Signatures of chaos in periodically driven quantum systems

We study out-of-time-order correlation (OTOC) for one-dimensional periodically driven hardcore bosons in the presence of Aubry-Andr\'e (AA) potential and show that both the spectral properties and the saturation values of OTOC in the steady state of these driven systems provide a clear distinction between the localized and delocalized phases of these models. Our results, obtained via exact numerical diagonalization of these boson chains, thus indicate that OTOC can provide a signature of drive-induced delocalization, even for systems which do not have a well-defined semiclassical (and/or large $N$ ) limit. We demonstrate the presence of such a signature by analyzing two different drive protocols for hardcore boson chains leading to distinct physical phenomena and discuss experiments which can test our theory.We study out-of-time-order correlation (OTOC) for one-dimensional periodically driven hardcore bosons in the presence of Aubry-Andr\'e (AA) potential and show that both the spectral properties and the saturation values of OTOC in the steady state of these driven systems provide a clear distinction between the localized and delocalized phases of these models. Our results, obtained via exact numerical diagonalization of these boson chains, thus indicate that OTOC can provide a signature of drive-induced delocalization, even for systems which do not have a well-defined semiclassical (and/or large $N$) limit. We demonstrate the presence of such a signature by analyzing two different drive protocols for hardcore boson chains leading to distinct physical phenomena and discuss experiments which can test our theory.

arXiv:1804.01545Physical Review ANov 27, 201835 citations

Signatures of Quantum Chaos in Classically Non-Chaotic Systems

Efim B. Rozenbaum, Leonid Bunimovich, Victor M. Galitski

Bulletin of the American Physical SocietyMar 5, 20190 citations

Observing the emergence of chaos in a many-particle quantum system

Jiří Tomkovič, Wolfgang Muessel, Helmut Strobel +4 more

Accessing the connection between classical chaos and quantum many-body systems has been a long-standing experimental challenge. Here, we investigate the onset of chaos in periodically driven two-component Bose-Einstein condensates, whose small quantum uncertainties allow for exploring the phase space with high resolution. By analyzing the uncertainties of time-evolved many-body states, we find signatures of elliptic and hyperbolic periodic orbits generated according to the Poincaré-Birkhoff theorem, and the formation of a chaotic region at increasing driving strengths. The employed fluctuation analysis allows for probing the phase-space structure by use of only short-time quantum dynamics.Accessing the connection between classical chaos and quantum many-body systems has been a long-standing experimental challenge. Here, we investigate the onset of chaos in periodically driven two-component Bose-Einstein condensates, whose small quantum uncertainties allow for exploring the phase space with high resolution. By analyzing the uncertainties of time-evolved many-body states, we find signatures of elliptic and hyperbolic periodic orbits generated according to the Poincaré-Birkhoff theorem, and the formation of a chaotic region at increasing driving strengths. The employed fluctuation analysis allows for probing the phase-space structure by use of only short-time quantum dynamics.

arXiv:1509.01809Sep 6, 20154 citations

Dynamical Chaos In Quantum Systems

A. G. Lazerson, Alexey Alexeevich Boikov

Izvestiya of Saratov University PhysicsJan 1, 20100 citations

Measuring signatures of quantum chaos in strongly-interacting systems

Gregory S. Bentsen, Brian G. Swingle, Monika Schleier-Smith +1 more

Bulletin of the American Physical SocietyJun 9, 20170 citations

N

) limit. We demonstrate the presence of such a signature by analyzing two different drive protocols for hardcore boson chains leading to distinct physical phenomena and discuss experiments which can test our theory.