Phase properties of optical linear amplifiers
Abstract
We examine the effects of linear amplification and attenuation on the quantummechanical 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 phaseinsensitive and phasesensitive 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 phaseinsensitive amplification the phase of the field undergoes timedependent 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 phaseoptimized states (relative to coherent states of the same intensity) is lost for power gains greater than the photoncloning value of 2. In contrast, phasesensitive amplifiers give rise to timedependent 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 phaseinsensitive amplifier. Further squeezing of the amplifier reduces the added phase noise proportionally. We find that it is possible, using phasesensitive amplifiers, to amplify phaseoptimized states by power gains considerably larger than 2 and still retain a reduced phase variance.
 Publication:

Physical Review A
 Pub Date:
 June 1994
 DOI:
 10.1103/PhysRevA.49.4985
 Bibcode:
 1994PhRvA..49.4985V
 Keywords:

 42.50.p;
 42.60.Da;
 Quantum optics;
 Resonators cavities amplifiers arrays and rings