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Linear Anyon Model with Rydberg Atoms

Aditya Banerjee

Published Sep 1, 2026• 0 citations
Publisher

Abstract

Master’s thesis by Aditya Banerjee, Master in Quantum Science and Technology, Facultat de Física, Universitat de Barcelona, academic year 2025–2026. Supervisor: Prof. Alessio Celi. First published in the university repository in September 2026. Abstract We propose a scheme for quantum-simulating the one-dimensional anyon-Hubbard model with Rydberg atoms. Starting from the generalized Jordan–Wigner transformation, which trades anyonic exchange statistics for a density-dependent Peierls phase, we encode the truncated local occupations {|0⟩, |1⟩, |2⟩} in the internal levels of Rydberg atoms driven by Raman lasers with site-dependent phases. Adiabatically eliminating the far-detuned intermediate states in the dispersive regime yields an effective bond Hamiltonian whose four tunnelling amplitudes we obtain in second-order perturbation theory. First, we show that the Raman scheme allows one to simulate pseudo-fermions with bosons, but not generic anyons: Floquet driving is necessary to engineer a generic statistical phase. In fact, we find that single-tone Floquet driving leads to density-dependent amplitudes, but it is not sufficient to achieve the desired density-dependent tunnelling. This calculation suggests that to achieve the phases one needs a drive with several tones, each resonant with one occupation-resolved process and each carrying its own phase, a mechanism similar to the one employed in the recent few-particle realization of the anyon-Hubbard model with ultracold neutral atoms in optical lattices. Files and provenance Masters_Thesis_Banerjee_Aditya.pdf is the thesis PDF downloaded from the University of Barcelona repository. Permanent institutional identifier: https://hdl.handle.net/2445/231684. linear-anyon-rydberg-thesis-code-and-data-2295996.zip archives the code and saved data from the accompanying GitHub repository, commit 22959963191fcbc4d283ec4b272b506ad6dd979b, archived on 18 October 2026. It includes the README, 10 Python scripts, two saved NumPy datasets and the source manifest, with their original file contents unchanged. An ARCHIVE_CONTENTS.txt file describes the package. Reference figures remain available in the linked GitHub repository at the identified commit. Consult the repository README for figure mappings, dependencies and limitations. Rights The CC BY-NC-ND 4.0 licence listed for this record applies to the thesis PDF, matching the institutional record. The accompanying GitHub snapshot is supplied with its original rights retained; the source repository contained no separate software licence, and this deposit does not grant an additional software licence.

