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arXiv:1112.0200

Quantum Transitions in Terms of non-Adiabatic Dressed States

Ivan Georgiev Koprinkov

Published Dec 1, 2011• 0 citations
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Abstract

Nonadiabatic dressed states of a quantum system interacting with an external electromagnetic field and the environment are presented. The relevant matrix elements within the specified states are found. A closed form expression of the quantum transitions based on the nonadiabatic dressed states is proposed for the first time.
DOI
10.48550/arxiv.1112.0200

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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.
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.
Analytical expressions for the quasienergies and corresponding semiclassical dressed states are obtained for a two-level quantum system driven by a nonresonant 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 is easily understood in terms of the quasienergy-level diagram and the allowed transitions between the different semiclassical dressed states.
This book provides a comprehensive introduction to the theory of the interaction between atoms and electromagnetic fields, an area which is central to the investigation of the fundamental concepts of quantum mechanics. The first four chapters describe the different forms of the interaction between atoms and radiation fields. The rest of the book deals with how these interactions lead to the formation of dressed states, in the presence of vacuum fluctuations, as well as in the presence of external fields. Also covered are the role of dressed atoms in quantum measurement theory, and the physical interpretation of vacuum radiative effects. Treating a key field on the boundary between quantum optics and quantum electrodynamics, the book will be of great use to graduate students, as well as to established experimentalists and theorists, in either of these areas.