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:1505.04387 · Physical Review Letters

Four-Dimensional Quantum Hall Effect with Ultracold Atoms

Hannah M. Price, Oded Zilberberg, Tomoki Ozawa, Iacopo Carusotto, Nathan Goldman

Published Nov 3, 2015• 257 citations
arXivHTMLPDF

Abstract

We propose a realistic scheme to detect the 4D quantum Hall effect using ultracold atoms. Based on contemporary technology, motion along a synthetic fourth dimension can be accomplished through controlled transitions between internal states of atoms arranged in a 3D optical lattice. From a semiclassical analysis, we identify the linear and nonlinear quantized current responses of our 4D model, relating these to the topology of the Bloch bands. We then propose experimental protocols, based on current or center-of-mass-drift measurements, to extract the topological second Chern number. Our proposal sets the stage for the exploration of novel topological phases in higher dimensions.

DOI
10.1103/physrevlett.115.195303

Related papers

Chiral ladders and the edges of quantum Hall insulators

Dario Hügel, Belén Paredes

The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as readily realizable bridges between one-dimensional spin-orbit (time-reversal) topological insulators and two-dimensional quantum Hall insulators. We reveal three instances of their promising potential: (i) they realize spin-orbit coupling, with the left-right leg degree of freedom playing the role of an effective spin, (ii) their energy bands and eigenstates exactly reproduce the topological chiral edge modes of two-dimensional Chern insulators, and (iii) they can be tailored to realize a topological phase transition from a trivial to a topological insulating phase. We propose realistic schemes to observe the chiral and topological properties of ladder systems with current optical lattice-based experiments. Our findings open a door to the exploration of the physics of the edges of quantum Hall insulators and to the realization of spin-orbit coupling and topological superfluid phases with ultracold atomic gases.

arXiv:1306.1190•Physical Review A•Feb 14, 2014•181 citations

Quantum anomalous Hall phase in a one-dimensional optical lattice

Sheng Liu, L. B. Shao, Qizhe Hou +1 more

We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin-orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin-orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.

Journal of Physics Condensed Matter•Jan 30, 2018•2 citations

Measurement of Chern numbers through center-of-mass responses

Hannah M. Price, Oded Zilberberg, Tomoki Ozawa +2 more

The remarkable quantization of the Hall conductivity is routinely observed in two-dimensional electron gases subject to strong magnetic fields. Such quantum transport experiments are performed by measuring the current that flows in 2D systems in response to an applied electric field, and result in a quantized conductance proportional to a topological index, known as the Chern number. Recently, a similar effect was proposed and observed in gases of ultracold atoms, when these are loaded into Bloch bands with a nonzero Chern number. In this context, the center of mass of the atomic gas performs a measurable differential drift, in direct analogy with the electronic Hall effect, from which the corresponding Chern number can be obtained. Such detection relies on the assumption that the center-of-mass drift of the atomic cloud is directly related to the current density, which itself depends on the Chern number of the band. Here, the authors carefully revisit and analyze the center-of-mass detection scheme. Interestingly, we find that the center-of-mass motion also depends on the particle density, which in the presence of magnetic perturbations, can be explicitly related to the topology of the band. Whereas this additional dependence offers a correction to existing experimental results, it opens up a rich variety of new possible quantized responses and detection schemes in 2D and 4D engineered systems, such as cold atoms and photonic lattices.

arXiv:1602.01696•Physical review. B./Physical review. B•Jun 6, 2016•86 citations

Realization of an atomic quantum Hall system in four dimensions

Jean-Baptiste Bouhiron, Aurélien Fabre, Qi Liu +5 more

Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to topological states predicted in dimensions D > 3. We report the realization of an atomic quantum Hall system evolving in four dimensions (4D), with two spatial dimensions and two synthetic ones encoded in the large spin of dysprosium atoms. We measure the nontrivial topological index of the ground band through a full characterization of the nonlinear electromagnetic response and observe the associated anisotropic hyperedge modes. We also excite nonplanar cyclotron motion, in contrast to the planar orbits in D ≤ 3. Our work may enable the investigation of strongly correlated topological liquids in 4D, generalizing fractional quantum Hall states.

Science•Apr 11, 2024•31 citations

Topological phases with ultracold atoms and photons

Alexandru Petrescu

We propose theoretical models that support topological phases and which are relevant to current experiments on lattices hosting photonic modes or ultracold atoms. In the first part of this thesis, we introduce a topological phase on a Kagom ́e lattice whose degrees of freedom are photons. In that context, we discuss two protocols to access the local Berry curvature and the Chern number of Bloch bands from semiclassical dynamics of wavepackets. Secondly, we obtain the phase diagram for bosons at unit filling with repulsive on–site interactions whose kinetic term corresponds to a Chern insulator defined on the honeycomb lattice. In the second part, we turn to recently realized quasi one–dimensional lattices, and un- cover their phase diagrams, comprising low–dimensional Meissner phases, chiral Mott insulating phases as well as abelian fractional quantum Hall states.

