1
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Li T, Li N, Guo M, Wu YJ. Phase- and temperature-driven chiral topological superfluids on a honeycomb lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:375601. [PMID: 38814243 DOI: 10.1088/1361-648x/ad51fa] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2024] [Accepted: 05/28/2024] [Indexed: 05/31/2024]
Abstract
The correlated spinful Haldane model exhibits rich topological phases consisting of chiral topological superfluids (TSFs) and topological spin density waves. However, most of previous studies mainly focus on the case with the fixed hopping phase or at zero temperature. In this paper, we study the attractive spinful Haldane model with arbitrary phase at finite temperature. The chiral TSFs with Chern numberC = 2 and 4 emerge driven by the phase and temperature. In particular, the temperature can drive aC = 2 topological superfluid from a trivial normal insulator phase at an appropriate interaction. The bulk topology of all TSFs is uncovered by the Wilson loop method, and confirmed by the responses of edge dislocations.
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Affiliation(s)
- Tong Li
- School of Sciences, Xi'an Technological University, Xi'an 710021, People's Republic of China
| | - Ning Li
- School of Sciences, Xi'an Technological University, Xi'an 710021, People's Republic of China
| | - Miaodi Guo
- School of Sciences, Xi'an Technological University, Xi'an 710021, People's Republic of China
| | - Ya-Jie Wu
- School of Sciences, Xi'an Technological University, Xi'an 710021, People's Republic of China
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2
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Wang B, Aidelsburger M, Dalibard J, Eckardt A, Goldman N. Cold-Atom Elevator: From Edge-State Injection to the Preparation of Fractional Chern Insulators. PHYSICAL REVIEW LETTERS 2024; 132:163402. [PMID: 38701474 DOI: 10.1103/physrevlett.132.163402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 03/12/2024] [Indexed: 05/05/2024]
Abstract
Optical box traps offer new possibilities for quantum-gas experiments. Building on their exquisite spatial and temporal control, we propose to engineer system-reservoir configurations using box traps, in view of preparing and manipulating topological atomic states in optical lattices. First, we consider the injection of particles from the reservoir to the system: this scenario is shown to be particularly well suited to activating energy-selective chiral edge currents, but also to prepare fractional Chern insulating ground states. Then, we devise a practical evaporative-cooling scheme to effectively cool down atomic gases into topological ground states. Our open-system approach to optical-lattice settings provides a new path for the investigation of ultracold quantum matter, including strongly correlated and topological phases.
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Affiliation(s)
- Botao Wang
- CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| | - Monika Aidelsburger
- Faculty of Physics, Ludwig-Maximilians-Universität München, Schellingstr. 4, D-80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, D-80799 Munich, Germany
| | - Jean Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - André Eckardt
- Technische Universität Berlin, Institut für Theoretische Physik, Hardenbergstrasse 36, 10623 Berlin, Germany
| | - Nathan Goldman
- CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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3
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Wu YJ, Tu W, Li N. Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:375601. [PMID: 35793693 DOI: 10.1088/1361-648x/ac7f19] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Accepted: 07/06/2022] [Indexed: 06/15/2023]
Abstract
Higher-order topological superconductors and superfluids (SFs) host lower-dimensional Majorana corner and hinge states since novel topology exhibitions on boundaries. While such topological nontrivial phases have been explored extensively, more possible schemes are necessary for engineering Majorana states. In this paper we propose Majorana corner states could be realized in a two-dimensional attractive quantum spin-Hall insulator with opposite in-plane Zeeman energy at two sublattice sites. The appropriate Zeeman field leads to the opposite Dirac mass for adjacent edges of a square sample, and naturally induce Majorana corner states. This topological phase can be characterized by Majorana edge polarizations, and it is robust against perturbations on random potentials and random phase fluctuations as long as the edge gap remains open. Our work provides a new possibility to realize a second-order topological SF in two dimensions and engineer Majorana corner states.
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Affiliation(s)
- Ya-Jie Wu
- School of Sciences, Xi'an Technological University, Xi'an 710032, People's Republic of China
| | - Wei Tu
- School of Sciences, Xi'an Technological University, Xi'an 710032, People's Republic of China
| | - Ning Li
- School of Sciences, Xi'an Technological University, Xi'an 710032, People's Republic of China
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4
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Li Q, Wu YJ, Yu J, He J. Phase driven topological states in correlated Haldane model on a honeycomb lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:275602. [PMID: 35439734 DOI: 10.1088/1361-648x/ac6851] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2022] [Accepted: 04/19/2022] [Indexed: 06/14/2023]
Abstract
Using mean field method and random phase approximation, we studied the phase driven topological exotic states in correlated Haldane model on a honeycomb lattice. It is found that topological spin density waves emerge with the phase change of next-nearest-neighbor hopping. We also investigated the topological properties of these spin density waves, including Chern number, edge state and Hall conductivity. Our work provides a new insight for topological phase transitions in correlated quantum anomalous Hall insulators.
