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Physical Review A

Floquet time crystals as quantum sensors of ac fields

Fernando Iemini, Rosario Fazio, Anna Sanpera

Published May 30, 2024• 42 citations
Publisher

Abstract

The authors investigate the use of time-crystal phases for metrology, providing a concrete proposal as quantum sensors of AC fields. Their performance shows several useful advantages due to their long-range spatiotemporal ordering, overcoming the shot noise limit along with long interrogation times and robustness.
DOI
10.1103/physreva.109.l050203

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The long range spatial and temporal ordering displayed by discrete time crystals, can become advantageous properties when used for sensing extremely weak signals. Here, we investigate their performance as quantum sensors of weak AC-fields and demonstrate, using the quantum Fisher information measure, that they can overcome the shot noise limit while allowing long interrogation times. In such systems, collective interactions stabilize their dynamics against noise making them robust enough to protocol imperfections.
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We study the emergence of the prethermal Floquet time crystal (pFTC) in disordered chiral multiferroic chains. The model is an extension of the usual periodically driven nearest-neighbor disordered Heisenberg chain, with additional next-nearest-neighbor Heisenberg couplings and Dzyaloshinskii-Moriya interactions due to external magnetic and electric couplings. We derive the phase diagram of the model, characterizing the magnetization, entanglement, and coherence dynamics of the system along the extended interactions. In addition, we explore the application of the pFTC as quantum sensors of AC fields. The sensor performance to estimate small AC fields is quantified through the quantum Fisher information (QFI) measure. The sensor offers several advantages as compared to those composed of noninteracting spins due to its intrinsic robustness, long coherent interrogation time, and many-body correlations. Specifically, the sensor can overcome the standard quantum limit ($\mathrm{SQL}\ensuremath{\sim}{\mathrm{Nt}}^{2}$) during the prethermal regime, reaching an optimum performance at the pFTC lifetime t∗{t}^{*}t∗, where the $\mathrm{QFI}/{\mathrm{Nt}}^{{*}^{2}}\ensuremath{\sim}{\mathrm{N}}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}>0$, scaling superlinarly with the number of spins. Different from full FTCs, the prethermal lifetime does not diverge in the thermodynamic limit, nevertheless it can be increasingly long with tuning system parameters.
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 ∼N2t2\sim N^2 t^2∼N2t2) 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.
Sensing periodic fields using quantum sensors has been an active field of research. In many of these scenarios, the quantum state of the probe is flipped regularly by the application of $\ensuremath{\pi}$ pulses to accumulate information about the target periodic field. The emergence of a discrete time crystalline phase, as a nonequilibrium phase of matter, naturally provides oscillations in a many-body system with an inherent controllable frequency. They benefit from long coherence time and robustness against imperfections, which makes them excellent potential quantum sensors. In this paper, through theoretical and numerical analysis, we show that a disorder-free discrete time crystal probe can reach the ultimate achievable precision for sensing a periodic field. As the amplitude of the periodic field increases, the discrete time crystalline order diminishes, and the performance of the probe decreases remarkably. Nevertheless, the obtained quantum enhancement in the discrete time crystal phase, which is experimentally accessible using standard projective measurements, shows robustness against different imperfections and dephasing noise in the protocol. Finally, we propose the implementation of our protocol in ultracold atoms in optical lattices.