Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2606.12409

A Pfaffian quantum Hall state of ultracold bosons

Joyce Kwan, Perrin Segura, Yanfei Li, Tizian Blatz, Annie Zhi, Brice Bakkali-Hassani, Annabelle Bohrdt, Martin Greiter, Fabian Grusdt, Markus Greiner

cond-mat.quant-gascond-mat.str-elphysics.atom-phquant-phSubmitted Jun 10, 2026• Announced Jun 11, 2026• 0 citations
arXivHTMLPDF

Abstract

Fractional quantum Hall states are a cornerstone of topological physics, hosting fractionally charged quasiparticles with exotic statistics that promise to enable topologically protected quantum information processing. Among these, the Pfaffian state introduced by Moore and Read implements a p-wave pairing structure that supports excitations with non-Abelian exchange statistics. Despite extensive study in electronic systems, direct access to its pairing structure has remained limited. Here we realize a three-particle bosonic Pfaffian state of ultracold $^{87}\mathrm{Rb}$ atoms in an optical lattice subject to a Floquet-engineered synthetic magnetic field. Using a Bayesian-optimized adiabatic protocol, we prepare a state exhibiting Pfaffian pairing correlations. Site-resolved measurements of multi-point density correlations reveal a pronounced suppression of short-range three-body coincidences, reflecting the underlying pairing structure. We further probe the state's transport response through Hall drift measurements. Our results establish a bottom-up approach to engineering non-Abelian topological order and lay the groundwork for future explorations of anyonic braiding in synthetic matter.

Comments
9+11 pages, 5+9 figures

Related papers

Realization of a fractional quantum Hall state with ultracold atoms

Julian Léonard, Sooshin Kim, Joyce Kwan +5 more

Strongly interacting topological matter exhibits fundamentally new phenomena with potential applications in quantum information technology. Emblematic instances are fractional quantum Hall states, where the interplay of magnetic fields and strong interactions gives rise to fractionally charged quasi-particles, long-ranged entanglement, and anyonic exchange statistics. Progress in engineering synthetic magnetic fields has raised the hope to create these exotic states in controlled quantum systems. However, except for a recent Laughlin state of light, preparing fractional quantum Hall states in engineered systems remains elusive. Here, we realize a fractional quantum Hall (FQH) state with ultracold atoms in an optical lattice. The state is a lattice version of a bosonic $ν=1/2$ Laughlin state with two particles on sixteen sites. This minimal system already captures many hallmark features of Laughlin-type FQH states: we observe a suppression of two-body interactions, we find a distinctive vortex structure in the density correlations, and we measure a fractional Hall conductivity of $σ_\text{H}/σ_0= 0.6(2)$ via the bulk response to a magnetic perturbation. Furthermore, by tuning the magnetic field we map out the transition point between the normal and the FQH regime through a spectroscopic probe of the many-body gap. Our work provides a starting point for exploring highly entangled topological matter with ultracold atoms.

arXiv:2210.10919•Oct 19, 2022•5 citations

Bosonic Pfaffian state in the Hofstadter-Bose-Hubbard model

Felix A. Palm, Maximilian Buser, Julian Léonard +3 more

Topological states of matter, such as fractional quantum Hall states, are an active field of research due to their exotic excitations. In particular, ultracold atoms in optical lattices provide a highly controllable and adaptable platform to study such new types of quantum matter. However, finding a clear route to realize non-Abelian quantum Hall states in these systems remains challenging. Here we use the density-matrix renormalization-group (DMRG) method to study the Hofstadter-Bose-Hubbard model at filling factor $\ensuremath{\nu}=1$ and find strong indications that at $\ensuremath{\alpha}=1/6$ magnetic flux quanta per plaquette the ground state is a lattice analog of the continuum non-Abelian Pfaffian. We study the on-site correlations of the ground state, which indicate its paired nature at $\ensuremath{\nu}=1$, and find an incompressible state characterized by a charge gap in the bulk. We argue that the emergence of a charge density wave on thin cylinders and the behavior of the two- and three-particle correlation functions at short distances provide evidence for the state being closely related to the continuum Pfaffian. The signatures discussed in this letter are accessible in current cold atom experiments and we show that the Pfaffian-like state is readily realizable in few-body systems using adiabatic preparation schemes.

arXiv:2011.02477•Physical review. B./Physical review. B•Apr 5, 2021•30 citations

Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons

Yuhe Zhang, G. J. Sreejith, Jainendra K. Jain

The possibility of realizing bosonic fractional quantum Hall effect in ultracold atomic systems suggests a new route to producing and manipulating anyons, by introducing auxiliary bosons of a different species that capture quasiholes and thus inherit their nontrivial braiding properties. States with localized quasiholes at any desired locations can be obtained by annihilating the auxiliary bosons at those locations. We explore how this method can be used to generate non-Abelian quasiholes of the Moore-Read Pfaffian state for bosons at filling factor $\ensuremath{\nu}=1$. We show that a Hamiltonian with an appropriate three-body interaction can produce two-quasihole states in two distinct fusion channels of the topological ``qubit.'' Characteristics of these states that are related to the non-Abelian nature can be probed and verified by a measurement of the effective relative angular momentum of the auxiliary bosons, which is directly related to their pair distribution function. Moore-Read states of more than two quasiholes can also be produced in a similar fashion. We investigate some issues related to the experimental feasibility of this approach, in particular, how large the systems should be for a realization of this physics and to what extent this physics carries over to systems with the more standard two-body contact interaction.

