Simulating and detecting the quantum spin Hall effect in the kagome optical lattice

Liu, Guocai; Zhu, Shi-Liang; Jiang, Shao-Jian; Sun, Fan‐Ko; Liu, Wei Ming

doi:10.1103/physreva.82.053605

Cited by 57 publications

(59 citation statements)

References 65 publications

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“…By construction it is clear that (i)P θ (k TRIM y ) reduces to standard TRP provided that M = N/2 is chosen [cf. (30)]. To check (ii), i.e., continuity ofP θ (k y ), we notice that all scalar products are continuous as a function of k y for fixed discretization into N points along k x .…”

Section: Discretized Version Of Continuous Time-reversal Polarizationmentioning

confidence: 99%

“…These could also be used to realize the band switching Hamiltonian (21) and for driving Bloch oscillations. In more conventional setups without atom chips, such as, e.g., the experiment [27] and the proposals [30,32,34], Bloch oscillations can, e.g., be driven using magnetic field gradients [16] or optical potentials. This would also allow the realization of Hamiltonian (21) for band switchings.…”

Section: Experimental Realization and Limitationsmentioning

confidence: 99%

“…For the simulation of the QSHE (or, more generally, a Z 2 topological insulator) with ultracold atoms artificial spin-orbit coupling (SOC) is required which has also been demonstrated experimentally [29]. Different SOC schemes have led to several proposals for the implementation of two- [30][31][32][33] and three-dimensional [32] TR-invariant topological insulators. In the recent experiment of the Munich group [27] Abelian SOC has successfully been implemented, which is sufficient for a realization of the QSHE.…”

Section: Introductionmentioning

confidence: 99%

“…A different approach to measure Chern numbers makes use of the Streda formula, relating them to the change in atomic density when a finite magnetic field is switched on [46,47]. Extensions of this method for detection of Z 2 topological phases were suggested [30,31], however, they only work when the Chern numbers for individual spins are well defined (which is generally not the case [48]). Recently also an interferometric method has been suggested to measure the Z 2 invariant of inversion-symmetric TR-invariant topological insulators [49].…”

Section: Introductionmentioning

confidence: 99%

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MeasuringZ2topological invariants in optical lattices using interferometry

2014

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We propose an interferometric method to measure Z 2 topological invariants of time-reversal invariant topological insulators realized with optical lattices in two and three dimensions. We suggest two schemes which both rely on a combination of Bloch oscillations with Ramsey interferometry and can be implemented using standard tools of atomic physics. In contrast to topological Zak phase and Chern number, defined for individual one-dimensional and two-dimensional Bloch bands, the formulation of the Z 2 invariant involves at least two Bloch bands related by time-reversal symmetry which one must keep track of in measurements. In one of our schemes this can be achieved by the measurement of Wilson loops, which are non-Abelian generalizations of Zak phases. The winding of their eigenvalues is related to the Z 2 invariant. We thereby demonstrate that Wilson loops are not just theoretical concepts but can be measured experimentally. For the second scheme we introduce a generalization of time-reversal polarization which is continuous throughout the Brillouin zone. We show that its winding over half the Brillouin zone yields the Z 2 invariant. To measure this winding, our protocol only requires Bloch oscillations within a single band, supplemented by coherent transitions to a second band which can be realized by lattice shaking.

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Section: Discretized Version Of Continuous Time-reversal Polarizationmentioning

confidence: 99%

Section: Experimental Realization and Limitationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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MeasuringZ2topological invariants in optical lattices using interferometry

2014

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“…This effective field can been simulated in cold atom by use of laser-induced-gaugefield method [33,34]. More details refer [35]. Therefore, the total effective vector potential and magnetic field can be written as…”

Section: Quantum Hall Effect Of Cold Atom In Kagomé Optical Latticementioning

confidence: 99%

Quantum information and many body physics with cold atoms

et al. 2012

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We review our recent theoretical advances in quantum information and many body physics with cold atoms in various external potential, such as harmonic potential, kagome optical lattice, triangular optical lattice, and honeycomb lattice. The many body physics of cold atom in harmonic potential is investigated in the frame of mean-field Gross-Pitaevskii equation. Then the quantum phase transition and strongly correlated effect of cold atoms in triangular optical lattice, and the interacting Dirac fermions on honeycomb lattice, are investigated by using cluster dynamical mean-field theory and continuous time quantum Monte Carlo method. We also study the quantum spin Hall effect in the kagome optical lattice. Observation of Bose-Einstein condensates (BECs) in gases of weakly interacting alkali-metal atoms has stimulated intensive studies of the nonlinear matter waves, where both bright and dark solitons have been observed [1][2][3] and the gap solitons are realized in a optical lattice experimentally [4,5]. Moreover, experimental realization of BECs, in which two (or more) internal states or different atoms can be populated, has stimulated great interests in vector solitons. In real experiments, both amplitude and sign of the scattering length can be modified by utilizing the Feshbach resonance. This technique provides a very promising method for the manipulation of atomic matter waves and the nonlinear excitations in BEC by tuning the interatomic interaction.With the development of the experiments, a new developing technology called optical lattices presents a highly controllable and clean system for studying strongly correlated system, in which the relevant parameter can be adjusted independently [6][7][8][9][10][11]. Optical lattices with different geometrical property can be set up by adjusting the propagation direc-*Corresponding author (email: wmliu@iphy.ac.cn) tions of laser beams, such as triangular [12], honeycomb [13] and optical lattice. The optical lattice system has gradually become a promising platform to simulate and study a lot of quantum phenomena in condensed-matter physics, because almost all parameters of the system can be well controlled.In this article, we review quantum information and many body physics with cold atoms. In Section 1, we consider the many-body physics of BEC in harmonic potential. Section 2 is devoted to investigate the quantum phase transition and strongly correlated effect of cold atoms in triangular optical lattice, and the interacting Dirac fermions on honeycomb lattice. In Section 3, we discuss the quantum spin Hall effect of cold atom in the kagome optical lattice. Finally, we summarize our results.

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Faithful simulation and detection of quantum spin Hall effect on superconducting circuits

Liu

Cao

Chen

et al. 2021

Quantum Engineering

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Topological states of quantum matter have inspired both fascinating physics findings and exciting opportunities for applications. Due to the overcomplicated structure of, as well as interactions between, real materials, a faithful quantum simulation of topological matter is very important in deepening our understanding of these states. This requirement puts the quantum superconducting circuits system as a good option for mimicking topological materials, owing to their flexible tunability and fine controllability. As a typical example herein, we realize a ℤ2‐type topological insulator featuring the quantum spin Hall effect state, using a coupled system of transmission‐line resonators and transmons. The single‐excitation eigenstates of each unit cell are used as a pseudo‐spin 1/2 system. The boundary of the topological phase transition is fixed in the phase diagram. Topological edge states are shown, which can be experimentally verified by detecting the population at the boundary of the plane. Compared with the previous simulations, this compositional system is fairly controllable, stable, and less limited. Therefore, our scheme provides a reliable platform for faithful quantum simulations of topological matter.

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Simulating and detecting the quantum spin Hall effect in the kagome optical lattice

Cited by 57 publications

References 65 publications

MeasuringZ2topological invariants in optical lattices using interferometry

MeasuringZ2topological invariants in optical lattices using interferometry

Quantum information and many body physics with cold atoms

Faithful simulation and detection of quantum spin Hall effect on superconducting circuits

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