Protecting Heisenberg scaling in quantum metrology via engineered dressed states

TL;DR

This paper proposes using engineered dressed states in quantum systems to maintain Heisenberg scaling in quantum metrology despite environmental noise, by exploiting spectral properties of the environment.

Contribution

It introduces a dressed state approach that can preserve quantum sensitivity scaling under noise, extending beyond traditional criteria.

Findings

Heisenberg scaling achievable with dressed states under certain environmental conditions.

Dressed states can enable quantum advantage even when Hamiltonian is outside the Lindblad span.

Application demonstrated in NV-center thermometry with magnetic noise.

Abstract

Quantum metrology promises precision beyond classical limits but environmental noise, unless properly controlled, reduces the quantum advantage to at most a constant improvement. A key challenge is therefore to design quantum control strategies that suppress noise while preserving sensitivity to the targeted signal. Here, we suggest to use dressed states generated by static fields to achieve this goal and show that success of this strategy depends on the spectral properties of the environment. For low-temperature noise, we show that Heisenberg scaling can be achieved if and only if the signal generator lies outside the linear span of the system-environment coupling operators. This implies that the proper dressed states may enable Heisenberg scaling even in cases where the well-known Hamiltonian-not-in-Lindblad-span criterion, evaluated without dressing, would forbid it. We illustrate dressed state metrology for the example of NV-center thermometry under magnetic-field fluctuations, with the framework readily applicable to other platforms.