Quadrature Squeezing Enhances Wigner Negativity in a Mechanical Duffing Oscillator

Generating macroscopic nonclassical quantum states is a long-standing challenge in physics. Anharmonic dynamics is an essential ingredient to generate these states, but for large mechanical systems, the effect of the anharmonicity tends to become negligible compared with the effect of decoherence. As a possible solution to this challenge, we propose using a motional squeezed state as a resource to effectively increase the anharmonicity. We analyze the production of negativity in the Wigner distribution of a quantum anharmonic resonator initially in a squeezed state. We find that initial squeezing increases the rate at which negativity is generated. We also analyze the effect of two common sources of decoherence—namely, energy damping and dephasing—and find that the detrimental effects of energy damping are suppressed by strong squeezing. In the limit of large squeezing, which is needed for state-of-the-art systems, we find good approximations for the Wigner function. Our analysis is significant for current experiments attempting to prepare macroscopic mechanical systems in genuine quantum states. We provide an overview of several experimental platforms featuring nonlinear behaviors and low levels of decoherence. In particular, we discuss the feasibility of our proposal with carbon nanotubes and levitated nanoparticles.