Dynamical stability of a many-body Kapitza pendulum

Roberta Citro; Emanuele G. Dalla Torre; Luca D'Alessio; Anatoli Polkovnikov; Mehrtash Babadi; Takashi Oka; Eugene Demler

doi:10.1016/j.aop.2015.03.027

Dynamical stability of a many-body Kapitza pendulum

Roberta Citro, Emanuele G. Dalla Torre, Luca D'Alessio, Anatoli Polkovnikov, Mehrtash Babadi, Takashi Oka, Eugene Demler

Department of Physics

Research output: Contribution to journal › Article › peer-review

77 Scopus citations

Abstract

We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine-Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and a numeric semiclassical calculation. Classical and quantum experiments are proposed to verify the validity of our results.

Original language	English
Pages (from-to)	694-710
Number of pages	17
Journal	Annals of Physics
Volume	360
DOIs	https://doi.org/10.1016/j.aop.2015.03.027
State	Published - 1 Sep 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.

Funding

The authors are grateful to T. Giamarchi, B. Halperin, D. Pekker, A. Russomanno, K. Sengupta, A. Tokuno for many useful discussions. The authors acknowledge the organizers of the KITP workshop on “Quantum Dynamics in Far from Equilibrium Thermally Isolated Systems”, during which this work was initiated, and the NSF Grant No. PHY11-25915 . ED acknowledges the support of Harvard-MIT CUA , NSF Grant No. DMR-07-05472 , AFOSR Quantum Simulation MURI , the ARO-MURI on Atomtronics, and the ARO-MURI Quism program. RC acknowledges the International Program of University of Salerno and the Harvard-MIT CUA . This research was supported by the Israel Science Foundation (Grant No. 1542/14 ). AP and LD acknowledge the support of NSF DMR-1206410 and AFOSR FA9550-13-1-0039 . MB was supported by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation .

Funders	Funder number
Harvard-MIT CUA
International Program of University of Salerno
National Science Foundation	1125846
Air Force Office of Scientific Research	FA9550-13-1-0039
Gordon and Betty Moore Foundation
Japan Society for the Promotion of Science	26400350
Israel Science Foundation	DMR-1206410, 1542/14

Keywords

Kapitza pendulum
Non-equilibrium physics
Periodic drive
Ultracold atom

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10.1016/j.aop.2015.03.027

Cite this

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abstract = "We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine-Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and a numeric semiclassical calculation. Classical and quantum experiments are proposed to verify the validity of our results.",

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AU - Dalla Torre, Emanuele G.

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AU - Babadi, Mehrtash

AU - Oka, Takashi

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AB - We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine-Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and a numeric semiclassical calculation. Classical and quantum experiments are proposed to verify the validity of our results.

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Dynamical stability of a many-body Kapitza pendulum

Abstract

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Keywords

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