Quantum and classical lyapunov exponents in atom-field interaction systems

Date

2019-01-15

Authors

Santos, Lea F.
Chávez-Carlos, Jorge
López-del-Carpio, B.
Bastarrachea-Magnani, Miguel A.
Stránský, Pavel
Lerma-Hernández, Sergio
Hirsch, Jorge G.

Journal Title

Journal ISSN

Volume Title

Publisher

American Physical Society

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.

Description

Research article, peer-review. Open Access.

Keywords

Quantum quench, Quantum chaotic transport, quantum chaos, Quantum statistical mechanics, Quantum-to-classical transition, Quantum chaotic systems, quantum billiards, General Physics, Quantum Information, Condensed Matter & Materials Physics

Citation

Santos, Lea F., Jorge Chávez-Carlos, B López-del-Carpio, Miguel A Bastarrachea-Magnani, Pavel Stránský, Sergio Lerma-Hernández, Jorge G Hirsch. (2019). Physical Review Letters 122(2): 021401.