Optimal Phase-Insensitive Force Sensing with Non-Gaussian States

TL;DR

This paper explores how non-Gaussian quantum states, especially N-spaced and number-squeezed Schrödinger cat states, can optimize force sensing in continuous quantum systems, even under decoherence and experimental constraints.

Contribution

It introduces a force-sensing scheme using phase-space randomization and excitation-number-resolving measurements, demonstrating the advantages of non-Gaussian states and optimal control in lossy environments.

Findings

N-spaced states approach the quantum sensing bound.

Non-Gaussian states are more resilient to decoherence than Gaussian states.

Number-squeezed Schrödinger cat states maximize sensitivity under realistic conditions.

Abstract

Quantum metrology enables sensitivity to approach the limits set by fundamental physical laws. Even a single continuous mode offers enhanced precision, with the improvement scaling with its occupation number. Due to their high information capacity, continuous modes allow for the engineering of quantum non-Gaussian states, which not only improve metrological performance but can also be tailored to specific experimental platforms and conditions. Recent advancements in control over continuous platforms operating in the quantum regime have renewed interest in sensing weak forces, also coupling to massive macroscopic objects. In this work, we investigate a force-sensing scheme where a physical process completely randomizes the direction of the induced phase-space displacement, and the unknown force strength is inferred through excitation-number-resolving measurements. We find that $N$-spaced states, where only every $N^{\text{th}}$ Fock state occupation is nonzero, approach the achievable sensing bound. Additionally, non-Gaussian states are shown to be more resilient against decoherence than their Gaussian counterparts with the same occupation number. While Fock states typically offer the best protection against decoherence, we uncover a transition in the metrological landscape -- revealed through a tailored decoherence-aware Fisher-information-based reward functional -- where experimental constraints favor a family of number-squeezed Schr\"odinger cat states. Specifically, by implementing quantum optimal control in a minimal spin-boson system, we identify these states as maximizing force sensitivity under lossy dynamics and finite system controllability. Our results provide a pathway for enhancing force sensing in a variety of continuous quantum systems, ranging from massive systems like mechanical oscillators to massless systems such as quantum light and microwave resonators.