Quantum control of mechanical systems via optimal nonharmonic potential engineering

Contrary to qubit-based, discrete systems, continuous quantum platforms enable encoding increased complexity into fewer physical systems through large-scale non-Gaussian states. Motion, as an exemplary continuous variable, can be manipulated through engineered nonharmonic potentials, which need not always yield strong nonlinearities. We present theoretical proposals for quantum control of mechanical motion across both strong and weak nonharmonic regimes. In the strongly nonlinear regime, relevant to atomic systems, we introduce time-dependent modulation of a nonharmonic potential that enables the generation of highly non-Gaussian states and universal operations within selected motional subspaces. In the weakly nonlinear regime, relevant to levitated massive nanoparticles, we propose dynamics in a static, wide double-well potential that support macroscopic quantum superpositions. Finally, we reconcile these approaches by showing that controlled potential modulation can extend non-Gaussian state preparation to weakly nonharmonic, massive levitated systems, providing a unified framework for mechanical quantum control.