Parametric systems

Parametric driving and its interplay with disorder and interactions in physical systems have led to numerous recent results, e.g., parametric resonance, synchronization, dynamical MBL, Floquet topological insulators, coherent destruction of tunnelling, and superfluid -insulator transitions in optical lattice systems. This contemporary research front opens up many opportunities as well as challenges. As initial steps in this direction, recently, we have revisited the simplest system of a harmonic oscillator subject to both parametric and external drives and were able to find novel sensing applications for nowadays technologies. Additionally, we have utilized parametric driving for proposing the generation of synthetic dimensions and gauges in atomic and photonic setups with prospects in bringing 4D topological physics to reality. Similarly, parametric drive is an inherent ingredient in realizing topological pumps, which we have demonstrated in both photonic and atomic setups. Last, we have predicted novel collective dynamic phases of parametrically driven light-matter systems.

As a result of our acquired experience and advanced methodology, we developed HarmonicBalance.jl -- a Julia package for solving nonlinear differential equations using the method of harmonic balance. Harmonic Balance methods efficiently approximate the dynamics of coupled resonator systems using a truncated Fourier expansion. The stationary states of the system are then obtained by solving a nonlinear system of equations that govern the amplitudes of the truncated ansatz. The package can assist numerous physics and engineering applications in out-of-equilibrium interacting systems.