Nature of the nonequilibrium phase transition in the non-Markovian driven Dicke model

Rex Lundgren, Alexey V. Gorshkov, and Mohammad F. Maghrebi
Phys. Rev. A 102, 032218 – Published 23 September 2020

Abstract

The Dicke model famously exhibits a phase transition to a superradiant phase with a macroscopic population of photons and is realized in multiple settings in open quantum systems. In this paper, we study a variant of the Dicke model where the cavity mode is lossy due to the coupling to a Markovian environment while the atomic mode is coupled to a colored bath. We analytically investigate this model by inspecting its low-frequency behavior via the Schwinger-Keldysh field theory and carefully examine the nature of the corresponding superradiant phase transition. Integrating out the fast modes, we can identify a simple effective theory allowing us to derive analytical expressions for various critical exponents including the dynamical exponent. We find excellent agreement with previous numerical results when the non-Markovian bath is at zero temperature; however, contrary to these studies, our low-frequency approach reveals that the same exponents govern the critical behavior when the colored bath is at finite temperature unless the chemical potential is zero. Furthermore, we show that the superradiant phase transition is classical in nature, while it is genuinely nonequilibrium. We derive a fractional Langevin equation and conjecture the associated fractional Fokker-Planck equation that captures the system's long-time memory as well as its nonequilibrium behavior. Finally, we consider finite-size effects at the phase transition and identify the finite-size scaling exponents, unlocking a rich behavior in both statics and dynamics of the photonic and atomic observables.

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  • Received 1 November 2019
  • Revised 25 June 2020
  • Accepted 24 July 2020
  • Corrected 19 April 2021

DOI:https://doi.org/10.1103/PhysRevA.102.032218

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Corrections

19 April 2021

Correction: The first entry in the fifth column of Table 1 was incorrect and has been fixed.

Authors & Affiliations

Rex Lundgren1, Alexey V. Gorshkov1,2, and Mohammad F. Maghrebi3

  • 1Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, College Park, Maryland 20742, USA
  • 2Joint Center for Quantum Information and Computer Science, National Institute of Standards and Technology and University of Maryland, College Park, Maryland 20742, USA
  • 3Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA

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Issue

Vol. 102, Iss. 3 — September 2020

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