系,量子干涉会显著影响弱场在介质中的传播,当Cos[2θ(t′)]＜0时探测光被放大,当Cos[2θ(t′)]＞0时探测光被减弱。而对于S_(12)→P_(32)体系,量子干涉的影响是放大探测光。本方案是一种更易于实际操作的实验方案,由于两场激发的偶极跃迁偏振方向不同,所以作为探测场的弱场在介质中的传播效应更易于与强场作用相分离,同时对强场作用形成的原子预置态的影响也更小,而且此方案更利于保持两脉冲的同步性,因为同步性是影响频域干涉条纹对比度的重要因素。
Three quantum interferences based on different physical mechanism,which derives from a weak field probing on the quantum states prepared by a Gaussian pulse,were demonstrated in this paper.Two projects about quantum state measurement were also presented.One is to measure the geometric phase of quantum state prepared by Gaussian pulse with interference fringes in the spectral domain,and the other is to measure the energy spacing of A-T splitting with incoherent light.The paper is divided into four parts:
Part one:
The quantum system prepared by Gaussian pulse was investigated firstly.It was found that the quantum phase cumulated during the weak nonadiabatic evolution cannot be neglected when the system stays in a non-eigenstate.In a resonant system,the constant phase difference between two eigenstates was cumulated because the degeneration of two quantum states at the start of the Gaussian pulse.In a nonresonant system,the subtle nonadiabatic evolution can also cumulate the phase difference.The cyclic point can be found in a quantum system driven by a Gaussian pulse and the geometric phase can be observed in this system.Secondly,By simulating numerically with density matrix motion equation and discerning the physical process with analytical expression,we found that the quantum phases are sensitive to the different quantum interference effects and the geometric phase plays an important role in the type-Ⅱquantum interference.In particular, the period of the signal for the different type quantum interferences is predicted correctly by our explicit formulation of various interference.Finally,based on the quantum interferences,a novel project to measure the geometric phase with fringes in spectral domain was present in this paper.To avoiding the tailor effect of the probe field,the probe pulse should be longer than the pump pulse.The nonadiabatic phase can be picked up by the typeⅠinterference and measured in spectral domain.The Geometric phase can be picked up by the typeⅡinterference and measured in spectral domain.The geometric phase in a nonresonant system can also be measured by this method.The typeⅠquantum interference will be depressed in a system driven by a linear chirp Gaussian pulse because of the selective population.
Part two:
Firstly,we study the oscillating of the transition in the two-state system driven by a linearly weak chirped pulse.The analytical expression of the wave function of the excited state is similar to the Fresnel diffraction by an edge.We show that the population oscillation results from the quantum diffraction of the wave function in time domain.Then in a system driven by the strong pulse,it was also obtained that the behavior of population on the final state is similar to the Fresnel diffraction by an edge.Moreover,the typeⅠquantum interference will change the phase of the probability function,and lead to a higher numbers of oscillation.The typeⅡquantum interference will affect the population prominently and lead to the population be modulated by the pulse area.
Part three:
A novel and high resolution method for measuring quantum states with incoherent light in the time-domain is presented.Taking Autler-Townes as an example,the physics process and the evolutive rule during measuring are discussed by an explicit and analytical formulation in detail;and the influence of measuring process on the quantum state is disclosed.With this method,the very small splitting of the energy-level and large energy-level space can be measured availably at the same time,while the transverse relaxation rate of the system can be obtained directly by testing the decay time of the signal.Comparing with the characteristics of the measuring methods between the time-domain and frequency-domain,we found that the measuring quantum states with incoherent light in the times-domain is robust and valid for disclosing information of the quantum stare entirely.
Part four:
A degenerate two-level atomic system was considered where a strong pulse prepared the quantum state,and a weak pulse with perpendicular polarization probed the quantum system.The strong pulse drives the parallel transition and the weak pulse connects the cross transition.It was found that in the system S_(1/2)→P_(1/2),the quantum interference affects the propagation of the weak pulse prominently.The probe field will be amplified where Cos[2θ(t′)]＜0 and absorbed where Cos[2θ(t′)]＞0.But in the system S_(1/2)→P_(3/2),the probe field will always be amplified.
引文
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