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Physical Review A

Semiclassical theory of a micromaser

Ángela M. Guzmán, Pierre Meystre, Ewan M. Wright

Published Sep 1, 1989• 42 citations
Publisher

Abstract

We present a semiclassical theory of the micromaser by using a consistent multiple-time-scale expansion of its dynamics. The time scale over which the semiclassical approximation is valid is established, and the effects of quantum and thermal fluctuations in the long-time limit are investigated. A thermodynamical analogy is introduced to interpret the steady-state properties of the micromaser, and we show that a simple model allowing for two-phase coexistence provides the best agreement between the semiclassical and quantum theories.

DOI
10.1103/physreva.40.2471

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We present a semiclassical theory of the micromaser by using a consistent multiple-time-scale expansion of its dynamics. The time scale over which the semiclassical approximation is valid is established, and the effects of quantum and thermal fluctuations in the long-time limit are investigated. A thermodynamical analogy is introduced to interpret the steady-state properties of the micromaser, and we show that a simple model allowing for two-phase coexistence provides the best agreement between the semiclassical and quantum theories.
A simple model of a maser or laser consisting of a single-mode field coupled to NNN identical two-level atoms is considered. The semiclassical approximation is equivalent to neglecting the statistical correlations between the atoms and the field. The accuracy of this approximation is investigated by writing equations of motion for the correlations. To obtain a complete, self-consistent set of equations, it is necessary to include correlations of the field with itself (related to the coherence of the field) and correlations between different atoms. Relaxations and an energy source are introduced phenomenologically into the equations of motion. They are then solved for the case of steady-state oscillation. It is found that the correlations are smaller than the terms kept in the semiclassical theory by the order of 1 over the number of photons present in the field, larger if thermal photons abound, but smaller if the field relaxation is dominant. Expressions are also found for the amplitude and phase fluctuations of the field. The latter yield a linewidth for the maser oscillator in agreement with earlier calculations, but obtained by a different method.
We present a semiclassical method for determining the phase distribution and the average photon number of a steady-state micromaser field pumped by a stream of resonant two-level atoms in a superposition of their upper and lower states. Assuming the field to have a photon number distribution with a single sharp peak, we find an equation for the amplitude and the phase of the steady-state field, which has two solutions. The stability analysis shows which one of the two is physically realizable. Using the very simple time evolution of particular atomic states, valid in the semiclassical limit, we find an expression for the phase distribution of the field that contains the mean photon number as a parameter. That can be determined from the stable solution.
We formulate the theory of a micromaser operating simultaneously on a one- and a two-photon atomic transition. Departing from the complete microscopic Hamiltonian for this composite `atom plus field' system, we derive the equations governing its behaviour in the semiclassical approximation and also the fully quantum mechanical master equation. Using parameters corresponding to existing realizations of the one- and two-photon micromaser, we obtain illustrative examples of some novel aspects of this system in the steady state as well as in dynamical evolution.
Abstract In the photon number distribution p(θ,k) of the micromaser, distinct structures are formed by the ridges connecting the peaks in the θ-k space. We refer to these structures as phases. By a simple condition we can distinguish between "semiclassical" and "quantum" regimes of operation near and far above threshold, respectively. In the semiclassical regime, the equations of state of the phases θ= θ(k) are monotonous and coincide with the steady state solutions of the semiclassical theory. They reflect typical features of the micromaser dynamics. The transition jumps, e. g., between the phases decrease with increasing pumping parameter θ, signifying the onset of the Jaynes-Cummings collapse. On increasing 9 further, the phases first disintegrate and then restructure into new kinds of phases in the quantum regime. The equations of state are no longer monotonous. Large single peaks, the quantum island states (QIS), develop in the neighborhoods of minima. The system undergoes oscillations between two kinds of quantum island states, QIS- and QIS+ , as a function of θ. The disintegration and transformation of phases recur periodically as θ is varied, and the phases in the semiclassical region are followed by consecutive phase structures in the quantum regime. The subsequent collapses and revivals of phases are directly connected to the Jaynes-Cummings collapse and revival. The observation of these phase structures and the accompanying QIS is experimentally feasible.
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.
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.