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Floquet Engineering of Non-Equilibrium Superradiance

by Lukas Broers, Ludwig Mathey

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Submission summary

Authors (as registered SciPost users): Lukas Broers
Submission information
Preprint Link: scipost_202208_00086v1  (pdf)
Date accepted: 2022-10-27
Date submitted: 2022-08-30 15:58
Submitted by: Broers, Lukas
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
  • Quantum Physics
Approaches: Theoretical, Computational


We demonstrate the emergence of a non-equilibrium superradiant phase in the dissipative Rabi-Dicke model. This phase is characterized by a photonic steady state that oscillates with a frequency close to the cavity frequency, in contrast to the constant photonic steady state of the equilibrium superradiant phase in the Dicke model. We relate this superradiant phase to the population inversion of Floquet states by introducing a Schwinger representation of the driven two-level systems in the cavity. This inversion is depleted near Floquet energies that are resonant with the cavity frequency to sustain a coherent light-field. In particular, our model applies to solids within a two-band approximation, in which the electrons act as Schwinger fermions. We propose to use this Floquet-assisted superradiant phase to obtain controllable optical gain for a laser-like operation.

Author comments upon resubmission

We thank the Editor and the referees for their work. We have provided detailed responses to both referees, attached as replies to their reports.

List of changes

We have reworked the first two paragraphs of Section 1 to now include discussions on other dynamical phases of the Dicke model and how the FSP is distinct, as suggested by referee 1. These include the dynamical normal phase, superradiant lasers in nitrogen vacancy center spins and the Floquet maser.

We have reworked the third paragraph of Section 1 to give a more clear description of the FSP mechanism and how it translates to solid-state models, motivated by the points raised by referee 1.

We have extended the explanation of our model in Eq. 1 by introducing two other models (Eq. 2 and Eq. 3) for comparison, motivated by the points raised by referee 2. This helps the reader understand the units and the meaning of our effective driving field strength.

We have largely extended the explanation and motivation of our dissipative model in the paragraph following Eq. 9. This includes a more concise phrasing regarding the good cavity regime, the dependence of the FSP on dissipation and the validity of the dissipative model, motivated by points raised by both referees.

We have corrected notational inconsistencies in several equations, leading to minor modifications, i.e. factors of 2, across the main text. This necessitated a recalculation of our numerics which we have performed. We have updated all figures and their captions accordingly. These modifications do not change the overall results or conclusions of the manuscript. We have modified the discussions of Fig. 2 to reflect those changes in the paragraph following Eq. 15.

We have reworked Fig. 2 (c) such that it now shows a zoom-in, as suggested by referee 1.

We have included a discussion of realistic energy scales at which the FSP occurs on the example of light-driven graphene in the second to last paragraph of Section 3, motivated by the points raised by referee 2.

We have reworked the paragraph following Eq. 22 to now be more precise regarding how we calculate the Floquet energies in the FSP, motivated by the points raised by referee 1.

We have introduced a new paragraph into Section 6, at second to last position, which emphasizes how the FSP is distinct from other recently discussed dynamical phases, related to the discussion in Section 1.

We have performed some corrections to the appendix, motivated by the points raised by referee 1.

Published as SciPost Phys. 14, 018 (2023)

Reports on this Submission

Anonymous Report 2 on 2022-10-19 (Invited Report)


The authors have address all my previous concerns. The manuscript can now be published.

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Anonymous Report 1 on 2022-9-6 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202208_00086v1, delivered 2022-09-06, doi: 10.21468/SciPost.Report.5648


My main concern with this manuscript was a comparison of the FSP with previously observed dynamical superradiant phases. This is now addressed by the authors and can be found in the conclusion of their manuscript. In addition, the authors have corrected a few minor mistakes, improved Fig.2-4, and added further information and discussions to their draft. With this I can now recommend publication of this manuscript in SciPost Physics.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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