Physical Emulation of Nonlinear Spin System Hamiltonians via Closed Loop Feedforward Control of a Collective Atomic Spin

In recent decades the field of quantum computation has seen remarkable development. While much progress has been made toward the realization of a fully digital, scalable, and fault tolerant quantum computer, there are still many essential challenges to overcome. In the interim, direct emulation of quantum systems of interest can fill an important gap not only for exploring fundamental questions about many-body physics and the quantum to classical transition, but also for potentially providing alternative methods to verify results from quantum simulations. In this work we will demonstrate a method utilizing closed loop control of the collective magnetic moment of an ensemble of cold neutral atoms via non-destructive measurements to emulate various spin system Hamiltonians. By modifying the feedback control law appropriately we are able to generate nonlinear dynamical behavior in the ensemble, allowing us to explore the physics of collective spin systems at mesoscopic scales. Moreover, controlling the number of atoms in the collective spin can potentially allow us to investigate these dynamics in the transition from fully quantum to the classical limit. In particular, we emulate two models: the Lipkin-Meshkov-Glick (LMG) Hamiltonian, and a closely related model, the Kicked Top. In the former case, we show that our system undergoes a symmetry-breaking phase transition in the expected parameter regime. In the latter, we explore two interesting aspects: the formation of chaos, and a dynamically driven time crystal phase. We will then discuss the advantages and limits of this approach.