Photon and photon-added intelligent states of coupled parametric oscillators

We study a quantum system of coupled oscillators subject to a periodic time dependence of its parameters. Using the Floquet-Lyapunov theory we derive linear non-Hermitian integrals of motion of the system and relate their covariance matrix to that of the canonical observables. The operator integrals allow us to construct states that saturate the Robertson uncertainty relation (intelligent states) for canonical operators and the corresponding photon-added states. We found explicit expressions for the wave function, Wigner function and covariance matrices of the latter. Copyright (C) 2021 EPLA