Continuous Observation of a Long Lived Prethermal Discrete Time Crystal by Two Frequency Driving*

We report the observation of long-lived Floquet prethermal discrete time crystals (PDTCs) in a three-dimensional

position disordered lattice of dipolar-coupled ¹³C nuclei in diamond at room temperature. We propose and

demonstrate a novel strategy of ``two frequency’’ driving, involving an interleaved application of slow and fast

drives of period τ and t respectively, that simultaneously prethermalize the spins along a Bloch sphere axis x,

while enabling observation of their dynamic evolution when periodically kicked away from x. The PDTC phase

appears as a robust period-doubling response of the spin magnetization interchanging between x and -x; our

experiments allow a unique means to study the formation and melting of this PDTC phase leveraging a

continuous interrogation of the spins during the fast drive. This permits the production of ``movies’’ of the time-

crystallization process with a clarity and experimental throughput orders of magnitude higher that previous

reports. With this, we report a highly long-lived PDTC lasting over 10s in time (corresponding to

>10⁵ pulses of the fast drive) and measurable in a single-shot of the experiment. Such rapid measurement enables a

detailed experimental characterization of the PDTC rigidity, informing on the role of prethermalization towards

stabilizing the DTC response. The two frequency drive approach represents the simplest generalization of DTCs to higher time

dimensions, and as such expands the toolkit for Floquet engineering. Overall, this work points to new opportunities available for

exciting and stabilizing far-from-equilibrium phases of matter in solids with hyperpolarizable, dilute, low-sensitivity nuclei.