Phase sensitivity of gain-unbalanced nonlinear interferometers

TL;DR

This paper investigates how gain imbalance and internal loss affect the phase sensitivity of nonlinear interferometers, revealing that the advantage of gain unbalancing depends on loss distribution and challenging the straightforward claim of Heisenberg scaling.

Contribution

It provides a detailed analysis of gain imbalance effects and internal loss on phase sensitivity, clarifying the conditions under which quantum advantage claims hold.

Findings

Gain unbalancing improves loss tolerance but does not enhance sensitivity.

Internal loss asymmetrically affects the performance depending on whether the source or analyzer dominates.

Heisenberg scaling claims are more nuanced in unbalanced setups.

Abstract

The phase uncertainty of an unseeded nonlinear interferometer, where the output of one nonlinear crystal is transmitted to the input of a second crystal that analyzes it, is commonly said to be below the shot-noise level but highly dependent on detection and internal loss. Unbalancing the gains of the first (source) and second (analyzer) crystals leads to a configuration that is tolerant against detection loss. However, in terms of sensitivity, there is no advantage in choosing a stronger analyzer over a stronger source, and hence the comparison to a shot-noise level is not straightforward. Internal loss breaks this symmetry and shows that it is crucial whether the source or analyzer is dominating. Based on these results, claiming a Heisenberg scaling of the sensitivity is more subtle than in a balanced setup.