Semiclassical origin of suppressed quantum chaos in Rydberg chains

TL;DR

This paper reveals that stable classical periodic orbits in generalized Rydberg chains explain the suppression of quantum chaos and long-lived oscillations in highly excited states, with coherence times increasing with spin size.

Contribution

It introduces a classical limit for Rydberg chains with arbitrary spin, uncovering stable periodic orbits that explain suppressed quantum chaos and long coherence times.

Findings

Stable classical periodic orbits exist in generalized Rydberg chains.

Quantum chaoticity is parametrically suppressed by these orbits.

Semi-classical coherence times grow as the square root of the spin S.

Abstract

The surprisingly long-lasting oscillations observed in the dynamics of highly excited states of chains of Rydberg atoms defy the expectation that interacting systems should thermalize fast. The phenomenon is reminiscent of wavepackets in quantum billiards that trace classical periodic orbits. While analogs of the associated scarred eigenfunctions have been found for Rydberg chains, an underlying classical limit hosting periodic orbits has remained elusive. Here we generalize the Rydberg (pseudospin $S=1/2$) system to a chain of arbitrary spin $S$. Its classical limit features unexpectedly stable periodic orbits that are essential to understand the emergence of robust, parametrically suppressed quantum chaoticity, with semi-classical coherence times diverging as $\sqrt{S}$. The classical limit successfully explains several empirical features of the quantum limit.