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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Guo Y, Yao H, Dhar S, Pizzino L, Horvath M, Giamarchi T, Landini M, Nägerl HC. Anomalous cooling of bosons by dimensional reduction. SCIENCE ADVANCES 2024; 10:eadk6870. [PMID: 38354241 PMCID: PMC10866542 DOI: 10.1126/sciadv.adk6870] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2023] [Accepted: 01/11/2024] [Indexed: 02/16/2024]
Abstract
Cold atomic gases provide a remarkable testbed to study the physics of interacting many-body quantum systems. Temperatures are necessarily nonzero, but cooling to the ultralow temperatures needed for quantum simulation purposes or even simply measuring the temperatures directly on the system can prove to be very challenging tasks. Here, we implement thermometry on strongly interacting two- and one-dimensional Bose gases with high sensitivity in the nanokelvin temperature range. Our method is aided by the fact that the decay of the first-order correlation function is very sensitive to the temperature when interactions are strong. We find that there may be a substantial temperature variation when the three-dimensional quantum gas is cut into two-dimensional slices or into one-dimensional tubes. Notably, the temperature for the one-dimensional case can be much lower than the initial temperature. Our findings show that this decrease results from the interplay of dimensional reduction and strong interactions.
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Affiliation(s)
- Yanliang Guo
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, Technikerstraße 25, Innsbruck 6020, Austria
| | - Hepeng Yao
- DQMP, University of Geneva, 24 Quai Ernest-Ansermet, Geneva CH-1211, Switzerland
| | - Sudipta Dhar
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, Technikerstraße 25, Innsbruck 6020, Austria
| | - Lorenzo Pizzino
- DQMP, University of Geneva, 24 Quai Ernest-Ansermet, Geneva CH-1211, Switzerland
| | - Milena Horvath
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, Technikerstraße 25, Innsbruck 6020, Austria
| | - Thierry Giamarchi
- DQMP, University of Geneva, 24 Quai Ernest-Ansermet, Geneva CH-1211, Switzerland
| | - Manuele Landini
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, Technikerstraße 25, Innsbruck 6020, Austria
| | - Hanns-Christoph Nägerl
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, Technikerstraße 25, Innsbruck 6020, Austria
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4
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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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5
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Tang Q, Ren B, Kompanets VO, Kartashov YV, Li Y, Zhang Y. Valley Hall edge solitons in a photonic graphene. OPTICS EXPRESS 2021; 29:39755-39765. [PMID: 34809332 DOI: 10.1364/oe.442338] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Accepted: 10/29/2021] [Indexed: 06/13/2023]
Abstract
We predict the existence and study properties of the valley Hall edge solitons in a composite photonic graphene with a domain wall between two honeycomb lattices with broken inversion symmetry. Inversion symmetry in our system is broken due to detuning introduced into constituent sublattices of the honeycomb structure. We show that nonlinear valley Hall edge states with sufficiently high amplitude bifurcating from the linear valley Hall edge state supported by the domain wall, can split into sets of bright spots due to development of the modulational instability, and that such an instability is a precursor for the formation of topological bright valley Hall edge solitons localized due to nonlinear self-action and travelling along the domain wall over large distances. Topological protection of the valley Hall edge solitons is demonstrated by modeling their passage through sharp corners of the Ω-shaped domain wall.
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6
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Yan Q, Cao E, Sun Q, Ao Y, Hu X, Shi X, Gong Q, Misawa H. Near-Field Imaging and Time-Domain Dynamics of Photonic Topological Edge States in Plasmonic Nanochains. NANO LETTERS 2021; 21:9270-9278. [PMID: 34670093 DOI: 10.1021/acs.nanolett.1c03324] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Time-domain dynamic evolution properties of topological states play an important role in both fundamental physics study and practical applications of topological photonics. However, owing to the absence of available ultrafast time-domain dynamic characterization methods, studies have mostly focused on the frequency-domain-based properties, and there are few reports demonstrating the time-domain-based properties. Here, we measured the dynamic near-field responses of plasmonic topological structures of gold nanochains with the configuration of the Su-Schrieffer-Heeger model by using ultrahigh spatial-temporal resolution photoemission electron microscopy. The dephasing time of plasmonic topological edge states increases with increasing the bulk lattice number that has a threshold requirement and finally reaches saturation. We directly revealed through simulation that there is a transient bulk state in the evolution of topological edge states, that is, the energy undergoes relaxation from oscillation between the bulk lattice and the edge. This work shows a new perspective of time-domain dynamic topological photonics.
