A cavity-QED simulator of slow and fast scrambling

TL;DR

This paper investigates information scrambling in a cavity QED system with large spins, revealing conditions for fast exponential growth of out-of-time order correlations and the influence of initial states and conserved quantities.

Contribution

It introduces a cavity QED model for studying scrambling, demonstrating how inhomogeneous couplings and initial spin orientations affect the growth of correlations.

Findings

Fast scrambling occurs with non-factorisable couplings and coplanar initial states.

OTOCs grow algebraically when conditions for fast scrambling are not met.

Initial state orientation and conserved quantities significantly influence scrambling dynamics.

Abstract

We study information scrambling, as diagnosed by the out-of-time order correlations (OTOCs), in a system of large spins collectively interacting via spatially inhomogeneous and incommensurate exchange couplings. The model is realisable in a cavity QED system in the dispersive regime. Fast scrambling, signalled by an exponential growth of the OTOCs, is observed when the couplings do not factorise into the product of a pair of local interaction terms, and at the same time the state of the spins points initially coplanar to the equator of the Bloch sphere. When one of these conditions is not realised, OTOCs grow algebraically with an exponent sensitive to the orientation of the spins in the initial state. The impact of initial conditions on the scrambling dynamics is attributed to the presence of a global conserved quantity, which critically slows down the evolution for initial states close to the poles of the Bloch sphere.