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Вестник Самарского государственного технического университета Серия Физико-математические науки

The influence functional method to the description of the dynamics of quantum systems interacting with the laser radiation

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

Published Jun 15, 2013• 0 citations
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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 singleand 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.
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.
We describe multilevel quantum systems dynamics in electromagnetic fields using the influence functional approach in path integration formalism. We obtain equations for the statistical density matrix and the probability of transitions of quantum systems induced by the electromagnetic field. The explicit form of the quantized electromagnetic field influence functional is concretized. Spontaneous transition of the quantum systems, the Rabi oscillations and their fluctuations are obtained. The two#photon photoelectric effect is explained.
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.
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.
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.
A method to build various integrable models for description of coherent excitation of multilevel media by laser pulses is suggested. Distribution functions over the energy levels of quantum systems depending on the time and frequency detuning are obtained. The distributions follow from Schrödinger equation exact solutions and give the complete dynamical description of laser-excited quantum multilevel systems. Interpretation based on the Fourier spectra of the probability amplitudes of a quantum system is presented. The spectra are expressed in terms of orthonormal polynomials and their weight functions. Matrix elements of the dipole transitions between levels are equal to coefficients of the recurrence formula for the orthonormal polynomial system. Some examples are presented. The Kravchuk oscillator family as an integrable model is constructed to describe the coherent excitation dynamics of multilevel resonance media. It is based on the use of the Kravchuk orthogonal polynomials. The Kravchuk oscillator excitation dynamics is described by the binomial distribution of energy level populations and the distribution parameter depends on excitation conditions. Two known basic models in quantum physics -- the harmonic oscillator and two-level system are the special representatives of the Kravchuk oscillator family.