Nonadiabatic Transition Probabilities: Applications in Spectroscopy and Quantum Thermodynamics

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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.