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Quantum Optics Journal of the European Optical Society Part B

Linewidth of a periodically pumped laser with sub-Poissonian photon statistics

Karol Życzkowski, Fritz Haake

Published Apr 1, 1992• 1 citation
Publisher

Abstract

The authors study the dynamical properties of a periodically pumped laser which displays sub-Poissonian photon statistics. Using a stroboscopic quantum map, they establish the linewidth for the ideal case where pump fluctuation and spontaneous emission are ineffective. Corrections due to spontaneous emission are also discussed.
DOI
10.1088/0954-8998/4/2/002

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The effect of the pump-noise on the statistical properties of the output photon-number is discussed. The master equation for the radiation field valid for any pump fluctuation with steady atomic injection is presented. Far above threshold, the characteristic function for the photon-number distribution is derived without truncating the master equation, the mean value and fluctuation of the output photon-number are also calculated. Thereby the condition of generating sub-Poissonian light is derived and the effect of the pump-noise on the higher-order moment of the output photon-number distribution is analyzed.
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The realization of the micromaser prompted theoretical interest in the fundamental problems of laser physics. In particular, it has been shown that the usual quantum theory of the laser can be recovered from the micromaser theory if a Poissonian average with respect to the time intervals between subsequent injections is taken. The problem of general injection statistics has not been fully resolved but, instead, has been circumvented in the following ways. Instead of the time period between successive injections, the number of injected atoms during a fixed time interval was considered as a stochastic variable and was averaged with respect to a general sub-Poissonian distribution. This led to a closed-form master equa tion, but correction terms arise when the effect of cavity damping is significant. In another approach a stroboscopic theory has been developed: The system is observed when a full cycle of pumping, firing, and decay is completed. This assumes observation of the system on a nonuniform time scale. Here we carry out the averaging over the time interval between subsequent injections with sub-Poissonian distribution, suggest a new compact master equation, and exploit some of its consequences. We show that this approach reproduces the previous ones if the cavity damping is negligible. The surprising result of our approach is that altering the pump statistics affects both the gain and the loss part of the laser dynamics.
The author presents a tutorial review of the quantum theory of the micromaser which allows for arbitrary (sub- as well as super-Poissonian) fluctuations of the pumping beam. In conventional reservoir theory the rate of change of the cavity field is a sum of the changes due to separate interaction with the individual reservoirs, i.e. the interactions are uncorrelated. In their approach, which is based on discrete mapping rather than a maser equation, corrections to reservoir theory arise due to correlations between these interactions. The magnitude of these terms is characterized by the quantity p/N ex . Here p, the parameter describing pump beam fluctuations, is the negative of the Mandel Q parameter of the pump beam so that p=1 corresponds to regular pumping, p=0 to Poissonian one and p<0 to super-Poissonian pump beam fluctuations. N ex is the number of atoms passing through the cavity during the lifetime of the intercavity field. The conventional reservoir limit (standard laser theory) is recovered if p=0 and/or N ex is large. In all other cases the interactions with the gain and loss reservoirs are correlated. The author presents analytical results to demonstrate the effect of pump regularity on steady-state problems (photon statistics, mean number of photons and photon number variance) as well as on transient phenomena (correlation function and spectrum). In particular, it is shown that the approach to equilibrium can have non-Markovian character.