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“Non-exponential spontaneous emission and resonance fluorescence between undistinguishable radiators


Author: Galeamov Elena
Degree:doctor of physics and mathematics
Speciality: 01.04.02 - Theoretical and mathematical physics
Year:2009
Scientific adviser: Nicolae Enache
doctor habilitat, professor, Institute of Applied Physics, Academy of Sciences of Moldova
Institution:
Scientific council:

Status

The thesis was presented on the 25 September, 2009
Approved by NCAA on the 5 November, 2009

Abstract

Adobe PDF document0.44 Mb / in romanian

Keywords

quantum optics, cooperative and coherent effects, spontaneous emission, electromagnetic field vacuum, indistinguishable radiators, bosons, quantum jumps, resonance fluorescence, traveling and standing wave, autocorrelation function, master equation.

Summary

The thesis is devoted to the study of cooperative effects and, namely, to the study of nonexponential spontaneous emission and resonance fluorescence which can be manifested through electromagnetic interactions between indistinguishable radiators.

Special attention is paid to the spontaneous emission of two hydrogen-like atoms in temporal intervals which are shorter or of the order of the delay time between radiators. For the rate of spontaneous emission the tendency to the exponential law was revealed. It was observed the non-local behaviour in the case of the interaction with the electromagnetic field (EMF) in the process of the spontaneous emission described by terms which reflect the Heisenberg principle of uncertainty. A mathematical method of elimination of electromagnetic field operators has been proposed without utilization of the dipole approach for the interactions of these radiators with the EMF. The behaviour of this system of radiators on small and long time intervals as compared with D/c was possible to describe due to this mathematical model. In this case, the classical and quantum effects "work" together over the establishment of the rate of the collective spontaneous emission between radiators. It has been demonstrated that in time intervals of the order of the delay time between radiators, the atom jumps from the excited state to the ground one in the fluctuating mode, the effect called in the literature as quantum jumps.

The cooperative resonance fluorescence of two-level atoms in the standing wave field of the resonator is investigated. The dependence of the dynamic Stark splitting on the positions of the atoms in the standing wave field has been found. The phenomenon of interference between the atoms that are in the stationary field of the cavity was analyzed. A conclusion was made that the autocorrelation function of two atoms being on the distance D>λ is much higher in the case of perpendicular dipole orientation than in the case of parallel dipole orientation relative to the direction rAB of the atoms.

Using the method for finding of the eigenfunctions and eigenvalues in the non-stationary case, the exact solution of the master Lindblad equation with the Einstein coefficients dependent on time was found. Using this solution, the time-dependent atomic inversion in the spontaneous emission process has been obtained. Both for resonance fluorescence and the cooperative spontaneous emission, the fluctuations of the photon numbers and EMF fluctuations on the detector have been investigated. It has been demonstrated that the second order Glauber correlation function does not depend on the cooperative interaction that takes place between the atoms. The following law has been established: when the number of atoms does not exceed the order of the Glauber function there is no dependence on the collective energy exchange between the radiators.

The basic results of the thesis were published in 23 scientific works (8 articles and 15 theses).