Prethermal Floquet time crystals in chiral multiferroic chains and applications as quantum sensors of AC fields

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 ${t}^{*}$, 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.