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Physical Review Letters

Statistical Properties of the Spectrum of the Two-Level System

Marek Kuś

Published Apr 1, 1985• 84 citations
Publisher

Abstract

Several statistical properties of the energy levels of a two-level atom interacting with one mode of quantized electromagnetic field are investigated in connection with possible "quantum-chaotic" behavior of the system.
DOI
10.1103/physrevlett.54.1343

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In this thesis, the properties of a strongly-coupled single-atom-cavity system are studied. Here, the atom predominantly interacts with only one mode of the electromagnetic field. Special attention was paid to the energy spectrum of the system, which consists of an anharmonic ladder of doublets. Developing a new laser cooling method for the preparation of the atom, it was possible for the first time to observe not only the first doublet, but also a state belonging to the second doublet in the optical spectrum. The quantization of light-matter interaction is confirmed by this observation, as the state can only be explained by a bonding of one atom to exactly two photons. Its excitation by a two-photon transition contains a nonlinearity at the level of single quanta. This leads to a dependency of the spectrum on the intensity of the impinging light.
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.