Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems

TL;DR

This paper investigates the relationship between quantum and classical chaos by analyzing the exponential growth of the out-of-time-ordered correlator (OTOC) in the Dicke model, a realistic interacting system, finding a close match with classical Lyapunov exponents.

Contribution

It demonstrates the quantum-classical correspondence of chaos in a realistic interacting system, extending previous results beyond simple one-body models.

Findings

OTOC grows exponentially in the Dicke model with parameters where the classical limit is chaotic.

The exponential growth rate of the OTOC closely matches the classical Lyapunov exponent.

Validates the quantum signature of chaos in a many-body interacting system.

Abstract

The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos. The growth rate is expected to coincide with the classical Lyapunov exponent. This quantum-classical correspondence has been corroborated for the kicked rotor and the stadium billiard, which are one-body chaotic systems. The conjecture has not yet been validated for realistic systems with interactions. We make progress in this direction by studying the OTOC in the Dicke model, where two-level atoms cooperatively interact with a quantized radiation field. For parameters where the model is chaotic in the classical limit, the OTOC increases exponentially in time with a rate that closely follows the classical Lyapunov exponent.