Nonadiabatic Transition Probabilities: Applications in Spectroscopy and Quantum Thermodynamics

密歇根州立大学的凯瑟琳·亨特教授获得了化学系化学理论、模型和计算方法项目的奖励，她开发了理论方法来理解量子力学系统从应用电磁场中吸收能量。该研究在太阳能转换、分子间能量传递、超快电子过程等方面具有重要意义。准确的描述在分子机器和纳米技术的设计中也很有价值。当一个分子或其他量子力学系统存在于外加场时，最低能态被这个场所改变。这个场也可以引起从这个“新”基态到激发态的转变。跃迁的量子描述是基于概率分析的。现存的跃迁概率理论是由p.a.m.狄拉克在90多年前提出的，远远早于激光的发明。这个理论没有区分具有能量吸收的量子系统的实际激发和由于场而引起的最低态能量的简单修改。朗道（l.d. Landau）和利夫希茨（e.m. Lifshitz）提出了一种不同的理论，该理论基于非绝热跃迁概率，它只解释了真正的激发态。亨特和她的同事们进一步发展了这一理论，表明来自应用场的功率吸收是由非绝热跃迁概率决定的。在这个项目中，非绝热理论被应用于描述能量摄取、能量传递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之中。亨特教授与本科生密切合作，让他们参与资助的研究项目，特别是那些来自少数族裔和残疾人士的研究项目。狄拉克的跃迁理论是建立在无扰动哈密顿量的瞬时本征态中时变薛定谔方程解的展开基础上的。用总系数的正方来求跃迁到激发态的概率。朗道和利夫希茨用狄拉克公式中的分部积分法把激发态系数分成绝热项和非绝热项。绝热项取决于扰动的瞬时值；这一项遵循玻恩和福克的绝热定理，描述系统初始状态对扰动的调整。非绝热项表征实际跃迁，并取决于扰动的时间导数；这一项决定了从外加电场吸收的功率。本项目对非绝热跃迁概率的应用进行了理论探讨，并与实验组合作进行了测试。当扰动场与跃迁频率非共振时，狄拉克形式与非绝热理论的区别尤为明显；当扰动场在一段时间内保持恒定时，这种差异也相当明显。可以预期，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跃迁概率正确形式的实验证据。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基态表面上继续演化。狄拉克理论和非绝热理论对扰动脉冲结束、系统返回基态后，振动波函数的干涉模式做出了不同的预测；这在实验中是可以验证的。该理论在描述染料分子荧光、斯塔克诱导绝热拉曼通道、飞秒受激拉曼光谱和其他超快过程中的应用正在探索中。热力学在量子层面上的应用也在研究中，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。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.