Optimal control in phase space applied to minimal-time transfer of thermal atoms in optical traps

We present an optimal control procedure for the nonadiabatic transport of ultracold neutral thermal atoms in optical tweezers arranged in a one-dimensional array, with the focus on reaching a minimal transfer time. The particle dynamics is modeled first using a classical approach through the Liouville equation and second through the quantum Wigner equation to include quantum effects. Both methods account for typical experimental noise described as stochastic effects through Fokker-Planck terms. The optimal control process is initialized with a trajectory computed for a single classical particle and determines the phase-space path that minimizes transport time and ensures high transport fidelity to the target trap. This approach provides a fast and efficient method for relocating atoms from an initial configuration to a desired target arrangement, minimizing time and energy costs while ensuring high fidelity. Such an approach may be highly valuable to initialize large atom arrays for quantum simulation or computation experiments.