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Physical Review Letters

Quantum jumps of the micromaser field: Dynamic behavior close to phase transition points

Oliver J. Benson, Georg A. Raithel, HERBERT WALTHER

Published May 30, 1994• 114 citations
Publisher

Abstract

The field of the one-atom maser, or micromaser, shows strong variations in certain parameter regions usually identified as phase transitions. In this paper the time development of the field in the vicinity of those regions is investigated. Depending on the parameters, spontaneous jumps or slow transitions between two metastable field values can be observed. Hystersis behavior also occurs. The results are explained by means of a quantum Monte Carlo simulation of the maser field as well as a Fokker-Planck description used earlier in micromaser theory.

DOI
10.1103/physrevlett.72.3506

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The field of the one-atom maser, or micromaser, shows strong variations in certain parameter regions usually identified as phase transitions. In this paper the time development of the field in the vicinity of those regions is investigated. Depending on the parameters, spontaneous jumps or slow transitions between two metastable field values can be observed. Hystersis behavior also occurs. The results are explained by means of a quantum Monte Carlo simulation of the maser field as well as a Fokker-Planck description used earlier in micromaser theory.
We study the dynamics of the single-atom maser, or micromaser, by means of the recently introduced method of thermodynamics of quantum jump trajectories. We find that the dynamics of the micromaser displays multiple space-time phase transitions, i.e., phase transitions in ensembles of quantum jump trajectories. This rich dynamical phase structure becomes apparent when trajectories are classified by dynamical observables that quantify dynamical activity, such as the number of atoms that have changed state while traversing the cavity. The space-time transitions can be either first order or continuous, and are controlled not just by standard parameters of the micromaser but also by nonequilibrium "counting" fields. We discuss how the dynamical phase behavior relates to the better known stationary-state properties of the micromaser.
In this paper recent experiments with the one–atom maser or micromaser are reviewed. They deal with the dynamical behavior of the field at parameter values where the field undergoes phase transitions. Furthermore, atomic interferences are observed in the micromaser when the inversion of the atoms leaving the cavity is measured while the cavity frequency is scanned across the atomic resonance. The interferences are due to the non–adiabatic mixing of dressed states at the entrance and exit holes of the maser cavity. The interference structures are triangular shaped and approximately equidistant. They are associated with the dynamics of the atom–field interaction, show quantum jumps and demonstrate bistability of the micromaser field.
We present the theory of a truly microscopic maser consisting of a single-mode high-Q resonator in which a monoenergetic beam of excited two-level atoms is injected at such a low flux that at most one atom at a time is present inside the cavity. Both a microscopic theory and a heuristic Fokker-Planck approach are presented. We show that the micromaser exhibits a number of novel features that are averaged out in usual masers and lasers. First, the field is in general sub-Poissonian, which reflects the quantization of both the field and its sources. Second, the onset of maser oscillations may be followed by a succession of abrupt transitions in the state of the field. Finally, as the atomic flux through the resonator is increased, the maser threshold acquires characteristics of a continuous phase transition, whereas the subsequent changes in the field distribution become analogous to first-order phase transitions.
We present the quantum theory of a microscopic maser operating on a degenerate two-photon transition between levels of the same parity. We derive both a master equation and a Fokker-Planck equation for this system, and show that quantum effects may have a substantial influence on the behavior of the maser. They modify the oscillation threshold and make external triggering of this maser unnecessary, whereas, according to semiclassical theory, such a triggering is required to start up the maser oscillation. We derive the phase-diffusion properties of the field and show that the diffusion coefficient is complex in this case, its imaginary part being associated with a frequency shift of the field inside the cavity. We show that, in steady state, the photon-number statistics is sub-Poissonian for a wide range of pumping rates.