Spectrum analysis with quantum dynamical systems

TL;DR

This paper establishes a fundamental quantum limit for spectral estimation accuracy in quantum systems, demonstrating near-optimal experimental performance and proposing a photon counting method that surpasses traditional techniques at low signal levels.

Contribution

It introduces a measurement-independent quantum limit for spectral estimation and proposes a photon counting method that achieves quantum-optimal performance in weak signal regimes.

Findings

Experimental performance with homodyne detection approaches the quantum limit.

Spectral photon counting outperforms homodyne detection at low SNR.

Theoretical proof of a fundamental quantum limit for spectral estimation.

Abstract

Measuring the power spectral density of a stochastic process, such as a stochastic force or magnetic field, is a fundamental task in many sensing applications. Quantum noise is becoming a major limiting factor to such a task in future technology, especially in optomechanics for temperature, stochastic gravitational wave, and decoherence measurements. Motivated by this concern, here we prove a measurement-independent quantum limit to the accuracy of estimating the spectrum parameters of a classical stochastic process coupled to a quantum dynamical system. We demonstrate our results by analyzing the data from a continuous optical phase estimation experiment and showing that the experimental performance with homodyne detection is close to the quantum limit. We further propose a spectral photon counting method that can attain quantum-optimal performance for weak modulation and a coherent-state input, with an error scaling superior to that of homodyne detection at low signal-to-noise ratios.