# Phonon dressing of a facilitated one-dimensional Rydberg lattice gas

### Submission summary

 As Contributors: Matteo Magoni Arxiv Link: https://arxiv.org/abs/2104.11160v2 (pdf) Date submitted: 2021-04-28 12:00 Submitted by: Magoni, Matteo Submitted to: SciPost Physics Academic field: Physics Specialties: Atomic, Molecular and Optical Physics - Theory Condensed Matter Physics - Theory Quantum Physics

### Abstract

We study the dynamics of a one-dimensional Rydberg lattice gas under facilitation (anti-blockade) conditions which implements a so-called kinetically constrained spin system. Here an atom can only be excited to a Rydberg state when one of its neighbors is already excited. Once two or more atoms are simultaneously excited mechanical forces emerge, which couple the internal electronic dynamics of this many-body system to external vibrational degrees of freedom in the lattice. This electron-phonon coupling results in a so-called phonon dressing of many-body states which in turn impacts on the facilitation dynamics. In our theoretical study we focus on a scenario in which all energy scales are sufficiently separated such that a perturbative treatment of the coupling between electronic and vibrational states is possible. This allows to analytically derive an effective Hamiltonian for the evolution of consecutive clusters of Rydberg excitations in the presence of phonon dressing. We analyze the spectrum of this Hamiltonian and show -- by employing Fano resonance theory -- that the interaction between Rydberg excitations and lattice vibrations leads to the emergence of slowly decaying bound states that inhibit fast relaxation of certain initial states.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 2104.11160v2 on 28 April 2021

## Reports on this Submission

### Strengths

1) Rigorous and clearly conveyed study of the dynamics of a 1D Rydberg lattice gas under excitation facilitation conditions
2) Analytical and numerical treatment of the hamiltonian of the system, providing a comprehensive discussion of its evolution
3) Explanation through Fano resonance theory of the observed inhibition of the relaxation of an initial state with a single Rydberg excitation

### Weaknesses

1) The choice of system to study may be better contextualized within the introduction
2) The experimental considerations sections is very valuable and may further benefit from expanding the discussion towards including current common experimental conditions

### Report

My overall view about the manuscript is very positive because it studies a topic relevant for the quantum simulation with Rydberg atoms community. Furthermore, the theoretical analysis is rigorous and clearly conveyed. This manuscript meets the acceptance criteria and it will be suitable for publication in SciPost Physics after a minor amendment. Please, find my list of suggestions in the requested changes section.

### Requested changes

1) The introduction would benefit by providing an improved contextualization of the choice of studying a 1D Rydberg lattice gas. Several experiments and theoretical studies have explored the facilitation process in a bulk gas and some have investigated the dynamics when an ordered trapping potential is present. The authors have implicitly covered this distinction through the references that they provided, but it may be helpful for the reader to have a more detailed introduction which would directly explain the choice of focusing this study on a 1D lattice gas system. May the existence of several experiments with reconfigurable tweezer arrays trapping ground state and/or Rydberg atoms provide a complimentary reason for this interest?
2) If possible, it may be helpful for the reader to provide an intuitive motivation of the advantage of using center of mass coordinates.
3) In figure 2 the authors describe several effects that emerge with increasing $k/\omega$ ratio. It may be of interest to note that the lower energy bands symmetry center shifts from $E/\Omega=0$ to negative values for larger $k/\omega$ ratios.
4) It may be beneficial to introduce explicitly the trap frequency $\omega$ at the beginning of section 2.
5) Would it be possible to provide an intuitive description of the origin of the repulsive potential shift $\alpha(k)$ when only one Rydberg excitation is present?
6) To simplify the comparison between the energy scales discussed in Sec 3,4 it would be convenient to write $\Gamma$ with the $2\pi$ factor, as done for the other quantities.
7) It would the interesting to expand the discussion in Sec 3,4 to a regime matching most of the current experiments, for example with $\omega=2\pi 100$ kHz and $\Omega=2\pi 20$ kHz. Would the predicted dynamics be close to the ones presented by the authors or would they change significantly? What would happen if the condition $\omega\gg\Omega$ is not respected?

• validity: high
• significance: good
• originality: high
• clarity: top
• formatting: perfect
• grammar: excellent