Discrete time crystal for periodic-field sensing with quantum-enhanced precision

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 $\pi$-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 ultra-cold atoms in optical lattices.