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:2308.07647 · Physical review. B./Physical review. B

Fermionic atoms in a spin-dependent optical lattice potential: Topological insulators with broken time-reversal symmetry

Igor Kuzmenko, Mirosław Brewczyk, Grzegorz Łach, Marek Trippenbach, Y. B. Band

Published Nov 25, 2024• 1 citation
arXivHTMLPDF

Abstract

We propose an approach to study the topological properties of matter. In this approach, fermionic atoms are placed in an external magnetic field and in a two-dimensional spin-dependent optical lattice (SDOL) created by intersecting laser beams with a superposition of polarizations. To demonstrate the utility of the SDOL-based technique we compute the topological invariants (Chern numbers) for the SDOL bands as a function of an external magnetic field and show the existence of a rich topology of the energy bands for this system which does not have parity-time-reversal symmetry. We explicitly consider $^{6}\mathrm{Li}\phantom{\rule{4pt}{0ex}}F=1/2$ atoms. Using a projection matrix method we observe topological phase transitions among an ordinary insulator, an Abelian topological insulator, and a non-Abelian topological insulator as the external magnetic field strength is varied. On introducing edges for the SDOL we find topological edge states (that are correlated with the band Chern numbers) that simultaneously exhibit nontrivial density and spin currents with both a rotational flow contribution and flow along the edge of the SDOL.

DOI
10.1103/physrevb.110.205430

Related papers

Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices

Michele Burrello, Ion Cosma Fulga, Emilio Alba +2 more

We analyze a tight-binding model of ultracold fermions loaded in an optical square lattice and subjected to a synthetic non-Abelian gauge potential featuring both a magnetic field and a translationally invariant SU(2) term. We consider in particular the effect of broken time-reversal symmetry and its role in driving nontrivial topological phase transitions. By varying the spin-orbit coupling parameters, we find both a semimetal-insulator phase transition and a topological phase transition between insulating phases with different numbers of edge states. The spin is not a conserved quantity of the system, and the topological phase transitions can be detected by analyzing its polarization in time-of-flight images, providing a clear diagnostic for the characterization of the topological phases through the partial entanglement between spin and lattice degrees of freedom.

arXiv:1308.0750•Physical Review A•Nov 15, 2013•21 citations

Spin-orbit coupling and topological states in an F=32 cold Fermi gas

Igor Kuzmenko, Tetyana Kuzmenko, Y. Avishai +1 more

In this work we study the possible occurrence of topological insulators for 2D fermions of high spin. They can be realized in cold fermion systems with ground-state atomic spin $F>\frac{1}{2}$, if the optical potential is properly designed, and spin-orbit coupling is relevant. The latter is shown to be induced by letting the fermions interact with a specially tuned arrangement of polarized laser beams. When the system is subject to a perpendicular magnetic field, time reversal symmetry is broken but the ensuing Hamiltonian is still endowed with a mirror symmetry. Topological insulators for fermions of higher spins are fundamentally distinct from those pertaining to spin $\frac{1}{2}$. The underlying physics reveals a plethora of positive and negative mirror Chern numbers, respectively, corresponding to chiral and antichiral edge states. Here, for simplicity, we concentrate on the case $F=\frac{3}{2}$ (which is suitable for $^{6}\mathrm{Li}$ or $^{2}\mathrm{H}$ atoms) but extension to higher spins (such as $^{40}\mathrm{K}$ whose ground-state spin is $F=\frac{9}{2}$) is straightforward.

arXiv:1801.05646•Physical review. B./Physical review. B•Oct 26, 2018•7 citations

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

Chern-number spectrum of ultracold fermions in optical lattices tuned independently via artificial magnetic, Zeeman, and spin-orbit fields

Man Hon Yau, C. A. R. Sá de Melo

We discuss the Chern number spectrum of ultracold fermions in square optical lattices as a function of artificial magnetic, Zeeman, and spin-orbit fields that can be tuned independently. We show the existence of topological quantum phase transitions induced by Zeeman and spin-orbit fields, where the total number and chirality of edge states change for fixed magnetic flux ratio, thus leading to topological-insulator phases which are different from those found at zero Zeeman and spin-orbit fields. We construct phase diagrams of chemical potential versus Zeeman field or spin-orbit coupling and characterize all insulating phases by their topological invariants. Lastly, we obtain a staircase structure in the filling factor versus chemical potential for various Zeeman and spin-orbit fields, showing the existence of incompressible states at rational filling factors derived from a generalized Diophantine equation.

arXiv:1811.00136•Physical Review A•Apr 25, 2019•5 citations

Chiral topological phases in optical lattices without synthetic fields

Hoi-Yin Hui, Mengsu Chen, Sumanta Tewari +1 more

Synthetic fields applied to ultracold quantum gases can realize topological phases that transcend conventional Bose and Fermi-liquid paradigms. Raman laser beams in particular are under scrutiny as a route to create synthetic fields in neutral gases to mimic ordinary magnetic and electric fields acting on charged matter. Yet external laser beams can impose heating and losses that make cooling into many-body topological phases challenging. We propose that atomic or molecular dipoles placed in optical lattices can realize a topological phase without synthetic fields by placing them in certain frustrated lattices. We use numerical modeling on a specific example to show that the interactions between dipolar fermions placed in a kagome optical lattice spontaneously break time-reversal symmetry to lead to a topological Mott insulator, a chiral topological phase generated entirely by interactions. We estimate realistic entropy and trapping parameters to argue that this intriguing phase of matter can be probed with quantum gases using a combination of recently implemented technologies.

