Exploring quantum signatures of chaos on a Floquet synthetic lattice

Ergodicity and chaos play an integral role in the behavior of dynamical systems and are crucial to the formulation of statistical mechanics. Still, a general understanding of how ergodicity and chaos emerge in the dynamical evolution of closed quantum systems remains elusive. Here, we develop an experimental platform for the realization of canonical quantum chaotic Hamiltonians based on quantum simulation with synthetic lattices. We map the angular momentum projection states of an effective quantum spin onto the linear momentum states of a Rb87 Bose-Einstein condensate, which can be alternatively viewed as synthetic lattice sites. This synthetic lattice, with local and dynamical control of tight-binding lattice parameters, enables new capabilities related to the experimental study of quantum chaos. In particular, the capabilities of our system let us tune the effective size of our spin, allowing us to illustrate how classical chaos can emerge from a discrete quantum system. Moreover, spectroscopic control over our synthetic lattice allows us to explore unique aspects of our spin's dynamics by measuring the out-of-time-ordered correlation function and enables future investigations into new symmetry classes of chaotic kicked-top systems.