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arXiv:quant-ph/0602061 · Journal of Physics B Atomic Molecular and Optical Physics

Non-adiabatic semiclassical dressed states

Ivan Georgiev Koprinkov

Published Sep 12, 2001• 6 citations
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Abstract

We introduce non-adiabatic semiclassical dressed states for a quantum system interacting with an electromagnetic field of variable amplitude and phase, in the presence of dumping. We also introduce a generalized adiabatic condition that allows one to find a closed-form solution for the dressed states. The influence of non-adiabatic factors on the dressed states due to the amplitude and phase field variations and dumping has been found.

DOI
10.1088/0953-4075/34/18/306

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We introduce non-adiabatic semiclassical dressed states for a quantum system interacting with an electromagnetic field of variable amplitude and phase, in the presence of dumping. We also introduce a generalized adiabatic condition that allows one to find a closed-form solution for the dressed states. The influence of non-adiabatic factors on the dressed states due to the amplitude and phase field variations and dumping has been found.
Nonadiabatic dressed states of a quantum system interacting with an external electromagnetic field and the environment are presented. The electromagnetic field is described in terms of carrier‐envelope concept. The amplitude and phase of the field are arbitrary functions of time, subject to a generalized adiabatic condition. The interaction with the environment is described my means of a dumping term in the Hamiltonian. The field time derivatives and the dumping play role of nonadiabatic factors. The main matrix elements within the nonadiabatic dressed states are found. A theory of quantum transitions based on the nonadiabatic dressed states is proposed for the first time.
A semiclassical approach to the dressed-atom theory is presented in which dressed energies and states are determined from the solutions of the semiclassical coupled equations for the atomic probability amplitudes. The semiclassical approach has an advantage over the standard quantum-mechanical approach, especially when an atom interacting with a nonmonochromatic field is considered, because the standard approach requires diagonalization of an infinite-dimensional Hamiltonian matrix for an evaluation of dressed energies and states. Explicit expressions for dressed states of a two-level atom interacting with a resonant monochromatic, bichromatic, and trichromatic field are given.
Analytical expressions for the semiclassical dressed states and corresponding quasienergies are obtained for a two-level quantum system driven by a non-resonant and/or strong laser field in a coherent state. These expressions are of first order in a proper perturbative expansion, and already contain all the relevant physical information on the dynamical and spectroscopic properties displayed by these systems under such particular conditions. The influence of the laser field parameters on transition frequencies, selection rules and line intensities can be easily understood in terms of the quasienergy-level diagram and the allowed transitions between the different semiclassical dressed states.
Using the non-perturbative method of dressed states introduced in previous publications, we study effects of the electromagnetic field on an atom, in the case the field is described by an ensemble of non interacting harmonic oscillators.This method allows to separate the whole system into the dressed atom and the dressed field, in terms of which a non-perturbative approach is possible.When applied to study atomic behaviours in cavities, the method accounts for experimentally observed inhibition of atomic decay in small cavities.