Angular displacements estimation enhanced by squeezing and parametric amplification

TL;DR

This paper proposes a modified Mach-Zehnder interferometer with parametric amplifiers to enhance angular displacement estimation, surpassing the standard quantum limit and approaching the quantum Cramér-Rao bound.

Contribution

It introduces a novel interferometric setup with PAs for improved angular displacement sensitivity and analyzes its performance under different detection methods and photon loss effects.

Findings

Surpasses the standard quantum limit in angular displacement sensitivity.

Approaches the quantum Cramér-Rao bound with homodyne detection.

Photon losses reduce sensitivity but the method remains advantageous.

Abstract

We theoretically study the angular displacements estimation based on a modified Mach-Zehnder interferometer (MZI), in which two optical parametric amplifiers (PAs) are introduced into two arms of the standard MZI, respectively. The employment of PAs can both squeeze the shot noise and amplify the photon number inside the interferometer. When the unknown angular displacements are introduced to both arms, we derive the multiparameter quantum Cram\'er-Rao bound (QCRB) using the quantum Fisher information matrix approach, and the bound of angular displacements difference between the two arms is compared with the sensitivity of angular displacement using the intensity detection. On the other hand, in the case where the unknown angular displacement is in only one arm, we give the sensitivity of angular displacement using the method of homodyne detection. It can surpass the standard quantum limit (SQL) and approach the single parameter QCRB. Finally, the effect of photon losses on sensitivity is discussed.