arXiv:1712.10238•Physical Review A•Aug 8, 2018•8 citations

Antiferromagnetic topological insulators in cold atomic gases

Andrew M. Essin, Victor Gurarie

We propose a spin-dependent optical lattice potential that realizes a three-dimensional antiferromagnetic topological insulator in a gas of cold, two-state fermions such as alkaline earths, as well as a model that describes the tight-binding limit of this potential. We discuss the physically observable responses of the gas that can verify the presence of this phase, in particular rapid rotation in response to the trap potential. We also point out how this model can be used to obtain two-dimensional flat bands with nonzero Chern number.

arXiv:1112.6013•Physical Review B•May 10, 2012•28 citations
We propose an approach to study the topological properties of matter. In this approach, fermionic atoms are placed in an external magnetic field and in a two-dimensional spin-dependent optical lattice (SDOL) created by intersecting laser beams with a superposition of polarizations. To demonstrate the utility of the SDOL-based technique we compute the topological invariants (Chern numbers) for the SDOL bands as a function of an external magnetic field and show the existence of a rich topology of the energy bands for this system which does not have parity-time-reversal symmetry. We explicitly consider 6LiF=1/2^{6}\mathrm{Li}\phantom{\rule{4pt}{0ex}}F=1/26LiF=1/2 atoms. Using a projection matrix method we observe topological phase transitions among an ordinary insulator, an Abelian topological insulator, and a non-Abelian topological insulator as the external magnetic field strength is varied. On introducing edges for the SDOL we find topological edge states (that are correlated with the band Chern numbers) that simultaneously exhibit nontrivial density and spin currents with both a rotational flow contribution and flow along the edge of the SDOL.
We analyze a tight-binding model of ultracold fermions loaded in an optical square lattice and subjected to a synthetic non-Abelian gauge potential featuring both a magnetic field and a translationally invariant SU(2) term. We consider in particular the effect of broken time-reversal symmetry and its role in driving nontrivial topological phase transitions. By varying the spin-orbit coupling parameters, we find both a semimetal-insulator phase transition and a topological phase transition between insulating phases with different numbers of edge states. The spin is not a conserved quantity of the system, and the topological phase transitions can be detected by analyzing its polarization in time-of-flight images, providing a clear diagnostic for the characterization of the topological phases through the partial entanglement between spin and lattice degrees of freedom.
In this work we study the possible occurrence of topological insulators for 2D fermions of high spin. They can be realized in cold fermion systems with ground-state atomic spin F>12F>\frac{1}{2}F>21​, if the optical potential is properly designed, and spin-orbit coupling is relevant. The latter is shown to be induced by letting the fermions interact with a specially tuned arrangement of polarized laser beams. When the system is subject to a perpendicular magnetic field, time reversal symmetry is broken but the ensuing Hamiltonian is still endowed with a mirror symmetry. Topological insulators for fermions of higher spins are fundamentally distinct from those pertaining to spin 12\frac{1}{2}21​. The underlying physics reveals a plethora of positive and negative mirror Chern numbers, respectively, corresponding to chiral and antichiral edge states. Here, for simplicity, we concentrate on the case F=32F=\frac{3}{2}F=23​ (which is suitable for 6Li^{6}\mathrm{Li}6Li or 2H^{2}\mathrm{H}2H atoms) but extension to higher spins (such as 40K^{40}\mathrm{K}40K whose ground-state spin is F=92F=\frac{9}{2}F=29​) is straightforward.
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 discuss the Chern number spectrum of ultracold fermions in square optical lattices as a function of artificial magnetic, Zeeman, and spin-orbit fields that can be tuned independently. We show the existence of topological quantum phase transitions induced by Zeeman and spin-orbit fields, where the total number and chirality of edge states change for fixed magnetic flux ratio, thus leading to topological-insulator phases which are different from those found at zero Zeeman and spin-orbit fields. We construct phase diagrams of chemical potential versus Zeeman field or spin-orbit coupling and characterize all insulating phases by their topological invariants. Lastly, we obtain a staircase structure in the filling factor versus chemical potential for various Zeeman and spin-orbit fields, showing the existence of incompressible states at rational filling factors derived from a generalized Diophantine equation.
Synthetic fields applied to ultracold quantum gases can realize topological phases that transcend conventional Bose and Fermi-liquid paradigms. Raman laser beams in particular are under scrutiny as a route to create synthetic fields in neutral gases to mimic ordinary magnetic and electric fields acting on charged matter. Yet external laser beams can impose heating and losses that make cooling into many-body topological phases challenging. We propose that atomic or molecular dipoles placed in optical lattices can realize a topological phase without synthetic fields by placing them in certain frustrated lattices. We use numerical modeling on a specific example to show that the interactions between dipolar fermions placed in a kagome optical lattice spontaneously break time-reversal symmetry to lead to a topological Mott insulator, a chiral topological phase generated entirely by interactions. We estimate realistic entropy and trapping parameters to argue that this intriguing phase of matter can be probed with quantum gases using a combination of recently implemented technologies.
We propose a spin-dependent optical lattice potential that realizes a three-dimensional antiferromagnetic topological insulator in a gas of cold, two-state fermions such as alkaline earths, as well as a model that describes the tight-binding limit of this potential. We discuss the physically observable responses of the gas that can verify the presence of this phase, in particular rapid rotation in response to the trap potential. We also point out how this model can be used to obtain two-dimensional flat bands with nonzero Chern number.