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Nonadiabatic Transition Probabilities: Applications in Spectroscopy and Quantum Thermodynamics

非绝热跃迁概率：在光谱学和量子热力学中的应用

基本信息

批准号：
1900399
负责人：
Katharine Hunt
金额：
$ 28万
依托单位：
Michigan State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-08-01 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1900399&HistoricalAwards=false
关键词：
Nonadiabatic Transition Probabilities Applications Spectroscopy

项目摘要

Professor Katherine Hunt of Michigan State University is supported by an award from the Chemical Theory, Models and Computational Methods program in the Division of Chemistry to develop theoretical approaches to understand the uptake of energy by a quantum mechanical system from an applied electromagnetic field. This research has important impacts in solar energy conversion, energy transfer between molecules, and ultrafast electronic processes. An accurate description is also valuable in the design of molecular machines and in nanotechnology. When a molecule or other quantum mechanical system is in the presence of an applied field, the lowest energy state is modified by this field. The field can also cause transitions from this "new" ground state to excited states. Quantum descriptions of transitions are based on a probabilistic analysis. The existing theory of transition probabilities was developed by P. A. M. Dirac over ninety years ago, long before lasers had been developed. This theory does not make a distinction between actual excitations of the quantum system with energy absorption, and simple modifications of the energy of the lowest state due to the field. L. D. Landau and E. M. Lifshitz suggested a different theory, based on nonadiabatic transition probabilities, which account exclusively for true excitations. Hunt and her coworkers have developed this theory further, to show that power absorption from an applied field is determined by the nonadiabatic transition probability. In this project, the nonadiabatic theory is applied to describe energy uptake, energy transfer processes, and quantum thermodynamic systems. Experimental means of determining the actual transition probability are identified during this project, and explored in collaboration with research groups in spectroscopy. Applications to quantum thermodynamic engines are also being analyzed. Professor Hunt works closely with undergraduate students, engaging them in the supported research project, in particular those from the underrepresented minority groups and persons with disabilities.Dirac's theory of transitions is based on an expansion of the solution of the time-dependent Schr'dinger equation in the instantaneous eigenstates of the unperturbed Hamiltonian. The norm-square of the total coefficient is used to find the probability of transition to an excited state. Landau and Lifshitz separated the excited-state coefficient into an adiabatic term and a nonadiabatic term, by integration by parts in Dirac's expression. The adiabatic term depends on the instantaneous value of the perturbation; this term follows the adiabatic theorem of Born and Fock and describes the adjustment of the initial state of the system to the perturbation. The nonadiabatic term characterizes actual transitions and depends on the time-derivative of the perturbation; this term determines the power absorption from an applied field. In this project, applications of nonadiabatic transition probabilities are explored theoretically and tested in collaboration with experimental groups. When a perturbing field is off-resonant with the transition frequency, the difference between Dirac's form and the nonadiabatic theory is particularly evident; the difference is also quite evident when the perturbing field is held constant for a period of time. It is anticipated that transitions between quantum states that are coupled to other degrees of freedom should show clear-cut experimental evidence of the correct form of the transition probability. When an electronic excitation occurs, the associated vibrational wave functions evolve on the excited-state potential energy surface; but the adiabatic component of the wave function continues to evolve on the perturbed ground-state surface. Dirac's theory and the nonadiabatic theory lead to different predictions for the interference patterns of vibrational wave functions, after a perturbing pulse has ended and the system has returned to the ground state; this is testable in experiments. Applications of the theory are being explored in describing the fluorescence of dye molecules, Stark-induced adiabatic Raman passage, femtosecond stimulated Raman spectroscopy, and other ultrafast processes. Applications in thermodynamics on the quantum level are also being investigated, with a focus on the power and efficiency of quantum engines. Participation in this project by women and members of underrepresented minority groups is strongly encouraged.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

密歇根州立大学的凯瑟琳·亨特教授得到了化学系化学理论、模型和计算方法计划颁发的奖项的支持，该奖项旨在开发理论方法来理解量子力学系统从应用电磁场中吸收能量。这项研究对太阳能转换、分子间的能量转移以及超快电子过程都有重要影响。准确的描述在分子机器和纳米技术的设计中也是有价值的。当分子或其他量子力学系统处于外场中时，最低能态会被外场修正。这个场也可以引起从这个“新的”基态到激发态的转变。跃迁的量子描述是基于概率分析的。现有的跃迁概率理论是由P·A·M·狄拉克在90多年前提出的，远远早于激光的发展。这一理论没有区分具有能量吸收的量子系统的实际激发，以及由于场而对最低态能量的简单修改。L.D.朗道和E.M.Lifshitz提出了一种不同的理论，该理论基于非绝热跃迁几率，该几率完全解释了真正的激发。亨特和她的同事进一步发展了这一理论，证明了来自外场的能量吸收是由非绝热跃迁几率决定的。在这个项目中，非绝热理论被应用于描述能量吸收、能量转移过程和量子热力学系统。在这个项目中确定了确定实际跃迁概率的实验方法，并与光谱学研究小组合作进行了探索。量子热力学引擎的应用也在分析中。亨特教授与本科生密切合作，让他们参与到受支持的研究项目中，特别是那些来自代表性不足的少数群体和残疾人的研究项目。狄拉克的转变理论基于非微扰哈密顿量的瞬时本征态中依赖时间的薛定谔方程的解的扩展。总系数的范数平方用来计算跃迁到激发态的几率。Landau和Lifshitz通过对狄拉克表达式中的部分积分，将激发态系数分成绝热项和非绝热项。绝热项依赖于微扰的瞬时值，它遵循Born和Fock的绝热定理，描述了系统初态对微扰的调节。非绝热项表征了实际的跃迁，并取决于微扰的时间导数；这一项决定了外加电场的能量吸收。在这个项目中，与实验小组合作，从理论上探索了非绝热跃迁几率的应用，并对其进行了测试。当微扰场与跃迁频率失谐时，狄拉克形式与非绝热理论之间的差异尤其明显；当微扰场在一段时间内保持不变时，差异也相当明显。预计耦合到其他自由度的量子态之间的跃迁应该显示出明确的实验证据，证明跃迁概率的正确形式。当电子激发发生时，相关的振动波函数在激发态势能面上演化，但波函数的绝热分量在扰动的基态面上继续演化。狄拉克理论和非绝热理论导致了对微扰脉冲结束和系统返回基态后振动波函数干涉图样的不同预测；这在实验中是可以检验的。人们正在探索该理论在描述染料分子的荧光、斯塔克诱导的绝热拉曼通道、飞秒受激拉曼光谱和其他超快过程中的应用。还在研究量子水平上的热力学应用，重点是量子引擎的功率和效率。强烈鼓励妇女和代表性不足的少数群体成员参与这一项目。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。