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Optics Letters

Reduction of quantum fluctuation and suppression of the Gordon–Haus effect with phase-sensitive linear amplifiers

Horace P. Yuen

Published Jan 1, 1992• 88 citations
Publisher

Abstract

Compared with the use of phase-insensitive linear quantum amplifiers of the same gain G, the use of phase-sensitive linear amplifiers on phase coherent classical light sources in an amplifier-attenuator chain reduces the total quantum noise power by a factor of 4, the homodyne noise variance by 2, and the photon number variance by 2-8 and suppresses the Kerr effect linear phase fluctuation variance as well as the soliton timing-error variance by 2G(2).

DOI
10.1364/ol.17.000073

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Compared with the use of phase-insensitive linear quantum amplifiers of the same gain G, the use of phase-sensitive linear amplifiers on phase coherent classical light sources in an amplifier-attenuator chain reduces the total quantum noise power by a factor of 4, the homodyne noise variance by 2, and the photon number variance by 2-8 and suppresses the Kerr effect linear phase fluctuation variance as well as the soliton timing-error variance by 2G(2).
We study the possibility of employing phase-sensitive parametric amplifiers to compensate for losses incurred by solitons propagating in optical fibers. As phase-sensitive amplification is free from the excess spontaneous noise associated with laser amplifiers, the only quantum noise source in such a system arises from the fiber losses. In addition, under phase-sensitive amplification, fluctuations in the soliton frequency are squeezed to one half of the vacuum level, thus producing a negligible contribution to the fluctuations in the soliton arrival time. This greatly reduces the Gordon–Haus jitter of the solitons. The performance of the phase-sensitive amplifier is compared with that of alternative noise-reduction schemes employing phase-insensitive amplifiers and spectral filters as well as with the limits on long-distance data transmission imposed by quantum mechanics.
We examine the effects of linear amplification and attenuation on the quantum-mechanical phase properties of light for fields with mean photon numbers of at least the order of 10. The phase probability density is found to satisfy a diffusion equation for both phase-insensitive and phase-sensitive amplifiers and attenuators. The solution is a convolution of the initial phase probability density with an infinite series of expanding Gaussians which clearly illustrates the diffusion of the phase. In particular, we find that for phase-insensitive amplification the phase of the field undergoes time-dependent uniform diffusion. In the limit of large amplification the diffusion ceases and the phase variance of the amplified light is given by the input phase variance plus an extra term which is equal to the phase variance of a coherent state of the same intensity as the initial field. We show that the reduced phase variance of phase-optimized states (relative to coherent states of the same intensity) is lost for power gains greater than the photon-cloning value of 2. In contrast, phase-sensitive amplifiers give rise to time-dependent nonuniform phase diffusion. The amount of phase diffusion depends on the relative phase angle between the light and the amplifier. If the peak of a relatively narrow phase probability density is near a minimum in the phase diffusion coefficient, then the phase noise added by the amplifier will be less than that found for a phase-insensitive amplifier. Further squeezing of the amplifier reduces the added phase noise proportionally. We find that it is possible, using phase-sensitive amplifiers, to amplify phase-optimized states by power gains considerably larger than 2 and still retain a reduced phase variance.
It has long been known that amplification will degrade an optical signal and will rapidly destroy any intrinsically quantum features that may have been associated with the input. However, devices that exhibit squeezed fluctuations in the gain or loss medium can reduce the detrimental effects of the inevitable amplifier noise. This makes it possible to retain nonclassical features (in particular squeezing) at higher levels of gain than is possible in conventional devices. In this paper we study the effect of these amplifiers on the photon-number fluctuations. We find that, for suitable inputs, phase-sensitive amplifiers can reduce the tendency for the photon-number distribution to spread and allow us to retain sub-Poissonian statistics at a higher level of gain than is possible in conventional devices.
The principal problem of light amplifiers is to find a means to amplify a coherent amplitude without decreasing the SNR. Consider a signal with amplitude squeezed quantum fluctuations, that is, less noise in the amplitude quadrature than the phase quadrature. The objective is to find a phase sensitive amplifier, which, while amplifying the coherent amplitude, adds quantum noise preferentially to the phase quadrature. We take as a concrete model for the amplifier an intracavity parametric amplifier. We go beyond the usual linear analysis and include the nonlinear regime where pump depletion is important. We find that in the linear region the quantum noise added by the amplification process may be reduced by squeezing the idler mode, while in the nonlinear regime the quantum fluctuations from the pump become more important. These results are of direct application to practical light amplifiers.
We demonstrate a balanced-homodyne LADAR receiver employing a phase-sensitive amplifier (PSA) to raise the effective photon detection efficiency (PDE) to nearly 100%. Since typical LADAR receivers suffer from losses in the receive optical train that routinely limit overall PDE to less than 50% thus degrading SNR, PSA can provide significant improvement through amplification with noise figure near 0 dB. Receiver inefficiencies arise from sub-unity quantum efficiency, array fill factors, signal-local oscillator mixing efficiency (in coherent receivers), etc. The quantum-enhanced LADAR receiver described herein is employed in target discrimination scenarios as well as in imaging applications. We present results showing the improvement in detection performance achieved with a PSA, and discuss the performance advantage when compared to the use of a phase-insensitive amplifier, which cannot amplify noiselessly.