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Affiliation(s)
- Qingmin Li
- College of Physics and Hebei Advanced Thin Film Laboratory, Hebei Normal University, Shijiazhuang 050024, People's Republic of China
| | - Ya-Jie Wu
- School of Sciences, Xi'an Technological University, Xi'an 710032, People's Republic of China
| | - Jing Yu
- Faculty of Science, Liaoning Petrochemical University, Fushun 113001, People's Republic of China
| | - Jing He
- College of Physics and Hebei Advanced Thin Film Laboratory, Hebei Normal University, Shijiazhuang 050024, People's Republic of China
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5
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Nie W, Peng ZH, Nori F, Liu YX. Topologically Protected Quantum Coherence in a Superatom. PHYSICAL REVIEW LETTERS 2020; 124:023603. [PMID: 32004058 DOI: 10.1103/physrevlett.124.023603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2019] [Revised: 10/01/2019] [Indexed: 06/10/2023]
Abstract
Exploring the properties and applications of topological quantum states is essential to better understand topological matter. Here, we theoretically study a quasi-one-dimensional topological atom array. In the low-energy regime, the atom array is equivalent to a topological superatom. Driving the superatom in a cavity, we study the interaction between light and topological quantum states. We find that the edge states exhibit topology-protected quantum coherence, which can be characterized from the photon transmission. This quantum coherence helps us to find a superradiance-subradiance transition, and we also study its finite-size scaling behavior. The superradiance-subradiance transition also exists in symmetry-breaking systems. More importantly, it is shown that the quantum coherence of the subradiant edge state is robust to random noises, allowing the superatom to work as a topologically protected quantum memory. We suggest a relevant experiment with three-dimensional circuit QED. Our study may have applications in quantum computation and quantum optics based on topological edge states.
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Affiliation(s)
- Wei Nie
- Institute of Microelectronics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing, China
| | - Z H Peng
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Key Laboratory for Matter Microstructure and Function of Hunan Province, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Physics Department, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - Yu-Xi Liu
- Institute of Microelectronics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing, China
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6
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Pozo O, Repellin C, Grushin AG. Quantization in Chiral Higher Order Topological Insulators: Circular Dichroism and Local Chern Marker. PHYSICAL REVIEW LETTERS 2019; 123:247401. [PMID: 31922878 DOI: 10.1103/physrevlett.123.247401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2019] [Indexed: 06/10/2023]
Abstract
The robust quantization of observables in units of universal constants is a hallmark of topological phases. We show that chiral higher order topological insulators (HOTIs), bulk insulators with chiral hinge states, present two unusual features related to quantization. First, we show that circular dichroism is quantized to an integer or zero depending on the orientation of the sample. This probe locates the hinge states, and can be used to distinguish different types of chiral HOTIs. Second, we find that the average of the local Chern marker over a single surface, an observable related to the surface Hall conductivity known to be quantized in the infinite slab geometry, is nonuniversal for a finite surface. This is due to a nonuniversal contribution of the hinge states, previously unaccounted for, that distinguishes surfaces of chiral HOTIs from Chern insulators. Our findings are relevant to establish higher order topology in systems such as the axion insulator candidate EuIn_{2}As_{2}, and cold atomic realizations.
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Affiliation(s)
- Oscar Pozo
- Instituto de Ciencia de Materiales de Madrid, and CSIC, Cantoblanco, 28049 Madrid, Spain
| | - Cécile Repellin
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Adolfo G Grushin
- University Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
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7
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Repellin C, Goldman N. Detecting Fractional Chern Insulators through Circular Dichroism. PHYSICAL REVIEW LETTERS 2019; 122:166801. [PMID: 31075039 DOI: 10.1103/physrevlett.122.166801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 06/09/2023]
Abstract
Great efforts are currently devoted to the engineering of topological Bloch bands in ultracold atomic gases. Recent achievements in this direction, together with the possibility of tuning interparticle interactions, suggest that strongly correlated states reminiscent of fractional quantum Hall (FQH) liquids could soon be generated in these systems. In this experimental framework, where transport measurements are limited, identifying unambiguous signatures of FQH-type states constitutes a challenge on its own. Here, we demonstrate that the fractional nature of the quantized Hall conductance, a fundamental characteristic of FQH states, could be detected in ultracold gases through a circular-dichroic measurement, namely, by monitoring the energy absorbed by the atomic cloud upon a circular drive. We validate this approach by comparing the circular-dichroic signal to the many-body Chern number and discuss how such measurements could be performed to distinguish FQH-type states from competing states. Our scheme offers a practical tool for the detection of topologically ordered states in quantum-engineered systems, with potential applications in solid state.
