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Digest on Nonlinear Optics: Materials, Phenomena and Devices

Quantum Noise Reduction In Optical Fields

Daniel F. Walls, Matthew J. Collett, Alistair S. Lane, R. B. Levien

Published Jan 1, 1990• 0 citations
Publisher

Abstract

Current laser systems have phase and amplitude fluctuations which are partially quantum in origin. The amplitude fluctuations of a highly stabilized laser are shot noise limited, that is they have quantum fluctuations due to the Poissonian fluctuations of photons in a coherent state. These photon number fluctuations have been shown to have an origin in the incoherent pumping mechanism used for standard lasers. It has recently been demonstrated experimentally that by suppressing the amplitude fluctuations of the pump a laser output with reduced amplitude fluctuations is possible. The phase fluctuations in a laser are due to phase diffusion and are substantially above the quantum limit. Techniques to reduce the laser phase fluctuations have been proposed making use of correlated spontaneous emission.

DOI
10.1109/nlo.1990.695808

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Current laser systems have phase and amplitude fluctuations which are partially quantum in origin. The amplitude fluctuations of a highly stabilized laser are shot noise limited, that is they have quantum fluctuations due to the Poissonian fluctuations of photons in a coherent state. These photon number fluctuations have been shown to have an origin in the incoherent pumping mechanism used for standard lasers. It has recently been demonstrated experimentally that by suppressing the amplitude fluctuations of the pump a laser output with reduced amplitude fluctuations is possible. The phase fluctuations in a laser are due to phase diffusion and are substantially above the quantum limit. Techniques to reduce the laser phase fluctuations have been proposed making use of correlated spontaneous emission.
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.
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.
This paper clarifies the origins of the standard quantum limit for the amplitude noise of a laser-oscillator outgoing field. The amplitude noise within the cavity bandwidth, \ensuremath{\Omega}\ensuremath{\le}\ensuremath{\omega}/Q, is ultimately caused by the pump amplitude fluctuation, while that above the cavity bandwidth, \ensuremath{\Omega}\ensuremath{\ge}\ensuremath{\omega}/Q, is due to the field zero-point fluctuation. The uncertainty product of the amplitude- and phase-noise spectra at an extremely high pumping level is still larger than the Heisenberg minimum-uncertainty product because of the presence of nonstationary phase-diffusion noise. In this sense, an ordinary laser oscillator is not a quantum-limited device. This paper suggests that a laser oscillator can produce an amplitude-squeezed state in itself if the pump amplitude fluctuation is suppressed below the ordinary shot-noise level. The paper discusses possible schemes for suppressing pump fluctuation, commutator bracket preservation without pump fluctuation, and resulting amplitude and phase spectra. The similarity of and difference between a pump-noise-suppressed laser and a cavity degenerate parametric amplifier are delineated.
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.
As discussed in the last three chapters, the fundamental source of noise in a laser is spontaneous emission. A simple pictorial model for the origin of the laser linewidth envisions it as being due to the random phase diffusion process arising from the addition of spontaneously emitted photons with random phases to the laser field. In this chapter we show that the quantum noise leading to the laser linewidth can be suppressed below the standard, i.e., Schawlow–Townes limit by preparing the atomic systems in a coherent superposition of states as in the Hanle effect and quantum beat experiments discussed in Chapter 7. In such coherently prepared atoms the spontaneous emission is said to be correlated. Lasers operating via such a phase coherent atomic ensemble are known as correlated spontaneous emission lasers (CEL). An interesting aspect of the CEL is that it is possible to eliminate the spontaneous emission quantum noise in the relative linewidths by correlating the two spontaneous emission noise events. A number of schemes exist in which quantum noise quenching below the standard limit can be achieved. In two-mode schemes a correlation between the spontaneous emisson events in two different modes of the radiation field is established via atomic coherence so that the relative phase between them does not diffuse or fluctuate. In a Hanle laser and a quantum beat laser this is achieved by pumping the atoms coherently such that every spontaneously emitting atom contributes equally to the two modes of the radiation, leading to a reduction and even vanishing of the noise in the phase difference.
The basic equations governing noise phenomena are derived from first principles and applied to examples in optical communications. Quantum noise arises from two sources, the momentum fluctuations of electrons at optical frequencies and the uncertainty-related fluctuations of the electromagnetic field. Shot noise results from the beating of the noise sources with the signal field. In high-gain amplifiers, the spontaneous-emission noise dominates shot noise and results in a noise figure of at least 3 dB. It is shown explicitly how, at high power, both the laser field and the laser noise source become classical. The increase in noise in lasers with open cavities is not due to enhanced spontaneous emission as once thought, but to single-pass amplification. The noise fields and spontaneous currents have Gaussian distributions, while nonlasing modes have exponential photon-number distributions. Low-frequency intensity fluctuations arise from the electric current driving the laser and can be sub-Poissonian, in contrast to shot noise, which has a Poissonian distribution. The calculational tools are a wave equation for the field operator and a rate equation for the carrier-number operator, each containing spontaneous current noise sources. The correlation functions of these sources are determined by the fluctuation-dissipation theorem. [S0034-6861(96)00503-X]