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Physical Review Letters

Quantum Noise in Phase Conjugation

Alexander L. Gaeta, Robert W. Boyd

Published Jun 20, 1988• 57 citations
Publisher

Abstract

We show by means of a quantum electrodynamic calculation that excess noise is inherent in the process of optical phase conjugation, both in that the state of the field leaving a phase-conjugate mirror can always be described classically (i.e., its phase-space density is positive semidefinite) and in that the fluctuations in the generated field are always greater than those predicted by Poisson statistics. Except in special cases, quantum noise imposes a limitation on the ability of phase conjugation to remove the effects of aberrations.

DOI
10.1103/physrevlett.60.2618

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We show by means of a quantum electrodynamic calculation that excess noise is inherent in the process of optical phase conjugation, both in that the state of the field leaving a phase-conjugate mirror can always be described classically (i.e., its phase-space density is positive semidefinite) and in that the fluctuations in the generated field are always greater than those predicted by Poisson statistics. Except in special cases, quantum noise imposes a limitation on the ability of phase conjugation to remove the effects of aberrations.
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A quantum theory of nearly degenerate backward four-wave mixing in a two-level atomic system is developed. The theory is used to calculate the quantum noise produced by a phase-conjugate mirror based on this system. The results indicate that in the case of pure radiative broadening the ideal quantum-noise limit is reached for relatively small pump-wave strengths and for relatively large probe-pump and pump-resonance detunings, so that the phase-conjugate reflectivity is far from its maximum value. Conversely, in the collisionally broadened case, operation closest to the quantum-noise limit occurs near the point of maximum reflectivity.
Quantum fluctuations and squeezing of the signal field generated by a degenerate optical parametric oscillator are sensitive to the phase and amplitude fluctuations of the second-harmonic pump. The analysis reported here extends our previous calculations for a perfectly monochromatic noise-free pump to allow for finite pump amplitude and phase fluctuations. We treat the typically intense pump field with its fluctuations as a classical Gaussian stochastic process in two limits: first, when the pump has amplitude fluctuations but its phase is fixed and second, when its phase diffuses but its amplitude is fixed. Since pump amplitude noise affects the evolution of the signal field multiplicatively, it has a lesser impact on the quantum fluctuations of the signal than pump phase diffusion which compromises such fluctuations via the extreme phase sensitivity of the parametric amplification process. For the latter limit, our calculations extend the work of Gea-Banacloche and Zubairy [Phys. Rev. A 42, 1742 (1990)] to cavities with arbitrary transmission coefficients for the bounding mirrors.
Quantisation of the electromagnetic field leads us simplistically to think of the field as fluctuating around some average value that could be predicted by a classical theory, whereas all statistical properties of the fluctuations must be derived from a quantum theory. The character of the fluctuations depends on the quantum state of the field. Even in a vacuum, where the average value of the field is zero, its mean square value due to fluctuations is positive. This quantum noise associated with these fluctuations is inherent and cannot be removed no matter how carefully we get rid of various environmental disturbances and fluctuations. But even though the quantum noise is here to stay, we can still control and manipulate it.