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Affiliation(s)
- C Repellin
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - N Goldman
- CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
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8
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Irsigler B, Zheng JH, Hofstetter W. Interacting Hofstadter Interface. PHYSICAL REVIEW LETTERS 2019; 122:010406. [PMID: 31012663 DOI: 10.1103/physrevlett.122.010406] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2018] [Revised: 08/02/2018] [Indexed: 06/09/2023]
Abstract
Two-dimensional topological insulators possess conducting edge states at their boundary while being insulating in the bulk. We investigate the edge state emergent at a smooth topological phase boundary of interacting fermions within a full real-space analysis of the time-reversal invariant Hofstadter-Hubbard model. We characterize the localization of the edge state and the topological phase boundary by means of the local compressibility, the spectral density, a generalized local spin Chern marker as well as the Hall response and find good agreement between all these quantities. Computing the edge state spectra at the interface we observe robustness of the edge state against fermionic two-body interactions and conclude that interactions only shift its position. Hence the bulk-boundary correspondence for the interacting system is confirmed. Since experimental probing of edge states remains a challenge in ultracold atom setups, we propose the detection of the local compressibility by measuring correlations with a quantum gas microscope.
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Affiliation(s)
- Bernhard Irsigler
- Institut für Theoretische Physik, Goethe-Universität, 60438 Frankfurt am Main, Germany
| | - Jun-Hui Zheng
- Institut für Theoretische Physik, Goethe-Universität, 60438 Frankfurt am Main, Germany
| | - Walter Hofstetter
- Institut für Theoretische Physik, Goethe-Universität, 60438 Frankfurt am Main, Germany
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9
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Dong XY, Grushin AG, Motruk J, Pollmann F. Charge Excitation Dynamics in Bosonic Fractional Chern Insulators. PHYSICAL REVIEW LETTERS 2018; 121:086401. [PMID: 30192623 DOI: 10.1103/physrevlett.121.086401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2017] [Revised: 04/06/2018] [Indexed: 06/08/2023]
Abstract
The experimental realization of the Harper-Hofstadter model in ultracold atomic gases has placed fractional states of matter in these systems within reach-a fractional Chern insulator state (FCI) is expected to emerge for sufficiently strong interactions when half-filling the lowest band. The experimental setups naturally allow us to probe the dynamics of this topological state; yet little is known about its out-of-equilibrium properties. We explore, using density matrix renormalization group simulations, the response of the FCI state to spatially localized perturbations. After confirming the static properties of the phase we show that the characteristic, gapless features are clearly visible in the edge dynamics. We find that a local edge perturbation in this model propagates chirally independent of the perturbation strength. This contrasts the behavior of single particle models with counterpropagating edge states, such as the noninteracting Harper-Hofstadter model, where the chirality is manifest only for weak perturbations. Additionally, our simulations show that there is inevitable density leakage from the first row of sites into the bulk, preventing a naive chiral Luttinger theory interpretation of the dynamics.
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Affiliation(s)
- Xiao-Yu Dong
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Adolfo G Grushin
- Department of Physics, University of California, Berkeley, California 94720, USA
- Institut Néel, CNRS and Université Grenoble Alpes, Grenoble, France
| | - Johannes Motruk
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Frank Pollmann
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
- Technische Universität München, Physics Department T42, 85747 Garching, Germany
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10
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Wu YJ, Li N, He J, Kou SP. Chiral quantum spin liquid on the repulsive Haldane-Hubbard model in square lattices. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:465601. [PMID: 28901957 DOI: 10.1088/1361-648x/aa8c65] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In this paper, we present a study on the repulsive Haldane-Hubbard model with spin-rotation symmetry in square lattices by deriving non-linear σ model for magnetic states. It is found that a chiral spin liquid state as the ground state of the correlated system exists in the [Formula: see text] topological spin-density wave proposed by Wu et al (2016 J. Phys.: Condens. Matter 28 115602), of which the low energy physics can be determined by the Chern-Simons-Hopf gauge field theory.
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Affiliation(s)
- Ya-Jie Wu
- School of Science, Xi'an Technological University, Xi'an 710032, People's Republic of China
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11
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Velasco CG, Paredes B. Realizing and Detecting a Topological Insulator in the AIII Symmetry Class. PHYSICAL REVIEW LETTERS 2017; 119:115301. [PMID: 28949240 DOI: 10.1103/physrevlett.119.115301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2016] [Indexed: 06/07/2023]
Abstract
Topological insulators in the AIII (chiral unitary) symmetry class lack experimental realization. Moreover, fractionalization in one-dimensional topological insulators has not been yet directly observed. Our work might open possibilities for both challenges. We propose a one-dimensional model realizing the AIII symmetry class which can be realized in current experiments with ultracold atomic gases. We further report on a distinctive property of topological edge modes in the AIII class: in contrast to those in the well-studied BDI (chiral orthogonal) class, they have nonzero momentum. Exploiting this feature we propose a path for the detection of fractionalization. A fermion added to an AIII system splits into two halves localized at opposite momenta, which can be detected by imaging the momentum distribution.
