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Quantum Electronics

Cooperative interaction of dressed atoms with a quantised mode of the electromagnetic field

Michael Z. Smirnov

Published Sep 30, 2000• 2 citations
Publisher

Abstract

The nonlinear dynamics of an open quantum system containing an arbitrary number of two-level atoms coupled with a classical polychromatic electromagnetic field and a quantised mode of the electromagnetic field is studied. Two particular cases of the elastic and inelastic interactions are considered. In the first case, the quantised mode is resonant with the transition between the quasi-energy levels corresponding to the same quasi-energy state, while in the second case, the levels involved in the interaction correspond to different quasi-energy states. For the elastic interaction, which can appear only in open quantum systems, an analytic solution of the Heisenberg equations is obtained. The time dependences of the population of quasi-energy states, the number of photons in the quantised mode, and photon statistics are numerically analysed for the inelastic interaction and at the crossing point of quasi-levels, when both types of the interaction are simultaneously present.

DOI
10.1070/qe2000v030n09abeh001818

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The nonlinear dynamics of an open quantum system containing an arbitrary number of two-level atoms coupled with a classical polychromatic electromagnetic field and a quantised mode of the electromagnetic field is studied. Two particular cases of the elastic and inelastic interactions are considered. In the first case, the quantised mode is resonant with the transition between the quasi-energy levels corresponding to the same quasi-energy state, while in the second case, the levels involved in the interaction correspond to different quasi-energy states. For the elastic interaction, which can appear only in open quantum systems, an analytic solution of the Heisenberg equations is obtained. The time dependences of the population of quasi-energy states, the number of photons in the quantised mode, and photon statistics are numerically analysed for the inelastic interaction and at the crossing point of quasi-levels, when both types of the interaction are simultaneously present.
The nonlinear dynamics of an open quantum system consisting of a “dressed” atom, i.e., an atom coupled with an external multifrequency electromagnetic field, and a single quantized mode of an electromagnetic field is studied. At different crossing points of the quasilevels of the dressed atom, the average number of photons in the quantized mode may either increase without limit with the passage of time or oscillate within finite limits. In the latter case a decrease of the number of photons is accompanied by regularization of their statistics, which may become sub-Poissonian.
An exact solution is found for the collective model of two identical two-level atoms that resonantly interact with a two-mode quantum electromagnetic field in an ideal cavity via two-photon nondegenerate transitions. In the case under study, at the initial moment, both field modes are in the coherent state and atoms are in the excited state. The time dependences of the atomic probabilities, the mean number of photons in the modes, and the statistics and squeezing of the photon modes are studied based on the exact solution.
Some quantum optical models possessing a transition from regular to chaotic dynamics and influence of 'quantum chaos' to photons statistics are investigated. Particular cases of semiclassical dynamics of a single atom and cooperative system of these atoms with (2j + 1) -- equidistant levels interacting with a quantized photon mode in an ideal cavity were considered. We take into account parametric pumping. Corresponding equations of motion are received without the rotation-wave approximation. It was demonstrated the scenario of transition to chaos, realized by doubling frequencies mechanism with growing of 'atom + field' coupling constant. Chaotic behavior and squeezing degree time dependence were obtained in computer simulations for coupling constant values of order of the atomic frequency, the calculation of the maximal Lyapunov coefficient for the dynamics of many two- level atoms interacting with photon cavity mode as function of 'atoms + field' interaction constant is performed. An influence of possible parametric instabilities of nonlinear media and effects of dissipation for atoms are discussed.
Abstract This chapter presents some of the models describing the time-dependent interaction between a simple atom and a field, which may be described either classically or fully quantum mechanically. A number of equivalent interaction pictures and the important rotating-wave approximation are introduced. The two-state dynamics of an atom coupled to a classical field is solved, starting with perturbation theory. Non-perturbative behaviour is analysed, leading to Rabi oscillations of the atomic probabilities. The Jaynes–Cummings model of the dynamics of a single two-state atom coupled to a single quantized mode of the electromagnetic field is solved leading to collapses and revivals of the excited state probability. An exactly soluble model of the coupling of a single state to a Bixon–Jortner quasi-continuum of discrete levels is analysed. Finally, the coherent interactions between two field modes, of the type common in nonlinear optics, are discussed.