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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Transition probabilities of molecular systems in presence-of-time-dependent electric fields

Inés Urdaneta, José Luis Paz, J. Récamier

Published Aug 14, 2001• 0 citations
Publisher

Abstract

Transition probabilities between quantum states of a molecular system interacting with a low intensity time dependent field were obtained. The molecular system is modeled as a quartic anharmonic oscillator, whereas the interaction with the electric field is described by the electric-dipole approximation. We apply Lie algebraic techniques and make use of iterative Bogoliubov transformations to derive an approximate expression for the evolution operator. The methodological procedure proposed by Yuen allows us to evaluate the final time evolution operator in a closed for, using the optical properties of the two- photon coherent state of the radiation field.

DOI
10.1117/12.437237

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Transition probabilities between quantum states of a molecular system interacting with a low intensity time dependent field were obtained. The molecular system is modeled as a quartic anharmonic oscillator, whereas the interaction with the electric field is described by the electric-dipole approximation. We apply Lie algebraic techniques and make use of iterative Bogoliubov transformations to derive an approximate expression for the evolution operator. The methodological procedure proposed by Yuen allows us to evaluate the final time evolution operator in a closed for, using the optical properties of the two- photon coherent state of the radiation field.
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In this work we analyze the time evolution of an atomic system in the presence of an electromagnetic field. The interaction between the field and the system is modeled within the dipole approximation. As a zero approximation we first model the system with a harmonic oscillator and consider the field as classical. As is well known, in this case the quantal result is identical with the classical one. Then we model the system with a Morse oscillator which we expand keeping up to fourth order terms in the displacement coordinate. We compare the response of the system for different depths of the potential and different intensities of the field.
The assumed existence of a time-independent Kubo-type operator renders possible an analytic expression for the evolution operator of a quantized system. For a multilevel system dipole interacting with a continuous-wave laser, the realization of a suitable Kubo-type transformation through an algebraic algorithm may require that the Hamiltonian operator of the system be simplified through, say, the imposition of the rotating-wave approximation and/or the appeal to transition dipole selection rules that validate the neglect of unimportant couplings. The resultant sparse Hamiltonian operator is arbitrarily constructed on the basis of the near-resonant laser coupling of the ground state to the excited states, but without direct appeal to the magnitude of the dipole coupling strength parameters. The implementation and associated computational aspects of a resolvent method for evaluating the evolution operator is discussed and illustrated through the calculation of the transition probabilities for the excitation of an anharmonic oscillator model of the CH stretch in CD3{\mathrm{CD}}_{3}CD3​H.
The excitation of atomic and molecular systems by propagating light in a two-photon state within the Wigner-Weisskopf approximation has been described using stochastic tools. The problem of a stochastic evolution of the quantum system, depending on the results of the measurement of the output field, was formulated and solved making use of the model of repeated interactions and measurement. We defined the discrete in-time interaction between the quantum system and its environment being the electromagnetic field approximated by a chain or chains of harmonic oscillators. We determined analytical formulae for quantum trajectories associated with one-dimensional and two-dimensional counting processes, corresponding respectively to unidirectional or bidirectional input field prepared in the two-photon states. We derived the formulae for the exclusive probability densities of photon counts that allow us to completely characterize the photon statistics of the output field. Finally, we showed how to apply the quantum trajectories to obtain the formula for the probability of the two-photon absorption for a three-level atom in a ladder configuration. The paper also includes a discussion on the optimal two-photon state that maximizes the two-photon absorption probability.