Discrete time crystal in a driven-dissipative Bose-Hubbard model with two-photon processes

We propose a scheme for discrete time crystals (DTCs) based on the metastability of the driven-dissipative Bose-Hubbard model, linking the two metastable states as such using rotation operations and two-photon processes. Numerical analyses in finite size, through the Gutzwiller Monte Carlo approach, validate our scheme, where the couplings between different sites are taken into account. Requiring only local dissipations and uniform rotations, our scheme is feasible on the state-of-the-art noisy intermediate-scale quantum platforms, e.g., superconducting circuits and ultracold atoms. The robustness of the proposed DTC is guaranteed by construction due to the metastability. Our scheme provides a simple test bed for studying the less explored field of nonequilibrium phases of matter in physics and exploring more possibilities of quantum simulations.