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:1102.5283 · Physical Review B

Dirac-Weyl fermions with arbitrary spin in two-dimensional optical superlattices

Zhihao Lan, Nathan Goldman, A. Bermúdez, W. Lu, Patrik Öhberg

Published Oct 14, 2011• 119 citations
arXivHTMLPDF

Abstract

Dirac-Weyl fermions are massless relativistic particles with a well-defined helicity which arise in the context of high-energy physics. Here we propose a quantum simulation of these paradigmatic fermions using multicomponent ultracold atoms in a two-dimensional square optical lattice. We find that laser-assisted spin-dependent hopping, specifically tuned to the $(2s+1)$-dimensional representations of the $\mathfrak{su}$(2) Lie algebra, directly leads to a regime where the emerging massless excitations correspond to Dirac-Weyl fermions with arbitrary pseudospin $s$. We show that this platform hosts two different phases: a semimetallic phase that occurs for half-integer $s$, and a metallic phase that contains a flat zero-energy band at integer $s$. These phases host a variety of interesting effects, such as a very rich anomalous quantum Hall effect and a remarkable multirefringent Klein tunneling. In addition, we show that these effects are directly related to the number of underlying Dirac-Weyl species and zero modes.

DOI
10.1103/physrevb.84.165115

Related papers

Massless Dirac fermions in a square optical lattice

Jing-Min Hou, Wen‐Xing Yang, Xiong-Jun Liu

We propose a scheme to simulate and observe massless Dirac fermions with cold atoms in a square optical lattice. A U(1) adiabatic phase is created by two laser beams for the tunneling of atoms between neighbor lattice sites. Properly adjusting the tunneling phase, we find that the energy spectrum has conical points in per Brillouin zone where band crossing occurs. Near these crossing points the quasiparticles and quasiholes can be considered as massless Dirac fermions. Furthermore, the anisotropic effects of massless Dirac fermions are obtained in the present square lattice model. The Dirac fermions as well as the anisotropic behaviors realized in our system can be experimentally detected with the Bragg spectroscopy technique.

arXiv:0902.4746•Physical Review A•Apr 21, 2009•63 citations

Single Dirac cone with a flat band touching on line-centered-square optical lattices

R. Shen, L. B. Shao, Baigeng Wang +1 more

Using ultracold atoms trapped in an optical lattice, we form a line-centered-square lattice in the condensed-matter physics, where a crossover from massive to massless Dirac fermion behavior can be easily achieved by tuning the laser intensities. The present Dirac fermions satisfy a three-component quantum equation for pseudospin-1 fermions, resulting in a single Dirac cone in the energy spectrum, a flat band touching at the Dirac point, and a vanishing Berry's phase. Interestingly, the massless Dirac fermions here may exhibit an all-angle Klein tunneling; i.e., the barrier is completely transparent for all incident angles.

Physical Review B•Jan 14, 2010•298 citations

Non-Abelian Optical Lattices: Anomalous Quantum Hall Effect and Dirac Fermions

Nathan Goldman, A. Kubasiak, A. Bermúdez +3 more

We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac fermions with cold atoms experiments. In particular, we show that the underlying Minkowski space-time can also be modified, reaching anisotropic regimes where a remarkable anomalous quantum Hall effect and a squeezed Landau vacuum could be observed.

arXiv:0903.2464•Physical Review Letters•Jul 14, 2009•194 citations

Weyl solitons in three-dimensional optical lattices

Ce Shang, Yuanlin Zheng, Boris A. Malomed

Weyl fermions are massless chiral quasiparticles existing in materials known as Weyl semimetals. Topological surface states, associated with the unusual electronic structure in the Weyl semimetals, have been recently demonstrated in linear systems. Ultracold atomic gases, featuring laser-assisted tunneling in three-dimensional optical lattices, can be used for the emulation of Weyl semimetals, including nonlinear effects induced by the collisional nonlinearity of atomic Bose-Einstein condensates. We demonstrate that this setting gives rise to topological states in the form of Weyl solitons at the surface of the underlying optical lattice. These nonlinear modes, being exceptionally robust, bifurcate from linear states for a given quasimomentum. The Weyl solitons may be used to design an efficient control scheme for topologically protected unidirectional propagation of excitations in light-matter-interaction physics. After the recently introduced Majorana and Dirac solitons, the Weyl solitons proposed in this work constitute the third (and the last) member in this family of topological solitons.

