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Physical Review A

Lasers with sub-Poissonian pump

Monika A. M. Marte, P. Zoller

Published Nov 1, 1989• 60 citations
Publisher

Abstract

It is shown that, introducing quantum-mechanical degrees of freedom for the pump field, one can model optical-pumping processes of a laser with sub-Poissonian statistics. For a class of pump models containing regular pumping at one end of the range and Poissonian pumping at the other, the exact stationary moments for the pump-field-averaged laser field are calculated in the strong-saturation limit of the lasing transition. It is demonstrated that, in a photodetection experiment of the laser output, complete noise suppression in the photocurrent fluctuation spectrum is, at least in principle, achievable. Finally, an approximate Fokker-Planck equation for photon distribution of the laser field with explicit appearance of the pump-light intensity correlation function in the diffusion term is derived and solved in the stationary limit.

DOI
10.1103/physreva.40.5774

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It is shown that, introducing quantum-mechanical degrees of freedom for the pump field, one can model optical-pumping processes of a laser with sub-Poissonian statistics. For a class of pump models containing regular pumping at one end of the range and Poissonian pumping at the other, the exact stationary moments for the pump-field-averaged laser field are calculated in the strong-saturation limit of the lasing transition. It is demonstrated that, in a photodetection experiment of the laser output, complete noise suppression in the photocurrent fluctuation spectrum is, at least in principle, achievable. Finally, an approximate Fokker-Planck equation for photon distribution of the laser field with explicit appearance of the pump-light intensity correlation function in the diffusion term is derived and solved in the stationary limit.
A recent analysis of the influence of the pump statistics on the laser output fluctuations is applied to the experimentally feasible case of a laser being pumped by light coming from a separate pump field cavity that is driven by a broad-band squeezed vacuum plus a coherent driving field. In contrast to the 'squeezed-reservoir laser', where a reservoir of squeezed modes coming from all directions coupled to the dipole moment of the lasing transition and leads to atomic phase decay inhibition and phase locking of the laser field, here the squeezed light merely pumps the gain atoms, that is gives rise to inversion of the laser transition. In analogy to photodetection theory the photon statistics of the laser output is calculated as a function of the photon statistics of the absorbed squeezed pump light. For the case of a squeezed pump field chosen to display sub-Poissonian statistics, it is demonstrated that the Mandel Q-parameter of the laser cavity output can theoretically reach the optimum value of Q=- 1 / 2 , similar to the case of a deterministic pumping mechanism.
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.
We identify a mechanism of dynamical pump-noise suppression in lasers. It is based on the recycling of the active laser electron from the lower to the upper laser level by a sequence of incoherent step processes. Although each of these steps corresponds to a Poisson process, i.e., is stochastic, the combination of many incoherent steps leads to a regular (deterministic) recycling of the laser electron and, correspondingly, a pump-noise suppression in the laser. The mechanism predicts sub-Poissonian laser output and intensity fluctuations beyond the shot-noise limit for incoherently pumped systems.
A laser with a Poissonian random pump, operated far above threshold, has Poissonian statistics both for the intracavity photon number and for extracavity photocounts. We analyze a pump-noise-suppressed laser using the positive P representation. When the pump noise is suppressed below a critical level, the intracavity photon-number distribution becomes sub-Poissonian.1,2 When the spontaneous decay of the upper lasing level is also eliminated, intracavity photon-number fluctuations can be diminished by a factor up to half. For counting times much shorter than the cavity decay time, the extracavity photocount statistics are essentially Poissonian, since cavity decay dominates. For counting times comparable with or larger than the cavity lifetime, the extracavity photocount statistics become sub-Poissonian. In the limit that intracavity photon-number fluctuations are diminished by one half, the extracavity photocount noise can be completely suppressed for counting times much longer than the cavity lifetime. The cavity mode occupies an incoherent superposition of two states 180° out of phase, both of which diffuse in phase. In the microlaser regime, quantum diffusion between these two states can result in 180° phase jumps, which are in addition to ordinary phase diffusion.
We study the effects of correlations between quantum and pump noises on fluctuations of the laser intensity in a saturation laser model. An approximative Fokker–Planck equation and analytic expressions of the steady-state probability distribution function (SPD) of the laser system are derived. Based on the SPD, the normalized mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that (i) the correlation strength λ of correlated noises always enhances the fluctuation of laser intensity; (ii) the correlation time τ of correlated noises strengthens the fluctuation of laser intensity for the below-threshold case but τ weakens it for the above-threshold case.
Using an extension of the Scully—Lamb laser theory we show that by insertion of nonlinear elements in the cavity, laser light with nonclassical sub—Poissonian photon statistics can be generated. For an N—photon absorber in the limit of small saturation the variance of the photon number distribution can be reduced by a factor of (+1/N) compared to Poissonian limit of the usual laser. When we generalize the type of such nonlinear elements to the case of a nonlinear feedback or Raman type nonlinear transition, the noise in the laser intensity can be reduced even further and approach the ideal limit, characterized by a Mandel Q parameter of Q = —1. Furthermore we show how this noise reduction via nonlinearities can be combined with a regular pump mechanism, which recently has been sugessted as a way to generate sub—Poissonian light. It turns out that in certain configurations the effect of both methods can be combined. Finally we show how this nonclassical behaviour is also reflected in a reduction of the output intensity power spectra below the shot noise level.