A quantum Kolmogorov-Arnold-Moser theorem in the anisotropic Dicke model and its possible implications in the hybrid Sachdev-Ye-Kitaev models

Understand

The classical Kolmogorov-Arnold-Moser (KAM) theorem provides the underlying mechanism for the stability of the solar system under some small chaotic perturbations.

• Despite many previous efforts, any quantum version of the KAM theorem remains elusive In this work, we provide a quantum KAM theorem in the context of the anisotropic Dicke model which is the most important quantum optics model.
• It describes a single mode of photons coupled to $ N $ qubits with both a rotating wave (RW) term and a counter-RW (CRW) term.
• As the ratio of the CRW over the RW term increases from zero to one, the systems evolves from quantum integrable to quantum chaotic.