The optimal strategy of two-photon interferometric sensing in diverse noise environments

TL;DR

This work addresses how environmental phase noise affects two-photon interferometric sensing with Hong-Ou-Mandel (HOM) and N00N-state interferometers. Using a Fisher-information framework and Gaussian phase-noise models, it analyzes both spectrally non-resolved and spectrally resolved detections, deriving the noise-entered probabilities and the corresponding FI for each scheme. The key finding is that HOM interferometry is largely insensitive to phase noise (via the biphoton frequency-difference channel), whereas N00N-state interferometry is highly sensitive (via the frequency-sum channel); spectrally resolved detection consistently outperforms non-resolved detection and enables saturation of the quantum Cramér-Rao bound at arbitrary delays, extending the ambiguity-free dynamic range beyond the biphoton coherence time. Collectively, the results provide a practical strategy for deploying two-photon interferometric sensing across diverse noise environments, guiding the choice of interferometer and detection regime for high- vs. low-noise settings and potentially extending operational sensing ranges.

Abstract

Quantum sensing based on two-photon interferometry manifests quantum superiority beyond the classical precision limit. However, this superiority is usually diminished inevitably by the noise. Here, we analyze the sensitivity of two typical two-photon interferometries to the noise, that is, Hong-Ou-Mandel (HOM) and N00N state interferometry. It is found that HOM (N00N state) interference, which depends on the biphoton frequency difference (sum), is insensitive (sensitive) to the phase noise in both the manners of spectrally non-resolved and resolved detections in practice, suggesting their potential applications of sensing for different noise scenarios. Furthermore, spectrally resolved detection outperforms spectrally non-resolved one for the two interferometries, especially for the scope that exceeds the coherence time of biphotons. The findings provide an optimal strategy for the practical applications of two-photon interferometric sensing in diverse noise environments.

Figures (2)

• Figure 1: Fisher information, in units of $\omega_{p}^2$, as a function of $\omega_{p} \tau$ for (a) $\gamma=0,V=1$, (b) $\gamma=0,V=0.9$, and (c) $\gamma=0.4,V=0.9$. The dashed and solid lines represent spectrally resolved and non-resolved results, respectively, when $\eta_{\epsilon}\omega_p$=0 (blue), 1 (orange), and 3 (green). The bold black lines represent the QCRB.
• Figure 2: Fisher information, in units of $\omega_{p}^2$, as a function of $\omega_{p} \tau$ for $\eta_{\epsilon}\omega_p$=0 (blue), 1 (orange), and 3 (green). The first and second rows represent spectrally non-resolved and resolved results, respectively. The insets provide enlarged views to show more details. The bold black lines represent the QCRB.