DOI
10.5281/zenodo.23443034

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Master’s thesis by Aditya Banerjee, Master in Quantum Science and Technology, Facultat de Física, Universitat de Barcelona, academic year 2025–2026. Supervisor: Prof. Alessio Celi. First published in the university repository in September 2026. Abstract We propose a scheme for quantum-simulating the one-dimensional anyon-Hubbard model with Rydberg atoms. Starting from the generalized Jordan–Wigner transformation, which trades anyonic exchange statistics for a density-dependent Peierls phase, we encode the truncated local occupations {|0⟩, |1⟩, |2⟩} in the internal levels of Rydberg atoms driven by Raman lasers with site-dependent phases. Adiabatically eliminating the far-detuned intermediate states in the dispersive regime yields an effective bond Hamiltonian whose four tunnelling amplitudes we obtain in second-order perturbation theory. First, we show that the Raman scheme allows one to simulate pseudo-fermions with bosons, but not generic anyons: Floquet driving is necessary to engineer a generic statistical phase. In fact, we find that single-tone Floquet driving leads to density-dependent amplitudes, but it is not sufficient to achieve the desired density-dependent tunnelling. This calculation suggests that to achieve the phases one needs a drive with several tones, each resonant with one occupation-resolved process and each carrying its own phase, a mechanism similar to the one employed in the recent few-particle realization of the anyon-Hubbard model with ultracold neutral atoms in optical lattices. Files and provenance Masters_Thesis_Banerjee_Aditya.pdf is the thesis PDF downloaded from the University of Barcelona repository. Permanent institutional identifier: https://hdl.handle.net/2445/231684. linear-anyon-rydberg-thesis-code-and-data-2295996.zip archives the code and saved data from the accompanying GitHub repository, commit 22959963191fcbc4d283ec4b272b506ad6dd979b, archived on 18 October 2026. It includes the README, 10 Python scripts, two saved NumPy datasets and the source manifest, with their original file contents unchanged. An ARCHIVE_CONTENTS.txt file describes the package. Reference figures remain available in the linked GitHub repository at the identified commit. Consult the repository README for figure mappings, dependencies and limitations. Rights The CC BY-NC-ND 4.0 licence listed for this record applies to the thesis PDF, matching the institutional record. The accompanying GitHub snapshot is supplied with its original rights retained; the source repository contained no separate software licence, and this deposit does not grant an additional software licence.
Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. However, the physics of one-dimensional (1D) anyons remains largely unexplored. Using ultracold bosonic Rb-87 atoms in an optical lattice, we realize and explore the anyon-Hubbard model, which hosts 1D anyons and features a rich phase diagram. We implement the model using techniques from Floquet engineering, realizing the statistical phase in the form of a density-dependent Peierls phase. Using our high-resolution imaging system, we explore both the dynamical and ground state behavior in the anyon-Hubbard model. In the first set of experiments, we probe 1D anyons via two-particle quantum walks, observing the anyonic Hanbury Brown-Twiss effect, as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. In the next set of experiments, we adiabatically prepare and probe ground states in the anyon-Hubbard model. First, we observe continuous fermionization in the density profile with increasing statistical phase. Then, we probe the chirality of the bound states in the anyon-Hubbard model, drawing similarities to a continuum model of 1D anyons. This work constitutes the first experimental study of the anyon-Hubbard model, and lays the foundation for exploration in the strongly correlated many-body regime.
Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. However, the physics of anyons in one dimension remains largely unexplored. In this work, we realize Abelian anyons in one dimension with arbitrary exchange statistics using ultracold atoms in an optical lattice, where we engineer the statistical phase through a density-dependent Peierls phase. We explore the dynamical behavior of two anyons undergoing quantum walks and observe the anyonic Hanbury Brown-Twiss effect as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. Our work forms the foundation for exploring the many-body behavior of one-dimensional anyons.
Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. Despite indications of a wealth of exotic phenomena, the physics of anyons in one dimension (1D) remains largely unexplored. Here, we realize Abelian anyons in 1D with arbitrary exchange statistics using ultracold atoms in an optical lattice, where we engineer the statistical phase via a density-dependent Peierls phase. We explore the dynamical behavior of two anyons undergoing quantum walks, and observe the anyonic Hanbury Brown-Twiss effect, as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. Our work forms the foundation for exploring the many-body behavior of 1D anyons.
We propose a simple scheme for mimicking the physics of one-dimensional anyons in an optical-lattice experiment. It relies on a bosonic representation of the anyonic Hubbard model to be realized via lattice-shaking-induced resonant tunneling against potential offsets, which are created by a combination of a lattice tilt and strong on-site interactions. No lasers additional to those used for the creation of the optical lattice are required. We also discuss experimental signatures of the continuous interpolation between bosons and fermions when the statistical angle θ is varied from 0 to π. Whereas the real-space density of the bosonic atoms corresponds directly to that of the simulated anyonic model, this is not the case for the momentum distribution. Therefore, we propose to use Friedel oscillations in the density as a probe for continuous fermionization of the bosonic atoms.
Quantum simulation with Rydberg ions in a Penning trap Authors: Wilson S. Martins, Markus Hennrich, Ferdinand Schmidt-Kaler, and Igor Lesanovsky This repository contains the numerical simulations used to generate the figures presented in the main text of the manuscript. All scripts are written in Python (.py) and generate output figures in the user's local directory. The most important folders in this repository are: https://github.com/matrices Contains the operators expressed in the fine-structure basis, truncated at orbital angular momentum l={S,P,…,H}. This includes, for example: The total Hamiltonian The dipole operator These matrices are used throughout the simulations. @figures Contains the post-processed figures in .pdf and .svg format used in the manuscript. The simulation scripts save pre-processed figures in this folder, which are subsequently edited for final presentation.