Periodic driving has emerged as a powerful tool to control, engineer, and characterize many-body quantum systems. However, the required pulse sequences are often complex, long, or require the ability to control the individual degrees of freedom. In this work, we study how a simple Carr-Purcell–Meiboom-Gill (CPMG)-like pulse sequence can be leveraged to enhance the coherence of a large ensemble of spin qubits and serve as an important characterization tool. We implement the periodic drive on an ensemble of dense nitrogen-vacancy (NV) centers in diamond and examine the effect of pulse rotation offset as a control parameter on the dynamics. We use a single diamond sample prepared with several spots of varying NV density, which, in turn, varies the NV-NV dipolar interaction strength. Counterintuitively, we find that rotation offsets deviating from the ideal 𝜋 pulse in the CPMG sequence (often classified as pulse errors) play a critical role in preserving coherence along an axis set by the 𝜋 pulses even at nominally zero rotation offset. The cause of the coherence preservation is an emergent effective field that scales linearly with the magnitude of the rotation offset for small offsets. In addition to extending coherence, we compare the rotation offset dependence of coherence to numerical simulations to measure the disorder and dipolar contributions to the Hamiltonian to quantitatively extract the densities of the constituent spin species within the diamond.

The discrete time crystal (DTC) is a nonequilibrium phase of matter that spontaneously breaks timetranslation symmetry. Disorder-induced many-body localization can stabilize the DTC phase by breaking ergodicity and preventing thermalization. Here, we observe the hallmark signatures of the manybody- localized DTC using a quantum simulation platform based on individually controllable carbon-13 nuclear spins in diamond. We demonstrate long-lived period-doubled oscillations and confirm that they are robust for generic initial states, thus showing the characteristic time-crystalline order across the many-body spectrum. Our results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.