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Physical Review A

Chaotic and cooperative regimes for the micromaser

R. Bonifacio, Giacomo Mauro D’Ariano, R. D. Seno, Nicoletta Sterpi

Published Apr 1, 1993• 7 citations
Publisher

Abstract

We describe the micromaser in the framework of an exact semiclassical model for regular injection, allowing the case of more than one atom at a time in the cavity to be considered. For high pumping and high atom fluxes we find a new kind of phase transition corresponding to a strongly nonlinear chaotic behavior. In addition to the customary period-doubling route to chaos, unexpected scenarios are exhibited, which are a consequence of the multistable competition between different attractors for time evolution.

DOI
10.1103/physreva.47.r2464

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We describe the micromaser in the framework of an exact semiclassical model for regular injection, allowing the case of more than one atom at a time in the cavity to be considered. For high pumping and high atom fluxes we find a new kind of phase transition corresponding to a strongly nonlinear chaotic behavior. In addition to the customary period-doubling route to chaos, unexpected scenarios are exhibited, which are a consequence of the multistable competition between different attractors for time evolution.
This chapter discusses the novel aspects of cavity QED that are not only relevant to traditional quantum optics (lasers and masers, coherence theory, non-classical fields, etc.), but simultaneously make contact with nonlinear dynamics and chaos. A micromaser consisting of a single-mode cavity in which two-level atoms are injected at such a low rate that at most one atom at a time is present inside the cavity. In recent work, a complete quantum theory of the micromaser, including resonator losses, is presented. A detailed study of the dynamics of the quantum-mechanical micromaser is called for, and it will hopefully contribute to a better understanding of quantum chaos in dissipative quantum mechanical systems. A semi-classical version of the micromaser is generally chaotic and exhibits a number of coexisting basins of attraction. The micromaser is a truly quantum-mechanical system which is within reach of experimental investigations.
Some quantum optical models possessing a transition from regular to chaotic dynamics and influence of `quantum chaos' to squeezing 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. Corresponding equations of motion are received without the rotation-wave approximation. Chaotic behavior and squeezing degree time dependence were obtained in computer simulations for coupling constant values or order of the atomic frequency.
A mesoscopic beam of two-level Rydberg atoms, prepared in the lower state, interacts with a coherently driven cavity mode. The dynamics is described by Maxwell-Bloch equations with atomic propagation. On resonance, the system was predicted to exhibit multistability, upper-branch instabilities, and self-pulsing. In the presence of atomic detuning its dynamical behavior is shown to include in addition period doubling, frequency locking, quasiperiodicity, and chaos, thus providing a remarkable example of nonlinear dynamics of a passive autonomous atomic system with propagation. \textcopyright{} 1996 The American Physical Society.
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.
A distinctive signature of the granulated nature of the electromagnetic field is the revivals known to occur in the dynamics of a two-level atom interacting with a single-field mode (Jaynes-Cummings model). The development of high-Q single-mode cavities combined with progress in Rydberg atom spectroscopy has led to a possibility of verifying these predictions. Revival experiments using micromasers have been performed by Walther et al. Here the cavity mode is first allowed to reach a steady state, and then probe atoms are injected into the resonator. By measuring their state as they exit the cavity, one can infer the state of the field. We show that the micromaser experiences Jaynes-Cummingslike revivals when the pump parameter θ is varied. However, in contrast to the conventional Jaynes-Cummings situation, which considers initially coherent fields, the micromaser photon statistics are usually not Poissonian and depend sensitively on θ. The micromaser revivals cannot be explained by a semiclassical theory or linearized quantum fluctuations about the semiclassical solution. Rather, an exact quantum treatment, considering fully the granularity of the cavity mode, is required.