Detecting quantum noise of a solid-state spin ensemble with dispersive measurement

TL;DR

This paper analyzes dispersive measurement protocols for solid-state spin ensembles, aiming to achieve quantum-limited precision and detect spin squeezing for quantum-enhanced metrology.

Contribution

It provides a theoretical framework for dispersive readout of inhomogeneously broadened spin ensembles and proposes a protocol to detect spin squeezing.

Findings

Conditions for quantum-limited measurement noise are derived.

A protocol for detecting spin squeezing is proposed.

Analysis of measurement noise sources informs experimental design.

Abstract

We theoretically explore protocols for measuring the spin polarization of an ensemble of solid-state spins, with precision at or below the standard quantum limit. Such measurements in the solid-state are challenging, as standard approaches based on optical fluorescence are often limited by poor readout fidelity. Indirect microwave resonator-mediated measurements provide an attractive alternative, though a full analysis of relevant sources of measurement noise is lacking. In this work we study dispersive readout of an inhomogeneously broadened spin ensemble via coupling to a driven resonator measured via homodyne detection. We derive generic analytic conditions for when the homodyne measurement can be limited by the fundamental spin-projection noise, as opposed to microwave-drive shot noise or resonator phase noise. By studying fluctuations of the measurement record in detail, we also propose an experimental protocol for directly detecting spin squeezing, i.e. a reduction of the spin ensemble's intrinsic projection noise from entanglement. Our protocol provides a method for benchmarking entangled states for quantum-enhanced metrology.