Enhanced Ramsey-based quantum metrology using dissipative spin amplification

Quantum metrology protocols exploiting ensembles of two-level systems and Ramsey-style measurements are ubiquitous. While spin squeezing can allow the sensitivity of these measurements to surpass the standard quantum limit (SQL), this is only a useful strategy if excess detection noise is sufficiently small compared to spin-projection noise. This is not the case in many settings, especially sensing protocols based on ensembles of solid-state defect spins. In this work, we present a phase-insensitive "spin amplification" protocol that allows one to dramatically improve the sensitivity of schemes limited by excess detection noise. Our method is based on exploiting collective spin decay, an effect that is usually seen as a nuisance because it limits spin-squeezing protocols. We show that this approach can allow a system with extremely imperfect detection to approach the SQL within a factor of 2. Our ideas are compatible with several state-of-the-art experimental platforms where an ensemble of solid-state spins (NV centers, SiV centers) is coupled to a common microwave or mechanical mode.