arXiv:1804.00837•Physical Review A•Apr 3, 2018•17 citations

Simulation and detection of Weyl fermions in ultracold Fermi gases with Raman-assisted spin-orbit coupling

Cheng-Gong Liang, Ze-Gang Liu, Han, Wei

Weyl fermion, also referred to as pseudo-magnetic monopole in momentum space, is an undiscovered massless elementary particle with half-integer spin predicted according to relativistic quantum field theory. Motivated by the recent experimental observation of Weyl semimetal band in ultracold Bose gases with Raman-assisted 3D spin-orbit coupling, we investigate the properties and possible observation of Weyl fermions in the low-energy quasi-particle excitations of ultracold Fermi gases. Following a previous suggestion that the existing Raman lattice scheme can be readily generalized to fermionic systems, here we discuss the movement of the Weyl points in the Brillouin Zone, as well as the creation and annihilation of Weyl fermions by adjusting the effective Zeeman field. The relevant topological properties are also demonstrated by calculating the Chern number. Furthermore, we propose how to experimentally verify the existence of the Weyl fermions and the associated quantum phase transition via density profile measurements.

arXiv:2206.13692•Jun 28, 2022•0 citations

Ultracold fermions in a graphene-type optical lattice

Kean Loon Lee, Benoît Grémaud, Rui Han +2 more

Some important features of the graphene physics can be reproduced by loading ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb symmetry and we address here its experimental feasibility. We analyze in great detail the optical lattice generated by the coherent superposition of three coplanar running laser waves with respective angles $2\ensuremath{\pi}/3$. The corresponding band structure displays Dirac cones located at the corners of the Brillouin zone and close to half-filling this system is well described by massless Dirac fermions. We characterize their properties by accurately deriving the nearest-neighbor hopping parameter ${t}_{0}$ as a function of the optical lattice parameters. Our semiclassical instanton method proves in excellent agreement with an exact numerical diagonalization of the full Hamilton operator in the tight-binding regime. We conclude that the temperature range needed to access the Dirac fermions regime is within experimental reach. We also analyze imperfections in the laser configuration as they lead to optical lattice distortions which affect the Dirac fermions. We show that the Dirac cones do survive up to some critical intensity or angle mismatches which are easily controlled in actual experiments. In the tight-binding regime, we predict, and numerically confirm, that these critical mismatches are inversely proportional to the square root of the optical potential strength. We also briefly discuss the interesting possibility of fine tuning the mass of the Dirac fermions by controlling the laser phase in an optical lattice generated by the incoherent superposition of three coplanar independent standing waves with respective angles $2\ensuremath{\pi}/3$.

