Effective versus Floquet theory for the Kerr parametric oscillator

Parametric gates and processes engineered from the perspective of the staticeffective Hamiltonian of a driven systemare central to quantum technology. How-ever, the perturbative expansions used toderive static effective models may not beable to efficiently capture all the relevantphysics of the original system.In thiswork, we investigate the conditions for thevalidity of the usual low-order static effective Hamiltonian used to describe a Kerroscillator under a squeezing drive. Thissystem is of fundamental and technological interest. In particular, it has been usedto stabilize Schr ''odinger cat states, whichhave applications for quantum computing.We compare the states and energies of theeffective static Hamiltonian with the ex-act Floquet states and quasi-energies ofthe driven system and determine the parameter regime where the two descriptionsagree. Our work brings to light the physicsthat is left out by ordinary static effectivetreatments and that can be explored bystate-of-the-art experiments.