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Affiliation(s)
- Carlos G Velasco
- Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, 80333 München, Germany and Instituto de Física Teórica CSIC/UAM, C/Nicolás Cabrera, 13-15 Cantoblanco, 28049 Madrid, Spain
| | - Belén Paredes
- Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, 80333 München, Germany and Instituto de Física Teórica CSIC/UAM, C/Nicolás Cabrera, 13-15 Cantoblanco, 28049 Madrid, Spain
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12
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Tran DT, Dauphin A, Grushin AG, Zoller P, Goldman N. Probing topology by "heating": Quantized circular dichroism in ultracold atoms. SCIENCE ADVANCES 2017; 3:e1701207. [PMID: 28835930 PMCID: PMC5562418 DOI: 10.1126/sciadv.1701207] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2017] [Accepted: 07/16/2017] [Indexed: 05/30/2023]
Abstract
We reveal an intriguing manifestation of topology, which appears in the depletion rate of topological states of matter in response to an external drive. This phenomenon is presented by analyzing the response of a generic two-dimensional (2D) Chern insulator subjected to a circular time-periodic perturbation. Because of the system's chiral nature, the depletion rate is shown to depend on the orientation of the circular shake; taking the difference between the rates obtained from two opposite orientations of the drive, and integrating over a proper drive-frequency range, provides a direct measure of the topological Chern number (ν) of the populated band: This "differential integrated rate" is directly related to the strength of the driving field through the quantized coefficient η0 = ν/ℏ2, where h = 2π ℏ is Planck's constant. Contrary to the integer quantum Hall effect, this quantized response is found to be nonlinear with respect to the strength of the driving field, and it explicitly involves interband transitions. We investigate the possibility of probing this phenomenon in ultracold gases and highlight the crucial role played by edge states in this effect. We extend our results to 3D lattices, establishing a link between depletion rates and the nonlinear photogalvanic effect predicted for Weyl semimetals. The quantized circular dichroism revealed in this work designates depletion rate measurements as a universal probe for topological order in quantum matter.
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Affiliation(s)
- Duc Thanh Tran
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| | - Alexandre Dauphin
- ICFO–Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - Adolfo G. Grushin
- Department of Physics, University of California, Berkeley, CA 94720, USA
- Institut Néel, CNRS and Université Grenoble Alpes, F-38042 Grenoble, France
| | - Peter Zoller
- International Solvay Institutes, Université Libre de Bruxelles, Campus Plaine, B-1050 Brussels, Belgium
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
| | - Nathan Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
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13
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Chen MN, Mei F, Su W, Wang HQ, Zhu SL, Sheng L, Xing DY. Topological phases of the kicked Harper-Kitaev model with ultracold atoms. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:035601. [PMID: 27845928 DOI: 10.1088/0953-8984/29/3/035601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We propose using ultracold atoms trapped in a one-dimensional periodically driven optical lattice to realize the Harper-Kitaev model, where the on-site energies are periodically kicked. Such a system provides a natural platform to study both Chern insulators and Majorana fermions. Based on calculating the quasienergy spectra, we find that both Floquet Majorana modes and Hall chiral edge modes could appear at the sample boundary in the gaps between the quasienergy bands. We also study the competition of topological superconductor and Chern insulator states in the model. We calculate the [Formula: see text] index and Floquet Chern number to characterize the above two different topological states, including the topological phase transitions in the kicked Harper-Kitaev model with the increase in the strength of the kick.
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Affiliation(s)
- M N Chen
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, People's Republic of China
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14
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Lin S, Zhang G, Li C, Song Z. Magnetic-flux-driven topological quantum phase transition and manipulation of perfect edge states in graphene tube. Sci Rep 2016; 6:31953. [PMID: 27554930 PMCID: PMC4995410 DOI: 10.1038/srep31953] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2016] [Accepted: 07/29/2016] [Indexed: 11/10/2022] Open
Abstract
We study the tight-binding model for a graphene tube with perimeter N threaded by a magnetic field. We show exactly that this model has different nontrivial topological phases as the flux changes. The winding number, as an indicator of topological quantum phase transition (QPT) fixes at N/3 if N/3 equals to its integer part [N/3], otherwise it jumps between [N/3] and [N/3] + 1 periodically as the flux varies a flux quantum. For an open tube with zigzag boundary condition, exact edge states are obtained. There exist two perfect midgap edge states, in which the particle is completely located at the boundary, even for a tube with finite length. The threading flux can be employed to control the quantum states: transferring the perfect edge state from one end to the other, or generating maximal entanglement between them.
