Ashok Ajoy

Prethermal discrete time crystals (PDTCs) are a nonequilibrium state of matter characterized by long-range spatiotemporal order, and exhibiting a subharmonic response stabilized by many-body interactions under periodic driving. The inherent robustness of time crystalline order to perturbations in the drive protocol makes DTCs promising for applications in quantum technologies. We exploit the susceptibility of PDTC order to deviations in its order parameter to devise highly frequency-selective quantum sensors for time-varying (AC) magnetic fields in a system of strongly-driven, dipolar-coupled 13C nuclear spins in diamond. Integrating a time-varying AC field into the PDTC allows us to exponentially increase its lifetime, with improvements of up to three orders of magnitude (44,204 cycles), and results in a strong resonant response in the time crystalline order parameter. The linewidth of our sensor is limited by the PDTC lifetime alone, as strong interspin interactions help stabilize DTC order. The sensor operates in the 0.5-50kHz range - a challenging frequency regime for sensors based on atomic vapor or electronic spins - and attains a competitive sensitivity. PDTC sensors are resilient to errors in the drive protocol and sample inhomogeneities, and are agnostic to the macroscopic details of the physical platform: the underlying physical principle applies equally to superconducting qubits, neutral atoms, and trapped ions.

Controlling the interaction graph between spins or qubits in a quantum simulator allows user-controlled tailoring of native interactions to achieve a target Hamiltonian. The flexibility of engineering long-ranged phonon-mediated spin-spin interactions in a trapped ion quantum simulator offers such a possibility. Trapped ions, a leading candidate for simulating computationally hard quantum many-body dynamics, are most readily trapped in a linear 1D chain, limiting their utility for readily simulating higher dimensional spin models. In this work, we introduce a hybrid method of analog-digital simulation for simulating 2D spin models and dynamically changing interactions to achieve a new graph using a linear 1D chain. The method relies on time domain Hamiltonian engineering through a successive application of Stark shift gradient pulses, and wherein the pulse sequence can simply be obtained from a Fourier series decomposition of the target Hamiltonian over the space of lattice couplings. We focus on engineering 2D rectangular nearest-neighbor spin lattices, demonstrating that the required control parameters scale linearly with ion number. This hybrid approach offers compelling possibilities for the use of 1D chains in the study of Hamiltonian quenches, dynamical phase transitions, and quantum transport in 2D and 3D. We discuss a possible experimental implementation of this approach using real experimental parameters.