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Physical Review A

Sub-Poissonian laser light by dynamic pump-noise suppression

Helmut Ritsch, P. Zoller, Crispin W. Gardiner, Daniel F. Walls

Published Sep 1, 1991• 82 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.44.3361

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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.
Based on the standard laser model of a large number N of model atoms resonantly coupled to a single lasing mode, we show that the nonlinear dynamics of the active atoms of the laser can lead to output-intensity fluctuations significantly reduced below the shot-noise level. We identify the multiple recycling of the active electron from the lower lasing level to the upper level through the pumping as the key process leading to this dynamic-pump-noise reduction. This process has been neglected in most of the standard treatments of the laser so far. We find that the results are closely related to recent calculations based on the assumption of an external regular pump. For the widely used four-level model of the active atoms, the intensity noise can be reduced 50% below the shot-noise level. Generalizing the model to an m-level system, we find a quantum-noise reduction by a factor of 1/2m/(m-1)(m\ensuremath{\ge}3), leading to perfect output-intensity noise reduction in the limit of a large number of intermediate steps in the recycling process of the active atoms. Finally, we demonstrate that the bandwidth of the noise reduction can be significantly enhanced using a nonlinear absorber in the cavity.
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).
The author reviews methods for generating sub-Poissonian light and related concepts. This light has energy fluctuations reduced below the level which corresponds to a classical Poissonian process (shot-noise level). After an introduction to the concept of nonclassical light, an overview is given of the main methods of quantum-noise reduction. Sub-Poissonian processes are exemplified in different areas of optics, ranging from single-atom resonance fluorescence to nonlinear optics, laser physics, and cavity quantum electrodynamics. Emphasis is placed on the conceptual foundations, and on developments in laser theory that lead to the possibility, already demonstrated experimentally, of linewidth narrowing and sub-Poissonian light generation in lasers and masers. The sources of quantum noise in these devices are analyzed, and four noise-suppression methods are discussed in detail: regularization of the pumping, suppression of spontaneous-emission noise, nonadiabatic evolution of the atomic variables, and twin-beam generation.
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.
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.
The quantum noise properties of atomic and semiconductor lasers are compared. The intensity fluctuation spectrum of the output field is calculated for the case of regularly, i.e., sub-Poissonian, pumped lasers. The effects of spontaneous emission on the output amplitude fluctuations may be suppressed in regularly pumped atomic lasers by requiring the lifetime of the lower lasing level to be short in comparison with that of the upper laser level. The output amplitude fluctuations then tend to zero at the laser frequency. In regularly pumped semiconductor lasers, net stimulated emission of photons dominates over spontaneous emission because of the combination of pumping and rapid intraband thermalization due to Coulomb scattering.