Effective versus Floquet theory for the Kerr parametric oscillator

TL;DR

This paper compares static effective Hamiltonian models with exact Floquet analysis for a Kerr parametric oscillator, highlighting the regimes where static approximations are valid and revealing physics missed by traditional static methods.

Contribution

It systematically evaluates the validity of low-order static effective Hamiltonians against Floquet theory for a driven Kerr oscillator, providing insights into their limitations and applicability.

Findings

Static effective Hamiltonians agree with Floquet states in certain parameter regimes.

Ordinary static treatments omit significant physics outside their validity range.

The work guides experimental exploration of driven Kerr systems.

Abstract

Parametric gates and processes engineered from the perspective of the static effective Hamiltonian of a driven system are central to quantum technology. However, the perturbative expansions used to derive static effective models may not be able to efficiently capture all the relevant physics of the original system. In this work, we investigate the conditions for the validity of the usual low-order static effective Hamiltonian used to describe a Kerr oscillator under a squeezing drive. This system is of fundamental and technological interest. In particular, it has been used to stabilize Schr\"odinger cat states, which have applications for quantum computing. We compare the states and energies of the effective static Hamiltonian with the exact Floquet states and quasi-energies of the driven system and determine the parameter regime where the two descriptions agree. Our work brings to light the physics that is left out by ordinary static effective treatments and that can be explored by state-of-the-art experiments.