Below-shot-noise capacity in phase estimation using nonlinear interferometers

TL;DR

This paper compares different nonlinear interferometer configurations for phase estimation, showing that the Mandel interferometer with differential detection offers the most robust shot-noise-limited sensitivity under realistic conditions.

Contribution

It provides a comparative analysis of three quantum-imaging schemes, highlighting the robustness of the Mandel interferometer with differential detection in practical scenarios.

Findings

Mandel interferometer with differential detection achieves the highest robustness.

Yurke interferometer can reach sub-shot-noise sensitivity under ideal conditions.

Performance of Yurke interferometer degrades in high-gain, lossy regimes.

Abstract

Over the past decade, several schemes for imaging and sensing based on nonlinear interferometers have been proposed and demonstrated experimentally. These interferometers exhibit two main advantages. First, they enable probing a sample at a chosen wavelength while detecting light at a different wavelength with high efficiency (bicolor quantum imaging and sensing with undetected light). Second, they can show quantum-enhanced sensitivities below the shot-noise limit, potentially reaching Heisenberg-limited precision in parameter estimation. Here, we compare three quantum-imaging configurations using only easily accessible intensity-based measurements for phase estimation: a Yurke-type SU(1,1) interferometer, a Mandel-type induced-coherence interferometer, and a hybrid scheme that continuously interpolates between them. While an ideal Yurke interferometer can exhibit Heisenberg scaling, this advantage is known to be fragile under realistic detection constraints and in the presence of loss. We demonstrate that differential intensity detection in the Mandel interferometer provides the highest and most robust phase sensitivity among the considered schemes, reaching but not surpassing the shot-noise limit, even in the presence of loss. Intensity measurements in a Yurke-type configuration can achieve genuine sub-shot-noise sensitivity under balanced losses and moderate gain; however, their performance degrades in realistic high-gain regimes. Consequently, in this regime, the Mandel configuration with differential detection outperforms the Yurke-type setup and constitutes the most robust approach for phase estimation.