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Physical Review A

Nonlinear features of a micromaser in the semiclassical limit

J. C. Retamal, C. Saavedra, Edmundo Lazo

Published Sep 1, 1993• 1 citation
Publisher

Abstract

We study the chaotic behavior of the internal field in a micromaser with injected atomic coherence. The quantum dynamics provides a return map in the semiclassical limit which we study as a function of the reduced atom-field interaction time. Bifurcations, chaos, and transitions between bifurcation sequences appear in a broad range of the parameter space.

DOI
10.1103/physreva.48.2482

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We study the chaotic behavior of the internal field in a micromaser with injected atomic coherence. The quantum dynamics provides a return map in the semiclassical limit which we study as a function of the reduced atom-field interaction time. Bifurcations, chaos, and transitions between bifurcation sequences appear in a broad range of the parameter space.
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.
We investigate the dynamics of a micromaser continuously driven by a resonant coherent field and pumped by atoms injected in superposition states. We formulate a master equation for the system, and by a Monte Carlo wave-function approach we describe the steady-state behavior as a function of atomic-transit time or driving-field intensity. The combined action of polarized atoms and driving field can lead to enhancement or suppression of coherence in system dynamics, including nonclassical effects such as quadrature squeezing, sub-Poissonian photon statistics, and revival of Rabi oscillations, as well as to shifts of the induced cavity-field phase. These results show the possibility of manipulating both the photon number and the phase of the cavity field.
The semiclassical and quantum dynamics of two ultrastrongly coupled nonlinear resonators cannot be explained using the discrete nonlinear Schrödinger equation or the Bose-Hubbard model, respectively. Instead, a model beyond the rotating wave approximation must be studied. In the semiclassical limit this model is not integrable and becomes chaotic for a finite window of parameters. For the quantum dimer we find corresponding regions of stability and chaos. The more striking consequence for both semiclassical and quantum chaos is that the tunneling time between the sites becomes unpredictable. These results, including the transition to chaos, can be tested in experiments with superconducting microwave resonators.
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.
Nonlinear systems, including atom–field interaction, are investigated due to their fundamental applications in quantum mechanics and rapidly growing fields of quantum communication, especially secure communication with chaotic dynamics. In this paper, we study the chaotic dynamics of a system consisting of an atomic Bose–Einstein condensate interacting with a quantized radiation field in a high-quality cavity with a periodically modulated length. The frequency modulation is adapted by a periodic time-dependent atom–field coupling strength. We use a semiclassical approach to decouple the atoms and field variables and then numerically solve the corresponding nonlinear dynamical equations of the system. Generally, the dynamics of the system sensitively depends on its initial conditions, thereby long-term prediction is impossible. We show that the system demonstrates the emergence of classical dynamical chaos from quantum electrodynamics. The chaotic behavior of energy transfer in the system can be enhanced by increasing the depth of frequency modulation. The strange attractor clearly illustrates that the system presents extremely exotic dynamics over a wide range of parameters. This implies that the dynamical quantities oscillate irregularly, never exactly repeating but always remaining in a bounded region of the phase space.