Study of Many-Body Spin Dynamics and Signatures of Discrete Time Crystal for Clock Transitions in a Solid-State System

Studying and controlling many-body interactions are central themes in quantum physics and information science, but computational complexities have posed challenges. In particular, Discrete Time Crystals, robust phases of matter in driven systems, result from many-body interactions and play an important role in understanding complex many-body systems. In this study, we investigate an ensemble of spins in a solid-state system, specifically rare-earth ions, to probe the signatures of discrete time crystals. These spins feature clock transitions and allow for long-range exchange interactions between them. Firstly, we demonstrate that spin-spin interactions dominate ensemble coherence, showcasing an ideal platform for studying many-body dynamics. Secondly, we achieve control over interaction strength by initializing varying spin populations. Lastly, through dynamic Hamiltonian engineering, we observe the emergence of robust subharmonic oscillations under periodic driving, providing evidence for the presence of a discrete time crystal. Our findings reveal rare-earth ions as a promising platform for studying many-body physics and offer valuable insights for their potential quantum applications.