arXiv:1505.06409•Physical Review B•Aug 10, 2015•32 citations

Particle-hole-symmetric model for a paired fractional quantum Hall state in a half-filled Landau level

William Hutzel, John J. McCord, Peter Raum +4 more

The fractional quantum Hall effect (FQHE) observed at half filling of the second Landau level is believed to be caused by a pairing of composite fermions captured by the Moore-Read Pfaffian wave function. The generating Hamiltonian for the Moore-Read Pfaffian is a purely three-body model that breaks particle-hole symmetry and lacks other properties, such as dominate two-body repulsive interactions, expected from a physical model of the FQHE. We use exact diagonalization to study the low-energy states of a more physical two-body generator model derived from the three-body model. We find that the two-body model exhibits the essential features expected from the Moore-Read Pfaffian: pairing, non-Abelian anyon excitations, and a neutral fermion mode. The model also satisfies constraints expected for a physical model of the FQHE at half-filling because it is short range, spatially decaying, particle-hole symmetric, and supports a roton mode with a robust spectral gap in the thermodynamic limit. Hence, this two-body model offers a bridge between artificial three-body generator models for paired states and the physical Coulomb interaction and can be used to further explore properties of non-Abelian physics in the FQHE.

arXiv:1811.02646•Physical review. B./Physical review. B•Jan 14, 2019•10 citations

Global Phase Diagram of the Fractional Quantum Hall Effect Arising from Repulsive Three-Body Interactions

Arkadiusz Wójs, Csaba Tőke, Jainendra K. Jain

The model of fermions in a magnetic field interacting via a purely three-body repulsive interaction has attracted interest because it produces, in the limit of short range interaction, the Pfaffian state with non-Abelian excitations. We show that this is part of a rich phase diagram containing a host of fractional quantum Hall states, a composite fermion Fermi sea, and a pairing transition. This is entirely unexpected, because the appearance of composite fermions and fractional quantum Hall effect is ordinarily thought to be a result of strong two-body repulsion. Recent breakthroughs in ultracold atoms have facilitated the realization of such a system, where this physics can be tested.

arXiv:1005.5493•Physical Review Letters•Nov 5, 2010•18 citations

The fractional quantum Hall effect at filling factor 5/2: numerically searching for non-abelian anyons

Michael R Peterson

We review some theoretical progress towards understanding the origin of the fractional quantum Hall effect at filling factor 5/2 using numerical techniques. The leading candidate thought to describe the physics is the Moore-Read Pfaffian state which supports non-abelian anyonic excitations. Interestingly, these excitations have possible applications in topologically protected quantum information processing. Specifically, we discuss how the finite-thickness of realistic quasi-two-dimensional systems stabilizes the Moore-Read Pfaffian in the fractional quantum Hall effect at 5/2 and the use of bilayer systems in the second Landau level to investigate the possible quantum phase transition between abelian and non-abelian fractional quantum Hall states.

