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Вестник Самарского государственного технического университета Серия Физико-математические науки

Описание динамики квантовых систем, взаимодействующих с лазерным излучением, методом функционала влияния

Александр Александрович Бирюков, Alexander Alexandrovich Biryukov, Марк Александрович Шлеенков, Mark Alexandrovich Shleenkov

Published Jan 1, 2013• 0 citations
Publisher

Abstract

The description of interacting multilevel quantum system and quantum electromagnetic field in terms of statistical density matrix is considered in path integral approach. The statistical operator and probability transitions of quantum system are represented as mean of electromagnetic field influence functional. The influence functionals are defined for specific models of electromagnetic field. The explicit form for single- and multimode electromagnetic field is concretized in cases when initial state of the field is represented by vacuum and pure coherent.

DOI
10.14498/vsgtu1178

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The description of interacting multilevel quantum system and quantum electromagnetic field in terms of statistical density matrix is considered in path integral approach. The statistical operator and probability transitions of quantum system are represented as mean of electromagnetic field influence functional. The influence functionals are defined for specific models of electromagnetic field. The explicit form for single- and multimode electromagnetic field is concretized in cases when initial state of the field is represented by vacuum and pure coherent.
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The description of interacting multilevel quantum system and quantum electromagnetic field in terms of statistical density matrix is considered in path integral approach. The statistical operator and probability transitions of quantum system are represented as mean of electromagnetic field influence functional. The influence functionals are defined for specific models of electromagnetic field. The explicit form for singleand multimode electromagnetic field is concretized in cases when initial state of the field is represented by vacuum and pure coherent.
In the path integral approach we describe evolution of interacting electromagnetic and fermionic fields by the use of density matrix formalism. The equation for density matrix and transitions probability for fermionic field is obtained as average of electromagnetic field influence functional. We obtain a formula for electromagnetic field influence functional calculating for its various initial and final state. We derive electromagnetic field influence functional when its initial and final states are vacuum. We present Lagrangian for relativistic fermionic field under influence of electromagnetic field vacuum.
We study the dynamics of multi-level quantum systems under the influence of electromagnetic field.Basing on the path integral approach to the quantum density matrix and transitions probability we represent functional averaging electromagnetic field influence.We demonstrate that the transition probability can be written as a path integral of real functional (the product of exponent and cosine).The numerical integration algorithm of the transitions probability in energy representation was developed.The numerical simulations of the quantum system dynamics under electromagnetic field action describe the well-known Rabi oscillations, their fluctuations and multi-photon quantum transitions.
Abstract We consider a system of interacting spinor and electromagnetic fields. We describe the quantum state of the fields by a statistical density matrix. We present the equation of evolution of the density matrix of the field system in the method of integration over trajectories. The evolution equation for the density matrix of the fermion field is obtained as an averaging of the functional of the influence of the electromagnetic field. An explicit form of the functional of the influence of the electromagnetic field is found. We present the equations of motion for the fermion field taking into account the influence of the vacuum of the electromagnetic field.