Nonlinear Sideband Cooling to a Cat State of Motion

Though cavity optomechanics has demonstrated great progress in the quantum control of engineered mechanical systems, the ability to prepare arbitrary quantum states of motion has remained elusive. Of particular interest are macroscopic superpositions of mechanical motion known as cat states, which have potential for applications in quantum information and metrology, as well as studies of the fundamental limits of quantum mechanics. Here I will present theoretical work detailing a novel mechanical cat state preparation technique that utilizes the intrinsic nonlinearity of a dispersive optomechanical system. We show that by applying two continuous pumps to an optomechanical cavity, one can dissipatively engineer two-phonon processes that overwhelm linear loss in the mechanical resonator and stabilize it into a cat state of motion. Analyzing this protocol using a master equation approach, we show that the mechanical cat state exhibits significant Wigner negativity for single-photon optomechanical coupling rates exceeding the decay rate of the cavity. Though currently unattainable using state-of-the-art optomechanical systems, I will conclude by presenting an update on our experimental efforts to realize this protocol using superconducting millimeter-wave circuits.