Operator Algebra: From Franck–Condon to Floquet Theory

V. Balakrishnan

A. Palma, L. Sandoval

Two mapping operators are used to relate the eigenstates of two distorted and displaced oscillators. It is found that these operators satisfy a nonabelian two-dimensional algebra. We exemplify the method by calculating the Franck-Condon integral for the case of two harmonic oscillator wells.

Umang Mehta

Sharad Joshi, Abhishek Shukla, Hemant Katiyar +2 more

The interaction of molecules with light may lead to electronic transitions and simultaneous vibrational excitations. Franck-Condon factors (FCFs) play an important role in quantifying the intensities of such vibronic transitions occurring during molecular photoexcitations. In this article, we describe a general method for estimating FCFs using a quantum information processor. The method involves the application of a translation operator followed by the measurement of certain projections. We also illustrate the method by experimentally estimating FCFs with the help of a three-qubit nuclear magnetic resonance quantum information processor. We describe two methods for the measurement of projections: (i) using the Moussa protocol and (ii) using diagonal tomography. The experimental results agree fairly well with the theory.

Jan Hamhalter

Haider R. Zaidi, Fan Hong-Yi

We disagree with the conclusions of the preceding Comment [Janszky and Yushin, Phys. Rev. A 39, 5437 (1989)]. It is shown in this Reply that a squeeze operator can also serve as the time evolution operator for a Franck-Condon transition, and that our previous interpretation is correct. It is also pointed out that the model Hamiltonian used in the preceding Comment is not appropriate for a Franck-Condon transition.