Generalised expression of the noise figure of phase sensitive amplifiers for an arbitrary number of modes

TL;DR

This paper derives a general quantum noise figure expression for phase sensitive amplifiers with multiple modes, showing how additional waves can degrade amplification noise performance.

Contribution

It provides the first analytical quantum derivation of PSA noise figure for arbitrary mode numbers, accounting for extra waves from nonlinear processes.

Findings

Noise figure depends on the number of interacting waves.

For six-wave interactions, noise figure degrades by 0.4 dB.

Compared to PIA, the scheme achieves a 10 dB NF under ideal conditions.

Abstract

Phase sensitive amplifiers (PSA), contrary to usual phase insensitive amplifiers (PIA), are in principle capable to achieve noiseless amplification, i.e. exhibit a quantum-limited noise figure (NF) of 0 dB. When implemented using four-wave mixing (FWM) in a nonlinear fiber, extra waves can be generated by undesired FWM processes, which may introduce extra input ports for vacuum fluctuations, thus potentially degrading the NF. In this situation, we give here a general analytical quantum derivation of the PSA NF, valid for an arbitrary number of nonlinearly coupled modes. This expression is usable as soon as a linear input-output relation can be found for the annihilation and creation operators of the involved modes. It predicts that the noise level depends on the number of interacting waves. We illustrate the usefulness of this expression in the case of six waves, corresponding to four interacting quantum modes. In this example the signal NF is degraded by 0.4 dB, compared to 10 dB obtained for PIA operation of the same scheme.