Quantum Metrology in Correlated Environments

TL;DR

This paper analytically derives the limits of frequency measurement precision in correlated environments, revealing conditions under which entangled states outperform standard Ramsey spectroscopy and how precision bounds depend on particle number and environment type.

Contribution

It provides a variational approach to determine precision bounds in correlated Markovian and non-Markovian environments, highlighting scenarios where entangled states enhance measurement resolution.

Findings

Optimal measurement surpasses standard Ramsey spectroscopy in correlated environments.

Precision bounds depend on particle number parity and environment type.

In some non-Markovian environments, the usual bounds can be reversed.

Abstract

We analytically obtain the precision bounds of frequency measurements in correlated Markovian and non-Markovian environments by using a variational approach. It is verified that in standard Ramsey spectroscopy setup, the metrological equivalence of product and maximally entangled states persists in maximally correlated Markovian and non-Markovian environments. We find that the optimal measurement can achieve a much higher resolution than standard Ramsey spectroscopy in the correlated environments. When the number of particles in the maximally entangled states is even, the precision bound decreases with interrogation time; and when the number is odd, the precision bound is independent of interrogation time, both in correlated Markovian and general non-Markovian environments. In addition, the opposite case can appear in some special non-Markovian environments.