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.

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.