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Soviet Journal of Quantum Electronics

Nonadiabatic excitation of degenerate two-level systems by laser radiation with a continuously variable frequency

Vladimir V. Likhanskii

Published Aug 31, 1981• 0 citations
Publisher

Abstract

Expressions are obtained for the probability of a nonadiabatic transition between two degenerate levels under the action of laser radiation with a continuously variable resonance frequency. It is shown that this problem reduces to the solution of the Landau–Zener problem for eigenvectors of the matrix of a transition between two degenerate levels.

DOI
10.1070/qe1981v011n08abeh008071

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Expressions are obtained for the probability of a nonadiabatic transition between two degenerate levels under the action of laser radiation with a continuously variable resonance frequency. It is shown that this problem reduces to the solution of the Landau–Zener problem for eigenvectors of the matrix of a transition between two degenerate levels.
We consider two quasimolecular states, one discrete and one quasistationary, whose dynamical coupling becomes possible only by absorption or emission of laser-field photons. In the presence of the laser field the initially discrete state also becomes quasistationary, with an energy continuum shifted with respect to the continuum into which the initially quasistationary state decays. For such an interacting system, the corresponding system of coupled equations is derived and then solved within the Landau-Zener and Demkov nonadiabatic-coupling models, with various assumptions about the time variation of decay widths. Closed-form expressions for the transition probabilities of the half and full collision are obtained. The considered general physical problem is related to electron-capture processes in slow ion--excited-atom (or atom--excited-ion) collisions in a laser field or to laser-assisted excitation-transfer processes in atom--excited-atom slow collisions.
The authors introduce a model for radiative collisions which allows one to obtain a simple analytical expression for the transition probability. This model basically consists of an improvement to the Landau-Zener model, in order to obtain a more realistic representation of the Hamiltonian of the system throughout the collision. They apply the results to the problem of radiative collisions when the dipole-dipole interaction is responsible for the energy transfer and obtain an analytical expression for the cross section as a function of the frequency and intensity of the laser field. Their results are compared with experimental results and reasonable agreement is obtained.
Some aspects of the Landau-Zener-type transition of a periodically driven two-level system with dephasing are clarified. Under the condition that the transition is well localized around the level-crossing region, the transition dynamics for the typical cases is described by simple formulas; namely, by the transfer-matrix method for the long-range coherence, by the application of the incoherent Landau-Zener formula for the short-range coherence, and by the strong-dephasing formula in the limit of complete decoherence.
The problem of a two-level atom interacting with a radiation pulse is studied in the limit that the atom-field detuning times the pulse duration is much greater than unity. Owing to the large atom-field detuning, transitions result from nonadiabatic coupling of the states by the field. The transition probability for the atom to be excited following the pulse is studied as a function of field strength for five different pulse shapes: hyperbolic secant, Lorentzian, hyperbolic secant squared, Lorentzian squared, and Gaussian. It is shown that the behavior of the transition probability differs qualitatively for these pulses. An explanation of this qualitative difference is given in terms of the Massey parameter. Numerical solutions are compared with asymptotic solutions and several anomalies are noted. In the limit of large field strength, a universal expression for the transition probability is found. An interesting feature of the solutions is that, in the limit of very large field strengths, the transition probability for a Gaussian pulse can approach unity despite the fact that the pulse has an exponentially small Fourier amplitude at the atom-field detuning. This apparent violation of the energy-time uncertainty principle is explained in terms of the nonlinear atom-field interactions.
The problem of a two-level atom interacting with a nonmonochromatic radiation pulse is studied both with and without the resonant approximation. Using the time-dependent perturbation theory, the analytical expressions for transition probability of the atom are obtained. It is shown how, depending on the value of the field strength, the atom's excitation probability can be obtained with the needed accuracy. It is shown that the upper level population of the atom exhibits oscillations which are absent in the resonant approximation. It is shown that absorption probability and dipole moment spectrum are governed by interference between the spectral components of a non- monochromatic radiation involved in nonlinear interaction process. Spectral distribution symmetry with respect to the resonance frequency being destroyed, the atom can be excited even if there is no resonant component in the pulse spectrum.