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

Science in China. Series G, Physics, mechanics & astronomy/Science in China. Series G, Physics, Mechanics & Astronomy

Detection of topological symmetry in the one-dimensional Afeck-Kennedy-Lieb-Tasaki model of integer spin with ultracold spinor atoms in optical lattices

Cui Hai

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

A scheme is proposed for detection of the topology in the one-dimensional Afeck-Kennedy-Lieb-Tasaki model, based on ultracold spinor atomic gas in an optical lattice. For this purpose, a global operation O(θ) is introduced with respect to the breaking of spinrotational symmetry. Consequently, the topology can be manifested unambiguously by identifying the special values of θ where the expectation value of the global operator with degenerate ground states is vanishing. Furthermore, experimentally θ can be detected readily by the interference of ultracold atomic gases. This scheme can be implemented readily in experiment since it does not need the addressing of individual atoms or the probing of a boundary.

Related papers

Detection of topological symmetry in the one-dimensional Affleck-Kennedy-Lieb-Tasaki model of integer spin with ultracold spinor atoms in optical lattices

H. T. Cui, Gui Yang, Junlong Tian

Science China Physics Mechanics and Astronomy•Oct 10, 2013•0 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

Realizing one-dimensional topological superfluids with ultracold atomic gases

Sylvain Nascimbène

We propose an experimental implementation of a topological superfluid with ultracold fermionic atoms. An optical superlattice is used to juxtapose a 1D gas of fermionic atoms and a 2D conventional superfluid of condensed Feshbach molecules. The latter acts as a Cooper pair reservoir and effectively induces a superfluid gap in the 1D system. Combined with a spin-dependent optical lattice along the 1D tube and laser-induced atom tunneling, we obtain a topological superfluid phase. In the regime of weak couplings to the molecular fl eld and for a uniform gas the atomic system is equivalent to Kitaev's model of a p-wave superfluid. Using a numerical calculation we show that the topological superfluidity is robust beyond the perturbative limit and in the presence of a harmonic trap. Finally we describe how to investigate some physical properties of the Majorana fermions located at the topological superfluid boundaries. In particular we discuss how to prepare and detect a given Majorana edge state.

arXiv:1210.0687•Journal of Physics B Atomic Molecular and Optical Physics•Jun 24, 2013•55 citations

Creation, manipulation and detection of Majorana fermions with cold atoms in optical lattice

Mei, Feng, Chuan-Jia Shan, Xun‐Li Feng +5 more

We propose an experimental scheme to simulate the transverse field Ising model with cold atoms trapped in one-dimensional optical lattice. Majorana fermions are created at the ends of the optical lattice segment in topological phase. By controlling the addressing lasers, one can move, fuse and braid them. We also show that the non-Abelian braiding statistics of Majorana fermions can be demonstrated unambiguously through the construction of two braiding operations and distinguishing the resulting two output orthogonal collective spin states. A nice feature of the scheme is that the strong fluorescence provided by the collective spin state can be readily detected in experiment.

arXiv:1204.3974•Apr 18, 2012•2 citations

Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator

Keola Wierschem, K. S. D. Beach

The strange correlator [Phys. Rev. Lett. 112, 247202 (2014)] has been proposed as a measure of symmetry protected topological order in one- and two-dimensional systems. It takes the form of a spin-spin correlation function, computed as a mixed overlap between the state of interest and a trivial local product state. We demonstrate that it can be computed exactly (asymptotically, in the Monte Carlo sense) for various Affleck-Kennedy-Lieb-Tasaki states by direct evaluation of the wave function within the valence bond loop gas framework. We present results for lattices with chain, square, honeycomb, cube, diamond, and hyperhoneycomb geometries. In each case, the spin quantum number $S$ is varied such that $2S$ (the number of valence bonds emerging from each site) achieves various integer multiples of the lattice coordination number. We introduce the concept of strange correlator loop winding number and point to its utility in testing for the presence of symmetry protected topological order.

arXiv:1603.03444•Physical review. B./Physical review. B•Jun 20, 2016•28 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
A scheme is proposed for detection of the topology in the one-dimensional Afeck-Kennedy-Lieb-Tasaki model, based on ultracold spinor atomic gas in an optical lattice. For this purpose, a global operation O(θ) is introduced with respect to the breaking of spinrotational symmetry. Consequently, the topology can be manifested unambiguously by identifying the special values of θ where the expectation value of the global operator with degenerate ground states is vanishing. Furthermore, experimentally θ can be detected readily by the interference of ultracold atomic gases. This scheme can be implemented readily in experiment since it does not need the addressing of individual atoms or the probing of a boundary.
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.
We propose an experimental implementation of a topological superfluid with ultracold fermionic atoms. An optical superlattice is used to juxtapose a 1D gas of fermionic atoms and a 2D conventional superfluid of condensed Feshbach molecules. The latter acts as a Cooper pair reservoir and effectively induces a superfluid gap in the 1D system. Combined with a spin-dependent optical lattice along the 1D tube and laser-induced atom tunneling, we obtain a topological superfluid phase. In the regime of weak couplings to the molecular fl eld and for a uniform gas the atomic system is equivalent to Kitaev's model of a p-wave superfluid. Using a numerical calculation we show that the topological superfluidity is robust beyond the perturbative limit and in the presence of a harmonic trap. Finally we describe how to investigate some physical properties of the Majorana fermions located at the topological superfluid boundaries. In particular we discuss how to prepare and detect a given Majorana edge state.
We propose an experimental scheme to simulate the transverse field Ising model with cold atoms trapped in one-dimensional optical lattice. Majorana fermions are created at the ends of the optical lattice segment in topological phase. By controlling the addressing lasers, one can move, fuse and braid them. We also show that the non-Abelian braiding statistics of Majorana fermions can be demonstrated unambiguously through the construction of two braiding operations and distinguishing the resulting two output orthogonal collective spin states. A nice feature of the scheme is that the strong fluorescence provided by the collective spin state can be readily detected in experiment.
The strange correlator [Phys. Rev. Lett. 112, 247202 (2014)] has been proposed as a measure of symmetry protected topological order in one- and two-dimensional systems. It takes the form of a spin-spin correlation function, computed as a mixed overlap between the state of interest and a trivial local product state. We demonstrate that it can be computed exactly (asymptotically, in the Monte Carlo sense) for various Affleck-Kennedy-Lieb-Tasaki states by direct evaluation of the wave function within the valence bond loop gas framework. We present results for lattices with chain, square, honeycomb, cube, diamond, and hyperhoneycomb geometries. In each case, the spin quantum number SSS is varied such that 2S2S2S (the number of valence bonds emerging from each site) achieves various integer multiples of the lattice coordination number. We introduce the concept of strange correlator loop winding number and point to its utility in testing for the presence of symmetry protected topological order.
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.