Observation of Continuous Time Crystal in a Spin Maser System

Abstract

Pair interaction potentials between atoms in a crystal are in general non-monotonic in distance, with a local minimum whose position gives the lattice constant of the crystal. A temporal analogue of this idea of crystal formation is still pending despite intensive studies on the time crystal phase. In a hybrid spin maser system with a time delay feedback, we report the observation of a continuous time crystal induced by a retarded interaction with a characteristic time scale. This nonequilibrium phase features a self-sustained oscillation with an emergent frequency other than the intrinsic Larmor precession frequency of the spin maser system. It is shown that the amplitude of the oscillation is robust against perturbation, while its time phase randomly distributes from 0 to $2\pi$ for different realizations, a signature of spontaneous continuous time translation symmetry breaking. This CTC phase emerges only when the feedback strength exceeds a critical value, at which the system experiences a first order phase transition. Such a retarded interaction induced CTC is closer to the original idea of crystal, compared to mechanisms in other time crystal proposals.