Achieving sub-shot-noise sensing at finite temperatures

Abstract

We investigate sensing of magnetic fields using quantum spin chains at finite temperature and exploit quantum phase crossovers to improve metrological bounds on the estimation of the chain parameters. In particular, we start by analyzing the X X spin chain. The magnetic sensitivity of this system is dictated by its magnetic susceptibility, which scales extensively (linearly) in the number of spins N . We introduce an iterative feed-forward protocol that actively exploits features of quantum phase crossovers to enable superextensive scaling of the magnetic sensitivity. Furthermore, we provide experimentally realistic observables to saturate the quantum metrological bounds. Finally, we extend our analysis on magnetic sensing to the Heisenberg X Y spin chain.