Minimizing Losses in a Classical Nonlinear Oscillator

Shortcuts to adiabaticity (STAs) have been used to make quick changes to a system while eliminating or minimizing disturbances to the system’s state. Especially in quantum systems, these shortcuts allow us to minimize inefficiencies and heating in experiments and quantum computing, but the theory of STAs can also be generalized to classical systems. We focus on one such STA, counter-diabatic (CD) driving, and numerically compare its performance in both the quantum and classical versions of a quartic nonlinear oscillator. More specifically, we choose a classical figure of merit, which quantifies the disturbances to the system’s state, and a classical variational technique, which optimizes our driving to minimize disturbances. We then quickly change the strength of the nonlinearity in both systems and compare the classical figure of merit and variational technique to their well-established quantum versions. A reliable method for CD driving in classical oscillators could have many applications, from minimizing heating in bosonic gases to investigating classical nonlinear systems with many degrees of freedom, such as the Fermi-Pasta-Ulam-Tsingou lattice.