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Affiliation(s)
- S. Lin
- School of Physics, Nankai University, Tianjin 300071, China
| | - G. Zhang
- College of Physics and Materials Science, Tianjin Normal University, Tianjin 300387, China
| | - C. Li
- School of Physics, Nankai University, Tianjin 300071, China
| | - Z. Song
- School of Physics, Nankai University, Tianjin 300071, China
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15
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Wu YJ, Li N, He J, Kou SP. Antiferromagnetic order driven chiral topological spin density waves on the repulsive Haldane-Hubbard model on square lattices. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:115602. [PMID: 26902387 DOI: 10.1088/0953-8984/28/11/115602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In this paper, based on mean-field approach and random-phase-approximation, we study the magnetic properties of the repulsive Haldane-Hubbard model on a square lattice. We find antiferromagnetic order driven topological spin density waves beyond Landau's symmetry-breaking paradigm, for which the effective low energy physics is determined by Chern-Simons-Hopf gauge field theories with different K matrices.
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Affiliation(s)
- Ya-Jie Wu
- School of Science, Xi'an Technological University, Xi'an 710032, People's Republic of China
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16
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Zhang SL, Lang LJ, Zhou Q. Chiral d-Wave Superfluid in Periodically Driven Lattices. PHYSICAL REVIEW LETTERS 2015; 115:225301. [PMID: 26650309 DOI: 10.1103/physrevlett.115.225301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2015] [Indexed: 06/05/2023]
Abstract
A chiral d-wave superfluid is a preliminary example of interacting topological matter. However, unlike s-wave superfluids prevalent in nature, its existence requires a strong d-wave interaction, a criterion that is difficult to access in ordinary systems. There is no experimental observation of such unconventional superfluid at the moment. Here, we present a new principle for creating a two-dimensional (2D) chiral d-wave superfluid using periodically driven lattices. Because of an imprinted 2D pseudospin-orbit coupling, where the sublattice index serves as the pseudospin, the s-wave interaction between two hyperfine spin states naturally creates a chiral d-wave superfluid. This scheme can be directly implemented in current experiments.
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Affiliation(s)
- Shao-Liang Zhang
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
| | - Li-Jun Lang
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
| | - Qi Zhou
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
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17
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Kitamura S, Tsuji N, Aoki H. Interaction-Driven Topological Insulator in Fermionic Cold Atoms on an Optical Lattice: A Design with a Density Functional Formalism. PHYSICAL REVIEW LETTERS 2015; 115:045304. [PMID: 26252693 DOI: 10.1103/physrevlett.115.045304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2014] [Indexed: 06/04/2023]
Abstract
We design an interaction-driven topological insulator for fermionic cold atoms in an optical lattice; that is, we pose the question of whether we can realize in a continuous space a spontaneous symmetry breaking induced by the interatom interaction into a topological Chern insulator. Such a state, sometimes called a "topological Mott insulator," has yet to be realized in solid-state systems, since this requires, in the tight-binding model, large off-site interactions on top of a small on-site interaction. Here, we overcome the difficulty by introducing a spin-dependent potential, where a spin-selective occupation of fermions in A and B sublattices makes the on-site interaction Pauli forbidden, while a sizeable intersite interaction is achieved by a shallow optical potential with a large overlap between neighboring Wannier orbitals. This puts the system away from the tight-binding model, so that we adopt density functional theory for cold atoms, here extended to accommodate noncollinear spin structures emerging in the topological regime, to quantitatively demonstrate the phase transition to the topological Mott insulator.
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Affiliation(s)
- Sota Kitamura
- Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan
| | - Naoto Tsuji
- Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan
| | - Hideo Aoki
- Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan
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18
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Hauke P, Lewenstein M, Eckardt A. Tomography of band insulators from quench dynamics. PHYSICAL REVIEW LETTERS 2014; 113:045303. [PMID: 25105629 DOI: 10.1103/physrevlett.113.045303] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2014] [Indexed: 06/03/2023]
Abstract
We propose a simple scheme for tomography of band-insulating states in one- and two-dimensional optical lattices with two sublattice states. In particular, the scheme maps out the Berry curvature in the entire Brillouin zone and extracts topological invariants such as the Chern number. The measurement relies on observing--via time-of-flight imaging--the time evolution of the momentum distribution following a sudden quench in the band structure. We consider two examples of experimental relevance: the Harper model with π flux and the Haldane model on a honeycomb lattice. Moreover, we illustrate the performance of the scheme in the presence of a parabolic trap, noise, and finite measurement resolution.
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Affiliation(s)
- Philipp Hauke
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstraße 21A, A-6020 Innsbruck, Austria and Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria
| | - Maciej Lewenstein
- ICFO-Institut de Ciències Fotòniques, Parc Mediterrani de la Tecnologia, E-08860 Castelldefels, Spain and ICREA-Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, E-08010 Barcelona, Spain
| | - André Eckardt
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany
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Celi A, Massignan P, Ruseckas J, Goldman N, Spielman IB, Juzeliūnas G, Lewenstein M. Synthetic gauge fields in synthetic dimensions. PHYSICAL REVIEW LETTERS 2014; 112:043001. [PMID: 24580445 DOI: 10.1103/physrevlett.112.043001] [Citation(s) in RCA: 117] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2013] [Indexed: 05/22/2023]
Abstract
We describe a simple technique for generating a cold-atom lattice pierced by a uniform magnetic field. Our method is to extend a one-dimensional optical lattice into the "dimension" provided by the internal atomic degrees of freedom, yielding a synthetic two-dimensional lattice. Suitable laser coupling between these internal states leads to a uniform magnetic flux within the two-dimensional lattice. We show that this setup reproduces the main features of magnetic lattice systems, such as the fractal Hofstadter-butterfly spectrum and the chiral edge states of the associated Chern insulating phases.
