Continuous sensing and parameter estimation with the boundary time-crystal

TL;DR

This paper investigates a boundary time-crystal system for quantum sensing, demonstrating that its sensitivity scales with system size and measurement time, and proposing a cascaded setup to surpass standard quantum limits.

Contribution

It introduces a novel sensing scheme based on boundary time-crystals, showing how quantum correlations enable enhanced sensitivity and proposing a feasible measurement protocol.

Findings

Sensitivity scales as √T N, achieving standard quantum limit in time and Heisenberg limit in particle number.

Emergent quantum correlations in the time-crystal phase underpin enhanced sensitivity.

Cascading two time-crystals surpasses the standard quantum limit in measurement sensitivity.

Abstract

A boundary time-crystal is a quantum many-body system whose dynamics is governed by the competition between coherent driving and collective dissipation. It is composed of $N$ two-level systems and features a transition between a stationary phase and an oscillatory one. The fact that the system is open allows to continuously monitor its quantum trajectories and to analyze their dependence on parameter changes. This enables the realization of a sensing device whose performance we investigate as a function of the monitoring time $T$ and of the system size $N$. We find that the best achievable sensitivity is proportional to $\sqrt{T} N$, i.e., it follows the standard quantum limit in time and Heisenberg scaling in the particle number. This theoretical scaling can be achieved in the oscillatory time-crystal phase and it is rooted in emergent quantum correlations. The main challenge is, however, to tap this capability in a measurement protocol that is experimentally feasible. We demonstrate that the standard quantum limit can be surpassed by cascading two time-crystals, where the quantum trajectories of one time-crystal are used as input for the other one.