Achieving a long lifetime synchronized state in a thermal vapor Rydberg time crystal

Abstract

Time crystals are a unique and recently discovered state of matter in which time-translational symmetry is spontaneously broken. Although this state has been observed across a variety of quantum systems, understanding the nature between driving, dissipation, and noise and the effects of these forces on the state lifetime remains elusive. Here, we study phase diffusion and entrainment of the time crystalline oscillatory state of a thermal-vapor Rydberg atom ensemble. We apply a pulsed rf heterodyne driving field which can entrain the oscillation frequency during the on driving period. During the off period, the entrained ensemble phase diffuses on a 1/$e$ timescale up to 2.3 ms -- significantly longer than the Rydberg state lifetime. We additionally study how the entrainment and phase diffusion timescales are affected by the strength and detuning of the rf driving field, and develop a classical Fokker-Planck model with an Adler-based driving term that reproduces the observed experimental findings. These results demonstrate the creation of a long-time synchronized time crystal Rydberg atom ensemble state, which could be utilized in applications requiring frequency and phase stability.