Precision optical displacement measurements using biphotons

TL;DR

This paper demonstrates how biphoton correlations can significantly improve the precision of optical displacement measurements, achieving Heisenberg scaling, and analyzes the effects of correlation strength and detector resolution.

Contribution

It introduces a biphoton-based method for enhanced optical displacement measurement and explores the transition from quantum to classical scaling with imperfect correlations.

Findings

Precision improves with stronger biphoton correlations.

Smallest resolvable displacement scales as inverse of biphoton number.

Heisenberg scaling achieved for small biphoton numbers.

Abstract

We propose and examine the use of biphoton pairs, such as those created in parametric down conversion or four-wave mixing, to enhance the precision and the resolution of measuring optical displacements by position-sensitive detection. We show that the precision of measuring a small optical beam displacement with this method can be significantly enhanced by the correlation between the two photons, given the same optical mode. The improvement is largest if the correlations between the photons are strong, and falls off as the biphoton correlation weakens. More surprisingly, we find that the smallest resolvable parameter of a simple split detector scales as the inverse of the number of biphotons for small biphoton number ("Heisenberg scaling"), because the Fisher information diverges as the parameter to be estimated decreases in value. One usually sees this scaling only for systems with many entangled degrees of freedom. We discuss the transition for the split-detection scheme to the standard quantum limit scaling for imperfect correlations as the biphoton number is increased. An analysis of an $N$-pixel detector is also given to investigate the benefit of using a higher resolution detector. The physical limit of these metrology schemes is determined by the uncertainty in the birth zone of the biphoton in the nonlinear crystal.