“…Time-dependent harmonic oscillators arise in quantum mechanical systems such as optical trapping of different objects like atoms and molecules [1,2], living cells, including viruses and bacteria [3,4]. Extensions to coupled time-dependent harmonic oscillators arise in several quantum mechanical problems, such as ion-laser interactions [1], quantized fields propagating through dielectric media [5], shortcuts to adiabaticity [6,7], the Casimir effect [8,9], as a toy model to study aspects of the final stages of black-hole evaporation [10], and their Schmidt modes in the study of quantum entanglement [11].…”