# Quantum limited measurement of space-time curvature with scaling beyond the conventional Heisenberg limit

## TL;DR

This paper demonstrates a quantum measurement method that surpasses the Heisenberg limit by using non-linear Kerr materials in an interferometer to detect space-time curvature effects with enhanced precision.

## Contribution

The authors introduce a non-linear interferometric scheme that achieves a super-Heisenberg scaling in phase estimation, surpassing traditional quantum limits.

## Key findings

- Achieved phase estimation scaling of 1/N^{eta} with eta > 1.
- Demonstrated amplification of non-linear phase shift via high-intensity probe fields.
- Showed potential for highly precise measurements of space-time curvature.

## Abstract

We study the problem of estimating the phase shift due to the general relativistic time dilation in the interference of photons using a non-linear Mach-Zender interferometer setup. By introducing two non-linear Kerr materials, one in the bottom and one in the top arm, we can measure the non-linear phase $\phi_{NL}$ produced by the space-time curvature and achieve a scaling of the standard deviation with photon number ($N$) of $1/N^{\beta}$ where $\beta > 1$, which exceeds the conventional Heisenberg limit of a linear interferometer ($1/N$). The non-linear phase shift is an effect that is amplified by the intensity of the probe field. In a regime of high number of photons, this effect can dominate over the linear phase shift.