Exact analysis of AC sensors based on Floquet time crystals

TL;DR

This paper analyzes Floquet time crystals as AC sensors, demonstrating how their quantum Fisher information can be optimized for high precision measurements over long times, with behavior characterized by phase transitions and specific initial states.

Contribution

It provides an analytical framework for understanding QFI dynamics in FTC-based sensors, revealing conditions for Heisenberg scaling and critical behavior at phase transitions.

Findings

Heisenberg scaling precision achieved with FTC sensors

QFI exhibits step-like temporal structure due to dephasing

Sensor performance captured by critical exponents at phase transition

Abstract

We discuss the behavior of general Floquet time crystals (FTCs), including prethermal ones, in closed systems acting as AC sensors. We provide an analytical treatment of their quantum Fisher information (QFI) dynamics, which characterizes the ultimate sensor accuracy. By tuning the direction and frequency of the AC field, we show how to induce transitions resonantly between macroscopic paired cat states in the FTC sensor. This allows for robust Heisenberg scaling precision (QFI $\sim N^2 t^2$) for exponentially long times in the system size. The QFI dynamics exhibit, moreover, a characteristic step-like structure in time due to the eventual dephasing along the cat subspaces. The behavior is discussed for various initial sensor preparations, including ground states and low- and high-correlated states. Furthermore, we examine the performance of the sensor along the FTC phase transition, with the QFI capturing its critical exponents. Our findings are presented for both linear and nonlinear response regimes and illustrated for a specific FTC based on the long-range interacting LMG model.