arXiv:0906.4158•Physical Review A•Oct 19, 2009•132 citations
Dirac-Weyl fermions are massless relativistic particles with a well-defined helicity which arise in the context of high-energy physics. Here we propose a quantum simulation of these paradigmatic fermions using multicomponent ultracold atoms in a two-dimensional square optical lattice. We find that laser-assisted spin-dependent hopping, specifically tuned to the (2s+1)(2s+1)(2s+1)-dimensional representations of the su\mathfrak{su}su(2) Lie algebra, directly leads to a regime where the emerging massless excitations correspond to Dirac-Weyl fermions with arbitrary pseudospin sss. We show that this platform hosts two different phases: a semimetallic phase that occurs for half-integer sss, and a metallic phase that contains a flat zero-energy band at integer sss. These phases host a variety of interesting effects, such as a very rich anomalous quantum Hall effect and a remarkable multirefringent Klein tunneling. In addition, we show that these effects are directly related to the number of underlying Dirac-Weyl species and zero modes.
We propose a scheme to simulate and observe massless Dirac fermions with cold atoms in a square optical lattice. A U(1) adiabatic phase is created by two laser beams for the tunneling of atoms between neighbor lattice sites. Properly adjusting the tunneling phase, we find that the energy spectrum has conical points in per Brillouin zone where band crossing occurs. Near these crossing points the quasiparticles and quasiholes can be considered as massless Dirac fermions. Furthermore, the anisotropic effects of massless Dirac fermions are obtained in the present square lattice model. The Dirac fermions as well as the anisotropic behaviors realized in our system can be experimentally detected with the Bragg spectroscopy technique.
Using ultracold atoms trapped in an optical lattice, we form a line-centered-square lattice in the condensed-matter physics, where a crossover from massive to massless Dirac fermion behavior can be easily achieved by tuning the laser intensities. The present Dirac fermions satisfy a three-component quantum equation for pseudospin-1 fermions, resulting in a single Dirac cone in the energy spectrum, a flat band touching at the Dirac point, and a vanishing Berry's phase. Interestingly, the massless Dirac fermions here may exhibit an all-angle Klein tunneling; i.e., the barrier is completely transparent for all incident angles.
We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac fermions with cold atoms experiments. In particular, we show that the underlying Minkowski space-time can also be modified, reaching anisotropic regimes where a remarkable anomalous quantum Hall effect and a squeezed Landau vacuum could be observed.
Weyl fermions are massless chiral quasiparticles existing in materials known as Weyl semimetals. Topological surface states, associated with the unusual electronic structure in the Weyl semimetals, have been recently demonstrated in linear systems. Ultracold atomic gases, featuring laser-assisted tunneling in three-dimensional optical lattices, can be used for the emulation of Weyl semimetals, including nonlinear effects induced by the collisional nonlinearity of atomic Bose-Einstein condensates. We demonstrate that this setting gives rise to topological states in the form of Weyl solitons at the surface of the underlying optical lattice. These nonlinear modes, being exceptionally robust, bifurcate from linear states for a given quasimomentum. The Weyl solitons may be used to design an efficient control scheme for topologically protected unidirectional propagation of excitations in light-matter-interaction physics. After the recently introduced Majorana and Dirac solitons, the Weyl solitons proposed in this work constitute the third (and the last) member in this family of topological solitons.
Weyl fermion, also referred to as pseudo-magnetic monopole in momentum space, is an undiscovered massless elementary particle with half-integer spin predicted according to relativistic quantum field theory. Motivated by the recent experimental observation of Weyl semimetal band in ultracold Bose gases with Raman-assisted 3D spin-orbit coupling, we investigate the properties and possible observation of Weyl fermions in the low-energy quasi-particle excitations of ultracold Fermi gases. Following a previous suggestion that the existing Raman lattice scheme can be readily generalized to fermionic systems, here we discuss the movement of the Weyl points in the Brillouin Zone, as well as the creation and annihilation of Weyl fermions by adjusting the effective Zeeman field. The relevant topological properties are also demonstrated by calculating the Chern number. Furthermore, we propose how to experimentally verify the existence of the Weyl fermions and the associated quantum phase transition via density profile measurements.
Some important features of the graphene physics can be reproduced by loading ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb symmetry and we address here its experimental feasibility. We analyze in great detail the optical lattice generated by the coherent superposition of three coplanar running laser waves with respective angles $2\ensuremath{\pi}/3$. The corresponding band structure displays Dirac cones located at the corners of the Brillouin zone and close to half-filling this system is well described by massless Dirac fermions. We characterize their properties by accurately deriving the nearest-neighbor hopping parameter t0{t}_{0}t0​ as a function of the optical lattice parameters. Our semiclassical instanton method proves in excellent agreement with an exact numerical diagonalization of the full Hamilton operator in the tight-binding regime. We conclude that the temperature range needed to access the Dirac fermions regime is within experimental reach. We also analyze imperfections in the laser configuration as they lead to optical lattice distortions which affect the Dirac fermions. We show that the Dirac cones do survive up to some critical intensity or angle mismatches which are easily controlled in actual experiments. In the tight-binding regime, we predict, and numerically confirm, that these critical mismatches are inversely proportional to the square root of the optical potential strength. We also briefly discuss the interesting possibility of fine tuning the mass of the Dirac fermions by controlling the laser phase in an optical lattice generated by the incoherent superposition of three coplanar independent standing waves with respective angles $2\ensuremath{\pi}/3$.