Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa

Peter Kirton, Mor M. Roses, Jonathan Keeling, Emanuele G. Dalla Torre

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201 Citations (Scopus)
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The Dicke model describes the coupling between a quantized cavity field and a large ensemble of two-level atoms. When the number of atoms tends to infinity, this model can undergo a transition to a superradiant phase, belonging to the mean-field Ising universality class. The superradiant transition was first predicted for atoms in thermal equilibrium and was recently realized with a quantum simulator made of atoms in an optical cavity, subject to both dissipation and driving. In this Progress Report, we offer an introduction to some theoretical concepts relevant to the Dicke model, reviewing the critical properties of the superradiant phase transition, and the distinction between equilibrium and nonequilibrium conditions. In addition, we explain the fundamental difference between the superradiant phase transition and the more common lasing transition. Our report mostly focuses on the steady states of atoms in single-mode optical cavities, but we also mention some aspects of real-time dynamics, as well as other quantum simulators, including superconducting qubits, trapped ions, and using spin-orbit coupling for cold atoms. These realizations differ in regard to whether they describe equilibrium or non-equilibrium systems.
Original languageEnglish
Article number1800043
Number of pages18
JournalAdvanced Quantum Technologies,
Issue number1-2
Early online date16 Oct 2018
Publication statusPublished - 13 Feb 2019


  • Dicke model
  • nonequilibrium
  • phase transitions
  • quantum optics
  • superradiance


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