# Nonlinear metrology with a quantum interface

## TL;DR

This paper introduces nonlinear quantum atom-light interfaces and demonstrates their potential for enhanced quantum metrology, allowing measurements beyond the Heisenberg limit using collective atomic variables.

## Contribution

It develops a nonlinear effective Hamiltonian framework for atom-light interactions in rubidium ensembles, enabling improved quantum measurement techniques.

## Key findings

- Metrologically relevant properties can be measured better than the Heisenberg limit.
- The interface allows both linear and nonlinear estimation of atomic quantities.
- Model Hamiltonians suitable for nonlinear quantum metrology are realized in $^{87}$Rb ensembles.

## Abstract

We describe nonlinear quantum atom-light interfaces and nonlinear quantum metrology in the collective continuous variable formalism. We develop a nonlinear effective Hamiltonian in terms of spin and polarization collective variables and show that model Hamiltonians of interest for nonlinear quantum metrology can be produced in $^{87}$Rb ensembles. With these Hamiltonians, metrologically relevant atomic properties, e.g. the collective spin, can be measured better than the "Heisenberg limit" $\propto 1/N$. In contrast to other proposed nonlinear metrology systems, the atom-light interface allows both linear and non-linear estimation of the same atomic quantities.