Tunable discrete time crystals*

Discrete time crystals (DTCs) are emergent non-equilibrium phases of periodically driven many-body systems, where multiple interacting bodies settle into a dynamical collective steady state, breaking the discrete time translational symmetry of the Hamiltonian. Several questions regarding DTCs remain unanswered, for example, their stability mechanism against drive heating and fluctuations, possibility of realization in a classical system and existence of multiple DTC phases beyond subharmonic entrainment [1]. Here, we report observation of multiple DTC phases, including subharmonic, anharmonic, and a novel biharmonic phase, stabilized by dissipation, in a nanoelectromechanical system (NEMS) based on coupled graphene and silicon nitride membrane resonators [2]. Experimental evidence for emergence of many-body features, existence of long-range time and spatial order, and rigidity against parameter fluctuations or noise confirm the time-crystalline nature of these symmetry-broken phases. Furthermore, controlled mechanical strain drive transitions between these

phases with different symmetries, thereby mapping the emergent time-crystalline phase diagram. Analysis of a mean-field model provides crucial insights into the dynamical nature of these phases. However, failure of the mean-field model at time-crystalline phase boundary confirms many-body nature of the emergent DTC phases. These observations of the rich phase diagram with a range of distinct DTC phases rival the complexity of time crystals to that of spatial crystals.