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Physical Review A

Quantum-noise suppression in lasers via memory-correlation effects

Claus Benkert, Marlan O. Scully, Abbas A. Rangwala, Wolfgang P. Schleich

Published Aug 1, 1990• 11 citations
Publisher

Abstract

We discuss the influence of atomic memory effects on the field fluctuations of a laser in a general context. We derive a Fokker-Planck equation for the field that takes into account the long lifetime of the lasing atoms. Using this equation, we discuss two consequences of atomic memory. First, we find that even in the presence of saturation, memory effects can lead to a reduction of spontaneous-emission noise for short measurement times. Second, we quite generally show that atomic memory effects lead to time-dependent diffusion coefficients.

DOI
10.1103/physreva.42.1503

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Physical Review A•Aug 1, 1993•3 citations
We discuss the influence of atomic memory effects on the field fluctuations of a laser in a general context. We derive a Fokker-Planck equation for the field that takes into account the long lifetime of the lasing atoms. Using this equation, we discuss two consequences of atomic memory. First, we find that even in the presence of saturation, memory effects can lead to a reduction of spontaneous-emission noise for short measurement times. Second, we quite generally show that atomic memory effects lead to time-dependent diffusion coefficients.
We demonstrate how spontaneous-emission noise in lasers and masers can be reduced through memory effects of the lasing atoms. We show that for short measurement times the spontaneous-emission noise can be smaller than the usual Schawlow-Townes limit. We discuss a general model for atomic memory effects and derive expressions for the noise correlation function, phase diffusion, and the emitted spectrum. Furthermore, we allow for a frequency distribution over the lasing atoms and hence account for Doppler broadening or a selective excitation of the atoms.
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.
An exact ccc-number generalized Fokker-Planck equation is derived for six noncommuting variables: the field variables, atomic populations, and atomic polarization of a laser model treated extensively by Lax. Langevin procedures yield the correct Fokker-Planck terms. Adiabatic eliminations are performed on the classical Markoff process given by the Fokker-Planck equation to compare with previous results. It is found that higher-order diffusion coefficients influence the second-order ones slightly during adiabatic elimination.
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 dressed-atom approach to the fluctuation problem in lasers is described. Such an approach allows one to analyze the fluctuations in various kinds of laser models. The intensity fluctuations in a regularly pumped laser are considered in the framework of the dressed-atom approach. The Fokker-Plank equation for the field density matrix is derived from first principles without heuristic assumptions. An alternative interpretation of the noise suppression in the regularly pumped laser is given. It is based upon the nonstationary picture for atomic variables. In such a regime the statistics of the output laser field may be controlled by the input statistics of the atomic initial conditions. It is the regular pump that provides the best input statistics. In the latter case the atoms are essentially nonstationary and coherently oscillate at the Rabi frequency. They are treated in a framework of the time-dependent picture in spite of the short atomic lifetime as compared with the cavity mode lifetime. The nonstationary version of the dressed-atom approach is employed to treat the regular pump case. It is demonstrated that a coherent coupling of the Rabi oscillations in the quadratic dressed-atom terms gives rise to a survival of a linear inverse proportional dependence of the atomic correlation functions upon field intensity. This survival in turn accounts for the anomalously large dressed-atom contribution to the fluctuations. Our results are in quantitative agreement with those of other approaches.