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Affiliation(s)
- A Celi
- ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain
| | - P Massignan
- ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain
| | - J Ruseckas
- Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, Vilnius 01108, Lithuania
| | - N Goldman
- Laboratoire Kastler Brossel, CNRS, UPMC, ENS, 24 rue Lhomond, F-75005 Paris, France
| | - I B Spielman
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742-4111, USA and National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - G Juzeliūnas
- Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, Vilnius 01108, Lithuania
| | - M Lewenstein
- ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, E-08860 Castelldefels (Barcelona), Spain and ICREA-Institució Catalana de Recerca i Estudis Avançats, E-08010 Barcelona, Spain
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20
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Plotnik Y, Rechtsman MC, Song D, Heinrich M, Zeuner JM, Nolte S, Lumer Y, Malkova N, Xu J, Szameit A, Chen Z, Segev M. Observation of unconventional edge states in 'photonic graphene'. NATURE MATERIALS 2014; 13:57-62. [PMID: 24193661 DOI: 10.1038/nmat3783] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2012] [Accepted: 09/18/2013] [Indexed: 06/02/2023]
Abstract
Graphene, a two-dimensional honeycomb lattice of carbon atoms, has been attracting much interest in recent years. Electrons therein behave as massless relativistic particles, giving rise to strikingly unconventional phenomena. Graphene edge states are essential for understanding the electronic properties of this material. However, the coarse or impure nature of the graphene edges hampers the ability to directly probe the edge states. Perhaps the best example is given by the edge states on the bearded edge that have never been observed-because such an edge is unstable in graphene. Here, we use the optical equivalent of graphene-a photonic honeycomb lattice-to study the edge states and their properties. We directly image the edge states on both the zigzag and bearded edges of this photonic graphene, measure their dispersion properties, and most importantly, find a new type of edge state: one residing on the bearded edge that has never been predicted or observed. This edge state lies near the Van Hove singularity in the edge band structure and can be classified as a Tamm-like state lacking any surface defect. The mechanism underlying its formation may counterintuitively appear in other crystalline systems.
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Affiliation(s)
- Yonatan Plotnik
- 1] Technion-Israel Institute of Technology, Technion City 32000, Haifa, Israel [2]
| | - Mikael C Rechtsman
- 1] Technion-Israel Institute of Technology, Technion City 32000, Haifa, Israel [2]
| | - Daohong Song
- 1] The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physical School and School of Physics, Nankai University, Tianjin 300457, China [2]
| | - Matthias Heinrich
- Institute of Applied Physics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Julia M Zeuner
- Institute of Applied Physics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Stefan Nolte
- Institute of Applied Physics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Yaakov Lumer
- Technion-Israel Institute of Technology, Technion City 32000, Haifa, Israel
| | - Natalia Malkova
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
| | - Jingjun Xu
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physical School and School of Physics, Nankai University, Tianjin 300457, China
| | - Alexander Szameit
- Institute of Applied Physics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Zhigang Chen
- 1] The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physical School and School of Physics, Nankai University, Tianjin 300457, China [2] Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
| | - Mordechai Segev
- Technion-Israel Institute of Technology, Technion City 32000, Haifa, Israel
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Kennedy CJ, Siviloglou GA, Miyake H, Burton WC, Ketterle W. Spin-orbit coupling and quantum spin Hall effect for neutral atoms without spin flips. PHYSICAL REVIEW LETTERS 2013; 111:225301. [PMID: 24329453 DOI: 10.1103/physrevlett.111.225301] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2013] [Revised: 10/25/2013] [Indexed: 06/03/2023]
Abstract
We propose a scheme which realizes spin-orbit coupling and the quantum spin Hall effect for neutral atoms in optical lattices without relying on near resonant laser light to couple different spin states. The spin-orbit coupling is created by modifying the motion of atoms in a spin-dependent way by laser recoil. The spin selectivity is provided by Zeeman shifts created with a magnetic field gradient. Alternatively, a quantum spin Hall Hamiltonian can be created by all-optical means using a period-tripling, spin-dependent superlattice.
