Controlling discrete time crystals via single-site operations in zero-field diamond quantum simulators

Abstract: Discrete time crystals (DTCs) have emerged as novel nonequilibrium phases of matter that spontaneously break discrete time-translation symmetry in periodically driven systems. Rigorous experimental validation of DTCs, which requires highly controllable quantum simulators, has stimulated extensive research across diverse fields in condensed matter physics and quantum information technologies. Among these advances, DTCs were demonstrated in a hybrid spin register within diamond, comprising a processor spin and surrounding memory spins. However, in conventional strategies involving a bias magnetic field, the field application effectively restricts the controllability of the processor spin. This limitation can be a significant barrier to the next goal of DTCs: achieving multifunctionality through enhanced local controllability. In this study, we theoretically propose multiple DTC protocols through the design of specific single-site control within the entire system. To this end, we consider a concrete model of a diamond-based quantum simulator operating without a bias magnetic field, thereby eliminating the restrictions on the processor spin. Our findings demonstrate that single-site operations enable access to DTCs with multiple distinct features in terms of periodicity and lifetime. Therefore, this approach provides a promising platform for creating diverse DTCs induced by single-site operations.