•Aug 27, 2015•0 citations

A two-dimensional realization of the parity anomaly

Nehal Mittal, Tristan Villain, Mathis Demouchy +4 more

Quantum anomalies arise when symmetries of a classical theory cannot be preserved upon quantization, leading to unconventional topological responses. A prominent example is the parity anomaly of a single two-dimensional Dirac fermion, which enforces a half-quantized Hall response. Anomaly inflow mechanism allows this effect to be observed at the surfaces of three-dimensional topological insulators, however, its realization in a genuinely two-dimensional system has remained elusive. Here we report the observation of a parity-anomalous Hall response at the critical point of a quantum Hall topological phase transition in a synthetic two-dimensional system of ultracold dysprosium atoms. By coupling a continuous spatial dimension to a finite synthetic dimension encoded in atomic spin states, we engineer tunable Chern bands with C = 0 and 1. At the transition, the bulk gap closes at a single Dirac point, where we observe a robust half-quantized Hall drift despite strong non-adiabatic excitations. We show that this response originates from the global structure of the band topology, is protected by an emergent parity symmetry at criticality, and disappears when parity is explicitly broken. Our work establishes synthetic quantum systems as a powerful platform to probe quantum anomalies and their interplay with topology and non-equilibrium dynamics.

cond-mat.quant-gasCross-listedarXiv:2603.22173•Mar 24, 2026
We propose a realistic scheme to detect the 4D quantum Hall effect using ultracold atoms. Based on contemporary technology, motion along a synthetic fourth dimension can be accomplished through controlled transitions between internal states of atoms arranged in a 3D optical lattice. From a semiclassical analysis, we identify the linear and nonlinear quantized current responses of our 4D model, relating these to the topology of the Bloch bands. We then propose experimental protocols, based on current or center-of-mass-drift measurements, to extract the topological second Chern number. Our proposal sets the stage for the exploration of novel topological phases in higher dimensions.
The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as readily realizable bridges between one-dimensional spin-orbit (time-reversal) topological insulators and two-dimensional quantum Hall insulators. We reveal three instances of their promising potential: (i) they realize spin-orbit coupling, with the left-right leg degree of freedom playing the role of an effective spin, (ii) their energy bands and eigenstates exactly reproduce the topological chiral edge modes of two-dimensional Chern insulators, and (iii) they can be tailored to realize a topological phase transition from a trivial to a topological insulating phase. We propose realistic schemes to observe the chiral and topological properties of ladder systems with current optical lattice-based experiments. Our findings open a door to the exploration of the physics of the edges of quantum Hall insulators and to the realization of spin-orbit coupling and topological superfluid phases with ultracold atomic gases.
We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin-orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin-orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.
The remarkable quantization of the Hall conductivity is routinely observed in two-dimensional electron gases subject to strong magnetic fields. Such quantum transport experiments are performed by measuring the current that flows in 2D systems in response to an applied electric field, and result in a quantized conductance proportional to a topological index, known as the Chern number. Recently, a similar effect was proposed and observed in gases of ultracold atoms, when these are loaded into Bloch bands with a nonzero Chern number. In this context, the center of mass of the atomic gas performs a measurable differential drift, in direct analogy with the electronic Hall effect, from which the corresponding Chern number can be obtained. Such detection relies on the assumption that the center-of-mass drift of the atomic cloud is directly related to the current density, which itself depends on the Chern number of the band. Here, the authors carefully revisit and analyze the center-of-mass detection scheme. Interestingly, we find that the center-of-mass motion also depends on the particle density, which in the presence of magnetic perturbations, can be explicitly related to the topology of the band. Whereas this additional dependence offers a correction to existing experimental results, it opens up a rich variety of new possible quantized responses and detection schemes in 2D and 4D engineered systems, such as cold atoms and photonic lattices.
Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to topological states predicted in dimensions D > 3. We report the realization of an atomic quantum Hall system evolving in four dimensions (4D), with two spatial dimensions and two synthetic ones encoded in the large spin of dysprosium atoms. We measure the nontrivial topological index of the ground band through a full characterization of the nonlinear electromagnetic response and observe the associated anisotropic hyperedge modes. We also excite nonplanar cyclotron motion, in contrast to the planar orbits in D ≤ 3. Our work may enable the investigation of strongly correlated topological liquids in 4D, generalizing fractional quantum Hall states.
We propose theoretical models that support topological phases and which are relevant to current experiments on lattices hosting photonic modes or ultracold atoms. In the first part of this thesis, we introduce a topological phase on a Kagom ́e lattice whose degrees of freedom are photons. In that context, we discuss two protocols to access the local Berry curvature and the Chern number of Bloch bands from semiclassical dynamics of wavepackets. Secondly, we obtain the phase diagram for bosons at unit filling with repulsive on–site interactions whose kinetic term corresponds to a Chern insulator defined on the honeycomb lattice. In the second part, we turn to recently realized quasi one–dimensional lattices, and un- cover their phase diagrams, comprising low–dimensional Meissner phases, chiral Mott insulating phases as well as abelian fractional quantum Hall states.
Quantum anomalies arise when symmetries of a classical theory cannot be preserved upon quantization, leading to unconventional topological responses. A prominent example is the parity anomaly of a single two-dimensional Dirac fermion, which enforces a half-quantized Hall response. Anomaly inflow mechanism allows this effect to be observed at the surfaces of three-dimensional topological insulators, however, its realization in a genuinely two-dimensional system has remained elusive. Here we report the observation of a parity-anomalous Hall response at the critical point of a quantum Hall topological phase transition in a synthetic two-dimensional system of ultracold dysprosium atoms. By coupling a continuous spatial dimension to a finite synthetic dimension encoded in atomic spin states, we engineer tunable Chern bands with C = 0 and 1. At the transition, the bulk gap closes at a single Dirac point, where we observe a robust half-quantized Hall drift despite strong non-adiabatic excitations. We show that this response originates from the global structure of the band topology, is protected by an emergent parity symmetry at criticality, and disappears when parity is explicitly broken. Our work establishes synthetic quantum systems as a powerful platform to probe quantum anomalies and their interplay with topology and non-equilibrium dynamics.