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Affiliation(s)
- Colin J Kennedy
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Georgios A Siviloglou
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Hirokazu Miyake
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - William Cody Burton
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Wolfgang Ketterle
- MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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22
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Dauphin A, Goldman N. Extracting the Chern number from the dynamics of a Fermi gas: implementing a quantum Hall bar for cold atoms. PHYSICAL REVIEW LETTERS 2013; 111:135302. [PMID: 24116789 DOI: 10.1103/physrevlett.111.135302] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2013] [Revised: 08/03/2013] [Indexed: 06/02/2023]
Abstract
We propose a scheme to measure the quantized Hall conductivity of an ultracold Fermi gas initially prepared in a topological Chern insulating phase and driven by a constant force. We show that the time evolution of the center of mass, after releasing the cloud, provides a direct and clear signature of the topologically invariant Chern number. We discuss the validity of this scheme, highlighting the importance of driving the system with a sufficiently strong force to displace the cloud over measurable distances while avoiding band-mixing effects. The unusual shapes of the driven atomic cloud are qualitatively discussed in terms of a semiclassical approach.
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Affiliation(s)
- Alexandre Dauphin
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium and Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
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23
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Liu XJ, Law KT, Ng TK, Lee PA. Detecting topological phases in cold atoms. PHYSICAL REVIEW LETTERS 2013; 111:120402. [PMID: 24093233 DOI: 10.1103/physrevlett.111.120402] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2013] [Indexed: 06/02/2023]
Abstract
Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic for neutral atoms. By establishing a natural correspondence between the time-reversal invariant topological insulator and the quantum anomalous Hall system, we show for a class of Chern insulators that the topology can be determined by only measuring Bloch eigenstates at highly symmetric points of the Brillouin zone. Furthermore, we introduce two experimental schemes, including the spin-resolved Bloch oscillation, to carry out the measurement. These schemes are highly feasible under realistic experimental conditions. Our results may provide a powerful tool to detect topological phases in cold atoms.
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Affiliation(s)
- Xiong-Jun Liu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA and Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
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24
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Grusdt F, Höning M, Fleischhauer M. Topological edge States in the one-dimensional superlattice Bose-Hubbard model. PHYSICAL REVIEW LETTERS 2013; 110:260405. [PMID: 23848851 DOI: 10.1103/physrevlett.110.260405] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2013] [Indexed: 06/02/2023]
Abstract
We analyze interacting ultracold bosonic atoms in a one-dimensional superlattice potential with alternating tunneling rates t1 and t2 and inversion symmetry, which is the bosonic analogue of the Su-Schrieffer-Heeger model. A Z2 topological order parameter is introduced which is quantized for the Mott insulating (MI) phases. Depending on the ratio t1/t2 the n=1/2 MI phase is topologically nontrivial, which results in many-body edge states at open boundaries. In contrast to the Su-Schrieffer-Heeger model the bosonic counterpart lacks chiral symmetry and the edge states are no longer midgap. This leads to a generalization of the bulk-edge correspondence, which we discuss in detail. The edge states can be observed in cold atom experiments by creating a step in the effective confining potential, e.g., by a second heavy atom species, which leads to an interface between two MI regions with filling n=1 and n=1/2. The shape and energy of the edge states as well as the conditions for their occupation are determined analytically in the strong coupling limit and in general by density-matrix renormalization group simulations.
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Affiliation(s)
- Fabian Grusdt
- Department of Physics and Research Center OPTIMAS, Technische Universität Kaiserslautern, D-67663 Kaiserslautern, Germany
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25
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Yao NY, Gorshkov AV, Laumann CR, Läuchli AM, Ye J, Lukin MD. Realizing fractional Chern insulators in dipolar spin systems. PHYSICAL REVIEW LETTERS 2013; 110:185302. [PMID: 23683213 DOI: 10.1103/physrevlett.110.185302] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2013] [Indexed: 06/02/2023]
Abstract
Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the ν = 1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific implementation, we analyze how to prepare and detect synthetic gauge potentials for the rotational excitations of ultracold polar molecules trapped in a deep optical lattice. With the motion of the molecules pinned, under certain conditions, these rotational excitations form a fractional Chern insulating state. We present a detailed experimental blueprint for its realization and demonstrate that the implementation is consistent with near-term capabilities. Prospects for the realization of such phases in solid-state dipolar systems are discussed as are their possible applications.
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Affiliation(s)
- N Y Yao
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
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26
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Wang L, Soluyanov AA, Troyer M. Proposal for direct measurement of topological invariants in optical lattices. PHYSICAL REVIEW LETTERS 2013; 110:166802. [PMID: 23679630 DOI: 10.1103/physrevlett.110.166802] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2013] [Indexed: 06/02/2023]
Abstract
We propose an experimental technique for classifying the topology of band structures realized in optical lattices, based on a generalization of topological charge pumping in quantum Hall systems to cold atoms in optical lattices. Time-of-flight measurement along one spatial direction combined with in situ detection along the transverse direction provides a direct measure of the system's Chern number, as we illustrate by calculations for the Hofstadter lattice. Based on an analogy with Wannier function techniques of topological band theory, the method is very general and also allows the measurement of other topological invariants, such as the Z(2) topological invariant of time-reversal symmetric insulators.