Journal of Physics Conference Series•Dec 20, 2012•5 citations
Fractional quantum Hall states are a cornerstone of topological physics, hosting fractionally charged quasiparticles with exotic statistics that promise to enable topologically protected quantum information processing. Among these, the Pfaffian state introduced by Moore and Read implements a p-wave pairing structure that supports excitations with non-Abelian exchange statistics. Despite extensive study in electronic systems, direct access to its pairing structure has remained limited. Here we realize a three-particle bosonic Pfaffian state of ultracold 87Rb^{87}\mathrm{Rb}87Rb atoms in an optical lattice subject to a Floquet-engineered synthetic magnetic field. Using a Bayesian-optimized adiabatic protocol, we prepare a state exhibiting Pfaffian pairing correlations. Site-resolved measurements of multi-point density correlations reveal a pronounced suppression of short-range three-body coincidences, reflecting the underlying pairing structure. We further probe the state's transport response through Hall drift measurements. Our results establish a bottom-up approach to engineering non-Abelian topological order and lay the groundwork for future explorations of anyonic braiding in synthetic matter.
Strongly interacting topological matter exhibits fundamentally new phenomena with potential applications in quantum information technology. Emblematic instances are fractional quantum Hall states, where the interplay of magnetic fields and strong interactions gives rise to fractionally charged quasi-particles, long-ranged entanglement, and anyonic exchange statistics. Progress in engineering synthetic magnetic fields has raised the hope to create these exotic states in controlled quantum systems. However, except for a recent Laughlin state of light, preparing fractional quantum Hall states in engineered systems remains elusive. Here, we realize a fractional quantum Hall (FQH) state with ultracold atoms in an optical lattice. The state is a lattice version of a bosonic ν=1/2ν=1/2ν=1/2 Laughlin state with two particles on sixteen sites. This minimal system already captures many hallmark features of Laughlin-type FQH states: we observe a suppression of two-body interactions, we find a distinctive vortex structure in the density correlations, and we measure a fractional Hall conductivity of σH/σ0=0.6(2)σ_\text{H}/σ_0= 0.6(2)σH​/σ0​=0.6(2) via the bulk response to a magnetic perturbation. Furthermore, by tuning the magnetic field we map out the transition point between the normal and the FQH regime through a spectroscopic probe of the many-body gap. Our work provides a starting point for exploring highly entangled topological matter with ultracold atoms.
Topological states of matter, such as fractional quantum Hall states, are an active field of research due to their exotic excitations. In particular, ultracold atoms in optical lattices provide a highly controllable and adaptable platform to study such new types of quantum matter. However, finding a clear route to realize non-Abelian quantum Hall states in these systems remains challenging. Here we use the density-matrix renormalization-group (DMRG) method to study the Hofstadter-Bose-Hubbard model at filling factor $\ensuremath{\nu}=1$ and find strong indications that at $\ensuremath{\alpha}=1/6$ magnetic flux quanta per plaquette the ground state is a lattice analog of the continuum non-Abelian Pfaffian. We study the on-site correlations of the ground state, which indicate its paired nature at $\ensuremath{\nu}=1$, and find an incompressible state characterized by a charge gap in the bulk. We argue that the emergence of a charge density wave on thin cylinders and the behavior of the two- and three-particle correlation functions at short distances provide evidence for the state being closely related to the continuum Pfaffian. The signatures discussed in this letter are accessible in current cold atom experiments and we show that the Pfaffian-like state is readily realizable in few-body systems using adiabatic preparation schemes.
The possibility of realizing bosonic fractional quantum Hall effect in ultracold atomic systems suggests a new route to producing and manipulating anyons, by introducing auxiliary bosons of a different species that capture quasiholes and thus inherit their nontrivial braiding properties. States with localized quasiholes at any desired locations can be obtained by annihilating the auxiliary bosons at those locations. We explore how this method can be used to generate non-Abelian quasiholes of the Moore-Read Pfaffian state for bosons at filling factor $\ensuremath{\nu}=1$. We show that a Hamiltonian with an appropriate three-body interaction can produce two-quasihole states in two distinct fusion channels of the topological ``qubit.'' Characteristics of these states that are related to the non-Abelian nature can be probed and verified by a measurement of the effective relative angular momentum of the auxiliary bosons, which is directly related to their pair distribution function. Moore-Read states of more than two quasiholes can also be produced in a similar fashion. We investigate some issues related to the experimental feasibility of this approach, in particular, how large the systems should be for a realization of this physics and to what extent this physics carries over to systems with the more standard two-body contact interaction.
The fractional quantum Hall effect (FQHE) observed at half filling of the second Landau level is believed to be caused by a pairing of composite fermions captured by the Moore-Read Pfaffian wave function. The generating Hamiltonian for the Moore-Read Pfaffian is a purely three-body model that breaks particle-hole symmetry and lacks other properties, such as dominate two-body repulsive interactions, expected from a physical model of the FQHE. We use exact diagonalization to study the low-energy states of a more physical two-body generator model derived from the three-body model. We find that the two-body model exhibits the essential features expected from the Moore-Read Pfaffian: pairing, non-Abelian anyon excitations, and a neutral fermion mode. The model also satisfies constraints expected for a physical model of the FQHE at half-filling because it is short range, spatially decaying, particle-hole symmetric, and supports a roton mode with a robust spectral gap in the thermodynamic limit. Hence, this two-body model offers a bridge between artificial three-body generator models for paired states and the physical Coulomb interaction and can be used to further explore properties of non-Abelian physics in the FQHE.
The model of fermions in a magnetic field interacting via a purely three-body repulsive interaction has attracted interest because it produces, in the limit of short range interaction, the Pfaffian state with non-Abelian excitations. We show that this is part of a rich phase diagram containing a host of fractional quantum Hall states, a composite fermion Fermi sea, and a pairing transition. This is entirely unexpected, because the appearance of composite fermions and fractional quantum Hall effect is ordinarily thought to be a result of strong two-body repulsion. Recent breakthroughs in ultracold atoms have facilitated the realization of such a system, where this physics can be tested.
We review some theoretical progress towards understanding the origin of the fractional quantum Hall effect at filling factor 5/2 using numerical techniques. The leading candidate thought to describe the physics is the Moore-Read Pfaffian state which supports non-abelian anyonic excitations. Interestingly, these excitations have possible applications in topologically protected quantum information processing. Specifically, we discuss how the finite-thickness of realistic quasi-two-dimensional systems stabilizes the Moore-Read Pfaffian in the fractional quantum Hall effect at 5/2 and the use of bilayer systems in the second Landau level to investigate the possible quantum phase transition between abelian and non-abelian fractional quantum Hall states.