Extracting Lyapunov exponents from the echo dynamics of Bose-Einstein condensates on a lattice

• Verfasst von: Tarkhov, Andrei E. [VerfasserIn]
• Verfasst von: Wimberger, Sandro [VerfasserIn]
• Verfasst von: Fine, Boris V. [VerfasserIn]
• Titel: Extracting Lyapunov exponents from the echo dynamics of Bose-Einstein condensates on a lattice
• Verf.angabe: Andrei E. Tarkhov, Sandro Wimberger, and Boris V. Fine
• E-Jahr: 2017
• Jahr: 28 August 2017
• Umfang: 7 S.
• Fussnoten: Gesehen am 12.07.2018
• Titel Quelle: Enthalten in: Physical review
• Ort Quelle: Woodbury, NY : Inst., 2016
• Jahr Quelle: 2017
• Band/Heft Quelle: 96(2017,2) Artikel-Nummer 023624, 7 Seiten
• ISSN Quelle: 2469-9934
• DOI: doi:10.1103/PhysRevA.96.023624
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1577547446

Abstract

We propose theoretically an experimentally realizable method to demonstrate the Lyapunov instability and to extract the value of the largest Lyapunov exponent for a chaotic many-particle interacting system. The proposal focuses specifically on a lattice of coupled Bose-Einstein condensates in the classical regime describable by the discrete Gross-Pitaevskii equation. We suggest to use imperfect time reversal of the system's dynamics known as the Loschmidt echo, which can be realized experimentally by reversing the sign of the Hamiltonian of the system. The routine involves tracking and then subtracting the noise of virtually any observable quantity before and after the time reversal. We support the theoretical analysis by direct numerical simulations demonstrating that the largest Lyapunov exponent can indeed be extracted from the Loschmidt echo routine. We also discuss possible values of experimental parameters required for implementing this proposal.