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Affiliation(s)
- Lei Wang
- Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
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27
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Abstract
Detecting topological order in cold-atom experiments is an ongoing challenge, the resolution of which offers novel perspectives on topological matter. In material systems, unambiguous signatures of topological order exist for topological insulators and quantum Hall devices. In quantum Hall systems, the quantized conductivity and the associated robust propagating edge modes--guaranteed by the existence of nontrivial topological invariants--have been observed through transport and spectroscopy measurements. Here, we show that optical-lattice-based experiments can be tailored to directly visualize the propagation of topological edge modes. Our method is rooted in the unique capability for initially shaping the atomic gas and imaging its time evolution after suddenly removing the shaping potentials. Our scheme, applicable to an assortment of atomic topological phases, provides a method for imaging the dynamics of topological edge modes, directly revealing their angular velocity and spin structure.
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28
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Liu XJ, Liu ZX, Cheng M. Manipulating topological edge spins in a one-dimensional optical lattice. PHYSICAL REVIEW LETTERS 2013; 110:076401. [PMID: 25166386 DOI: 10.1103/physrevlett.110.076401] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2012] [Indexed: 05/22/2023]
Abstract
We propose to observe and manipulate topological edge spins in a one-dimensional optical lattice based on currently available experimental platforms. Coupling the atomic spin states to a laser-induced periodic Zeeman field, the lattice system can be driven into a symmetry protected topological (SPT) phase, which belongs to the chiral unitary (AIII) class protected by particle number conservation and chiral symmetries. In the free-fermion case the SPT phase is classified by a Z invariant which reduces to Z(4) with interactions. The zero edge modes of the SPT phase are spin polarized, with left and right edge spins polarized to opposite directions and forming a topological spin qubit (TSQ). We demonstrate a novel scheme to manipulate the zero modes and realize single spin control in an optical lattice. The manipulation of TSQs has potential applications to quantum computation.
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Affiliation(s)
- Xiong-Jun Liu
- Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA and Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA and Department of Physics, Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
| | - Zheng-Xin Liu
- Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Meng Cheng
- Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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29
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Barnett R, Boyd GR, Galitski V. SU(3) spin-orbit coupling in systems of ultracold atoms. PHYSICAL REVIEW LETTERS 2012; 109:235308. [PMID: 23368222 DOI: 10.1103/physrevlett.109.235308] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2012] [Indexed: 06/01/2023]
Abstract
Motivated by the recent experimental success in realizing synthetic spin-orbit coupling in ultracold atomic systems, we consider N-component atoms coupled to a non-Abelian SU(N) gauge field. More specifically, we focus on the case, referred to here as "SU(3) spin-orbit-coupling," where the internal states of three-component atoms are coupled to their momenta via a matrix structure that involves the Gell-Mann matrices (in contrast to the Pauli matrices in conventional SU(2) spin-orbit-coupled systems). It is shown that the SU(3) spin-orbit-coupling gives rise to qualitatively different phenomena and in particular we find that even a homogeneous SU(3) field on a simple square lattice enables a topologically nontrivial state to exist, while such SU(2) systems always have trivial topology. In deriving this result, we first establish an equivalence between the Hofstadter model with a 1/N Abelian flux per plaquette and a homogeneous SU(N) non-Abelian model. The former is known to have a topological spectrum for N>2, which is thus inherited by the latter. It is explicitly verified by an exact calculation for N=3, where we develop and use a new algebraic method to calculate topological indices in the SU(3) case. Finally, we consider a strip geometry and establish the existence of three gapless edge states-the hallmark feature of such an SU(3) topological insulator.
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Affiliation(s)
- Ryan Barnett
- Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA
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Cocks D, Orth PP, Rachel S, Buchhold M, Le Hur K, Hofstetter W. Time-reversal-invariant Hofstadter-Hubbard model with ultracold fermions. PHYSICAL REVIEW LETTERS 2012; 109:205303. [PMID: 23215500 DOI: 10.1103/physrevlett.109.205303] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2012] [Revised: 07/10/2012] [Indexed: 06/01/2023]
Abstract
We consider the time-reversal-invariant Hofstadter-Hubbard model which can be realized in cold-atom experiments. In these experiments, an additional staggered potential and an artificial Rashba-type spin-orbit coupling are available. Without interactions, the system exhibits various phases such as topological and normal insulator, metal as well as semi-metal phases with two or even more Dirac cones. Using a combination of real-space dynamical mean-field theory and analytical techniques, we discuss the effect of on-site interactions and determine the corresponding phase diagram. In particular, we investigate the semi-metal to antiferromagnetic insulator transition and the stability of different topological insulator phases in the presence of strong interactions. We compute spectral functions which allow us to study the edge states of the strongly correlated topological phases.
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Affiliation(s)
- Daniel Cocks
- Institut für Theoretische Physik, Goethe-Universität, 60438 Frankfurt/Main, Germany
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