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Annual Meeting Optical Society of America

The effect of pseudo-trapping states on the micromaser dynamics

Pál Bogár, János A. Bergou

Published Jan 1, 1993• 0 citations
Publisher

Abstract

Finding the location of the pseudo-trapping states (PTS)— for which βk=Sin2(θ(n/Nex)1/2)=0—in the micromaser photonstatistics, one can notice that the barriers formed by these states determine the main structure of the photon distribution, namely the sequence of phases in the behavior of the system.
DOI
10.1364/oam.1993.faa.1

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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 photon statistics of a micromaser with a nonzero thermal background for a large range of the pumping parameter \ensuremath{\theta}. The photon statistics are examined in a two-dimensional space, parametrized by \ensuremath{\theta} and k, where k is the photon number. For values of \ensuremath{\theta} which are not too large, there are prominent peaks in the photon-number distribution. The locations of these peaks are determined by well-defined structures in \ensuremath{\theta}-k space. These structures lie along curves in this space. As \ensuremath{\theta} is increased, these structures disappear and the number distribution becomes diffuse. When \ensuremath{\theta} becomes sufficiently large, however, new structures which are well localized in \ensuremath{\theta} and k appear. We call these states ``island states.'' These states exhibit a strong squeezing of the photon number and are fairly insensitive to the thermal background. Their noise increases slowly due to fluctuations of the atomic beam as long as the spread in values of the pump parameter \ensuremath{\theta} is smaller than the distance between the islands. Bistable behavior can be induced by fluctuations that overlap adjacent island states. We also present the photon statistics of a micromaser pumped by atoms in a mixture (incoherent superposition) of their upper and lower levels. It is shown that the noise in island states can be drastically reduced by an optimum amount of injected absorption. These features render these states experimentally feasible, so that they could be used for generating squeezed quantum states of the radiation field that are well localized in \ensuremath{\theta} and k.
We study the spectrum of a one-photon micromaser through the approach of the two-time correlation function. First, we derive two general formulas for the two-time correlation function and for the micromaser spectrum. Then, we focus our attention on trapped states of the micromaser. We examine the line shapes and linewidth of the micromaser spectrum. We find that the half width at half maximum of the spectrum can be less than the smallest decay rate of the off-diagonal density matrix elements ${\mathrm{\ensuremath{\rho}}}_{\mathit{n},}$n+1{\mathit{n}}_{+1}n+1​(t), that a hole can appear at the center of the spectrum, and that the spectrum can be split by shifted spectral components. Using a simple example in which the micromaser spectrum is exactly Lorentzian, we also show that two very close photon-number distributions can correspond to two very different natural linewidths.
We investigate synchronization effects in quantum self-sustained oscillators theoretically using the micromaser as a model system. We use the probability distribution for the relative phase as a tool for quantifying the emergence of preferred phases when two micromasers are coupled together. Using perturbation theory, we show that the behavior of the phase distribution is strongly dependent on exactly how the oscillators are coupled. In the quantum regime where photon occupation numbers are low we find that, although synchronization effects are rather weak, they are nevertheless significantly stronger than expected from a semiclassical description of the phase dynamics. We also compare the behavior of the phase distribution with the mutual information of the two oscillators and show that they can behave in rather different ways.