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Time evolution of an atomic system in the presence of a time dependent electric field

J. Récamier, José Luis Paz

Published Jan 1, 1999• 0 citations
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Abstract

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.

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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.
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.
A theoretical study of the dynamical behaviors of the interaction between a two-level atom with a Morse potential in the framework of the Jaynes–Cummings model (JCM) is discussed. We show that this system is equivalent to an intensity-dependent coupling between the two-level atom and the non-deformed single-mode radiation field in the presence of an additional nonlinear interaction. We study the dynamical properties of the system such as, atomic population inversion, the probability distribution of cavity-field, the Mandel parameter and atomic dipole squeezing. It is shown how the depth of the Morse potential can be affected by non-classical properties of the system. Moreover, the temporal evolution of the Husimi-distribution function is explored.
We study the time evolution of an atom suddenly coupled to a thermal radiation field. As a simplified model of the atom-electromagnetic field system we use a system composed by a harmonic oscillator linearly coupled to a scalar field in the framework of the recently introduced dressed coordinates and dressed states. We show that the time evolution of the thermal expectation values for the occupation number operators depend exclusively on the probabilities associated with the emission and absorption of field quanta. In particular, the time evolution of the number operator associated with the atom is given in terms of the probability of remaining in the first excited state and the decay probabilities from this state by emission of field quanta of frequencies ωkω_kωk​. Also, it is showed that independent of the initial state of the atom, it thermalizes with the thermal radiation field in a time scale of the order of the inverse coupling constant.
We develop a nonperturbative model for the response of atomic electrons to oscillating external electric fields, valid in the physical regime where the central electric force is well described by an inverse square law and where the driven oscillations preserve the principal quantum number. We use the model to calculate the odd-harmonic electric-dipole radiation from a single atom driven by a laser field. The exact time-dependent eigensolutions of the model illustrate Zel’dovich’s concept of quasi-energy for sinusoidally time-dependent Hamiltonians. The validity and applicability of the model and suggested improvements are briefly discussed.