On Nonlinear Amplification: Improved Quantum Limits for Photon Counting

TL;DR

This paper demonstrates that nonlinear photon amplification can surpass the fundamental limits of linear amplification for photon detection, enabling more efficient single-photon detection by exploiting frequency shifts and noise suppression.

Contribution

It introduces a theoretical framework for nonlinear photon-number amplification, deriving new limits and transformations that improve upon traditional linear amplification constraints.

Findings

Nonlinear amplification can outperform linear limits in photon detection.

Frequency shifting in nonlinear processes helps suppress thermal noise.

The framework applies to practical systems like electron-shelving.

Abstract

We show that detection of single photons is not subject to the fundamental limitations that accompany quantum linear amplification of bosonic mode amplitudes, even though a photodetector does amplify a few-photon input signal to a macroscopic output signal. Alternative limits are derived for \emph{nonlinear} photon-number amplification schemes with optimistic implications for single-photon detection. Four commutator-preserving transformations are presented: one idealized (which is optimal) and three more realistic (less than optimal). Our description makes clear that nonlinear amplification takes place, in general, at a different frequency $\omega'$ than the frequency $\omega$ of the input photons. This can be exploited to suppress thermal noise even further up to a fundamental limit imposed by amplification into a single bosonic mode. A practical example that fits our description very well is electron-shelving.