## SciPost Submission Page

# The Vacua of Dipolar Cavity Quantum Electrodynamics

### by Michael Schuler, Daniele De Bernardis, Andreas M. Läuchli, Peter Rabl

### Submission summary

As Contributors: | Andreas Läuchli · Michael Schuler |

Arxiv Link: | https://arxiv.org/abs/2004.13738v2 (pdf) |

Date submitted: | 2020-07-06 02:00 |

Submitted by: | Schuler, Michael |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Quantum Physics |

### Abstract

The structure of solids and their phases is mainly determined by static Coulomb forces while the coupling of charges to the dynamical, i.e., quantized degrees of freedom of the electromagnetic field plays only a secondary role. Recently, it has been speculated that this general rule can be overcome in the context of cavity quantum electrodynamics (QED), where the coupling of dipoles to a single field mode can be dramatically enhanced. Here we present a first exact analysis of the ground states of a dipolar cavity QED system in the non-perturbative coupling regime, where electrostatic and dynamical interactions play an equally important role. Specifically, we show how strong and long-range vacuum fluctuations modify the states of dipolar matter and induce novel phases with unusual properties. Beyond a purely fundamental interest, these general mechanisms can be important for potential applications, ranging from cavity-assisted chemistry to quantum technologies based on ultrastrongly coupled circuit QED systems.

###### Current status:

### Submission & Refereeing History

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## Reports on this Submission

### Anonymous Report 1 on 2020-8-3 Invited Report

### Strengths

1. Studies a relevant problem of the interaction between cavity-mediated and short range interactions.

2. Identifies several novel and unanticipated forms of order - collective subradiant phase, and three sublattice superradiant states.

3. Shows how some of this physics can be understood by an effective model in the strong matter-light coupling limit.

4. Provides a good analysis of finite size effects and fluctuations near the phase boundaries.

### Weaknesses

In light of SciPost acceptance criterion 6, "Provide (directly in appendices, or via links to external repositories) all reproducibility-enabling resources: explicit details of experimental protocols, datasets and processing methods, processed data and code snippets used to produce figures, etc.;", I note that while this theoretical paper does clearly describe the methods that are used, the authors do not provide a link to a code repository or the direct numerical results of the simulations.

### Report

The manuscript by Schuler et al. discusses the phase diagram of a model of dipoles interacting both through a global cavity-mediated interaction, and through local (screened) electrostatic interactions. Such a model has been derived by some of the authors as the multipolar gauge form of effective Hamiltonian in previous work. The key purpose of this paper is to explore the consequences of this Hamiltonian and the nature of its ground state through finite-size exact diagonalization.

The work finds novel phases arise due to the competition of the two interactions, particularly in the context of the frustrated triangular lattice. I believe the results on the appearance of three sublattice superradiant states from the competition of frustrated Ising interactions and long range interactions are significant and could be considered both groundbreaking and as potentially opening up a new area of research. The results are clearly presented, and the manuscript sets this work in context of most other relevant work in this field (see below). For these reasons, I believe the work should be published. There are a few minor issues the authors should consider before publication noted below.

### Requested changes

1. On page 4, when commenting on the importance of including electrostatic screening for a consistent treatment of a cavity, it may be relevant to cite [Andras Vukics and Peter Domokos, Phys. Rev. A 86, 053807 (2012)], which made a similar point.

2. On page 6, above Eq. 4, there is a statement that the correlations functions are related to second order moments of the phase order parameters, while the equation written in (4) appear to relate them to first order moments of order parameters. This should be clarified.

3. On page 11, there is a comment about the apparent connection between the current results and supersolidity. In this context, there seems a far more immediate connection to make to experiments on cold atoms in cavities with Raman pumping, where there is competition between long-range cavity mediated interactions and short ranged interactions and hopping. e.g. [Klinder et al., Phys. Rev. Lett. 115, 230403 (2015); Landig et al, Nature 532, 476 (2016)]. While the nature of interactions there differs from the current problem, there may be relevant connections to draw.

4. On page 11, "has been constraint" should read "has been constrained"

5. On pages 15/16, in the text of section E and the caption of figure 8, there are references to the states (1,1-1) having peaks at the "edges of the hexagonal boundaries". From the figure, it appears this phrasing is referring to there being peaks at the corners of the hexagonal boundary. If correct, stating these are at the corners would be clearer.

6. Consider providing open data for the results of the numerical simulation, or access to a code repository to allow reproduction of these simulations.