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Physical Review A

Pump-induced correlation between two lasers

Antonio Zelaquett Khoury

Published Aug 1, 1999• 6 citations
Publisher

Abstract

We have studied the intensity correlation between two lasers induced by the pumping mechanism. This correlation is studied through the noise spectrum of the intensity difference between the two lasers. We have shown, in the context of atomic lasers, that this spectrum may be smaller than the corresponding shot noise if the pumping noises of the two lasers are correlated. 85% noise reduction with respect to shot noise is predicted under reasonable operating conditions.

DOI
10.1103/physreva.60.1610

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We have studied the intensity correlation between two lasers induced by the pumping mechanism. This correlation is studied through the noise spectrum of the intensity difference between the two lasers. We have shown, in the context of atomic lasers, that this spectrum may be smaller than the corresponding shot noise if the pumping noises of the two lasers are correlated. 85% noise reduction with respect to shot noise is predicted under reasonable operating conditions.
We study in detail the influence of pumping statistics on the laser dynamics. We apply the technique of quantum Langevin operators and generalize the corresponding noise operators to incorporate the statistical properties of the pump mechanism. These equations are then used to derive expressions for the phase and intensity fluctuations of lasers with various pump statistics. We find that a reduction of pump noise can lead to a significant squeezing of the photon number noise below the shot-noise limit. This is in complete agreement with our previous analysis, which used a density-operator approach.
We consider the problem of reducing the contributions of pump and spontaneous-emission noise to the output noise of a laser field. We consider two models based on an atomic medium, one analytic, the other involving numerical simulation of a sequence of pump cycles. The predictions of both models are shown to agree. For regular pump excitation the intensity fluctuations of a laser well above threshold may be reduced to zero at the cavity resonance frequency if the ratio of the lifetimes of the upper and lower lasing levels is sufficiently large that spontaneous emission is suppressed. When the atomic lifetimes are comparable, spontaneous emission reduces the amount of noise reduction. For example, for equal atomic lifetimes regular pump excitation will result in a maximum noise reduction in the output field of one-half the shot-noise limit.
We show that the nonlinear dynamics of the active atoms in conventionally pumped multilevel laser systems can lead to output intensity fluctuations significantly below the shot noise level1,2 (see also Refs, 3-5). Our calculations are based on the standard model of the laser which assumes a large number of atoms resonantly coupled to a single lasing mode. We identify the multiple recycling of the active electron from the lower lasing level to the upper level through pumping as the key process leading to this dynamic pump noise reduction. It is required that (i) the pump rates be comparable to the decay rates of the atom, and (ii) we have a closed repumping cycle, and a constant number of atoms. We find that the results are closely related to recent calculations based on the assumption of an external regular pump6 (for noise reduction in semiconductor lasers, see Ref. 7).
We propose a new kind of correlated-spontaneous-emission laser in which the electromagnetic field is driven by coherently prepared atoms. Such a system constitutes a very simple correlated-emission scheme in that it involves only single-photon transitions, whereas all previous studies were based on correlated photon pairs. We find that for low intensities the fluctuations in the photon number can be reduced below the standard limit while the phase noise is unaffected by the atomic coherence. However, the amount of noise reduction crucially depends on the fluctuations of the pump mechanism. In the high-intensity limit the photon-number fluctuations can be reduced even further. It is possible to achieve a complete quenching of the spontaneous-emission noise and even squeezing, depending on the atomic coherence and the statistical properties of the pump mechanism. Additionally we find a large reduction in the phase fluctuations. In contrast to the amplitude noise, this reduction is independent of the pump noise.
The intensity fluctuations of a three-level laser are known to drop below shot noise in the presence of depletion of the ground state. We study the fluctuations of the laser output as a function of the parameter $\ensuremath{\varepsilon},$ defined as the fraction of atoms needed for the laser to operate. For a sufficiently small number of active atoms, the value of $\ensuremath{\varepsilon},$ and thereby the ground-state depletion, can be appreciable even for modest pumping. This suggests that the intensity fluctuations in the laser output would decrease below shot noise as the number of active atoms is reduced. A microscopic approach that uses a quantum-trajectory method and a macroscopic approach using semiclassical rate equations both show, however, that rather than decreasing, the intensity fluctuations actually increase with $\ensuremath{\varepsilon}.$ We find that the fluctuations of the output are determined by the dependence of the cycle time of the atoms on the number of photons in the laser mode.