Towards the generation of mechanical Kerr-cats: awakening the perturbative quantum Moyal corrections to classical motion

The quantum to classical transition is determined by the interplay of a trio of parameters: dissipation, nonlinearity, and macroscopicity. Why is nonlinearity needed to see quantum effects? And, is not an ordinary pendulum quite nonlinear already? In this manuscript, we discuss the parameter regime where the dynamics of a massive oscillator should be quantum mechanical in the presence of dissipation. We review the outstanding challenge of the dynamical generation of highly quantum mechanical cat states of a massive 'pendulum', known as Kerr-cats. We argue that state-of-the-art cold atom experiments may be in a position to reach such a nonlinear regime, which today singles out superconducting quantum circuits. A way to stabilize Schrodinger cat superpositions of a mechanical atomic oscillator via parametric squeezing and further protected by an unusual form of quantum interference is discussed. The encoding of a neutral atom Kerr-cat qubit is proposed.