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Affiliation(s)
- Qiuchen Yan
- State Key Laboratory for Mesoscopic Physics and Department of Physics, Collaborative Innovation Center of Quantum Matter and Frontiers Science Center for Nano-optoelectronics, Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, P.R. China
- Research Institute for Electronic Science, Hokkaido University, Sapporo 001-0021, Japan
| | - En Cao
- Research Institute for Electronic Science, Hokkaido University, Sapporo 001-0021, Japan
| | - Quan Sun
- Yangtze Delta Institute of Optoelectronics, Peking University, Nantong, Jiangsu 226010, P.R. China
| | - Yutian Ao
- State Key Laboratory for Mesoscopic Physics and Department of Physics, Collaborative Innovation Center of Quantum Matter and Frontiers Science Center for Nano-optoelectronics, Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, P.R. China
| | - Xiaoyong Hu
- State Key Laboratory for Mesoscopic Physics and Department of Physics, Collaborative Innovation Center of Quantum Matter and Frontiers Science Center for Nano-optoelectronics, Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, P.R. China
- Yangtze Delta Institute of Optoelectronics, Peking University, Nantong, Jiangsu 226010, P.R. China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, P.R. China
| | - Xu Shi
- Creative Research Institution, Hokkaido University, Sapporo 001-0021, Japan
| | - Qihuang Gong
- State Key Laboratory for Mesoscopic Physics and Department of Physics, Collaborative Innovation Center of Quantum Matter and Frontiers Science Center for Nano-optoelectronics, Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, P.R. China
- Yangtze Delta Institute of Optoelectronics, Peking University, Nantong, Jiangsu 226010, P.R. China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, P.R. China
| | - Hiroaki Misawa
- Research Institute for Electronic Science, Hokkaido University, Sapporo 001-0021, Japan
- Center for Emergent Functional Matter Science, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan
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7
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Wavefront dislocations reveal the topology of quasi-1D photonic insulators. Nat Commun 2021; 12:3571. [PMID: 34117232 PMCID: PMC8196168 DOI: 10.1038/s41467-021-23790-w] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Accepted: 05/11/2021] [Indexed: 11/25/2022] Open
Abstract
Phase singularities appear ubiquitously in wavefields, regardless of the wave equation. Such topological defects can lead to wavefront dislocations, as observed in a humongous number of classical wave experiments. Phase singularities of wave functions are also at the heart of the topological classification of the gapped phases of matter. Despite identical singular features, topological insulators and topological defects in waves remain two distinct fields. Realising 1D microwave insulators, we experimentally observe a wavefront dislocation – a 2D phase singularity – in the local density of states when the systems undergo a topological phase transition. We show theoretically that the change in the number of interference fringes at the transition reveals the topological index that characterises the band topology in the insulator. Topological properties are defined from singularities of the wave functions delocalised in the bulk of the material, but most experimental manifestations remain indirect. Here, the authors observe a wavefront dislocation as a direct evidence of the phase singularity of the delocalised wave functions in 1D microwave photonic insulators.
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8
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Motruk J, Na I. Detecting Fractional Chern Insulators in Optical Lattices through Quantized Displacement. PHYSICAL REVIEW LETTERS 2020; 125:236401. [PMID: 33337233 DOI: 10.1103/physrevlett.125.236401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Accepted: 10/22/2020] [Indexed: 06/12/2023]
Abstract
The realization of interacting topological states of matter such as fractional Chern insulators (FCIs) in cold atom systems has recently come within experimental reach due to the engineering of optical lattices with synthetic gauge fields providing the required topological band structures. However, detecting their occurrence might prove difficult since transport measurements akin to those in solid state systems are challenging to perform in cold atom setups and alternatives have to be found. We show that for a ν=1/2 FCI state realized in the lowest band of a Harper-Hofstadter model of interacting bosons confined by a harmonic trapping potential, the fractionally quantized Hall conductivity σ_{xy} can be accurately determined by the displacement of the atomic cloud under the action of a constant force which provides a suitable experimentally measurable signal for detecting the topological nature of the state. Using matrix-product state algorithms, we show that, in both cylinder and square geometries, the movement of the particle cloud in time under the application of a constant force field on top of the confining potential is proportional to σ_{xy} for an extended range of field strengths.
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Affiliation(s)
- Johannes Motruk
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Ilyoun Na
- Department of Physics, University of California, Berkeley, California 94720, USA
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9
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Delacrétaz LV, Glorioso P. Breakdown of Diffusion on Chiral Edges. PHYSICAL REVIEW LETTERS 2020; 124:236802. [PMID: 32603169 DOI: 10.1103/physrevlett.124.236802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2020] [Accepted: 05/21/2020] [Indexed: 06/11/2023]
Abstract
We show that dirty quantum Hall systems exhibit large hydrodynamic fluctuations at their edge that lead to anomalously damped charge excitations in the Kardar-Parisi-Zhang universality class ω≃ck-iDk^{3/2}. The dissipative optical conductivity of the edge is singular at low frequencies σ(ω)∼1/ω^{1/3}. These results are direct consequences of the charge continuity relation, the chiral anomaly, and thermalization on the edge-in particular translation invariance is not assumed. Diffusion of heat similarly breaks down, with a universality class that depends on whether the bulk thermal Hall conductivity vanishes. We further establish the theory of fluctuating hydrodynamics for surface chiral metals, where charge fluctuations give logarithmic corrections to transport.
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Affiliation(s)
- Luca V Delacrétaz
- Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Paolo Glorioso
- Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA
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10
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Zhang W, Chen X, Kartashov YV, Konotop VV, Ye F. Coupling of Edge States and Topological Bragg Solitons. PHYSICAL REVIEW LETTERS 2019; 123:254103. [PMID: 31922795 DOI: 10.1103/physrevlett.123.254103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2019] [Indexed: 06/10/2023]
Abstract
The existence of the edge states at the interface between two media with different topological properties is protected by symmetry, which makes such states robust against structural defects or disorder. We show that, if a system supports more than one topological edge state at the interface, even a weak periodic deformation may scatter one edge state into another without coupling to bulk modes. This is the Bragg scattering of the edge modes, which in a topological system is highly selective, with closed bulk and backward scattering channels, even when conditions for resonant scattering are not satisfied. When such a system bears nonlinearity, Bragg scattering enables the formation of a new type of soliton-topological Bragg solitons. We report them in a spin-orbit-coupled (SOC) Bose-Einstein condensate in a homogeneous honeycomb Zeeman lattice. An interface supporting two edge states is created by two different SOCs, with the y component of the synthetic magnetic field having opposite directions at different sides of the interface. The reported Bragg solitons are found to be stable.
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Affiliation(s)
- Weifeng Zhang
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Xianfeng Chen
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Yaroslav V Kartashov
- Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region, 108840, Russia
| | - Vladimir V Konotop
- Departamento de Física and Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8, Lisboa 1749-016, Portugal
| | - Fangwei Ye
- State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
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11
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Longhi S. Probing topological phases in waveguide superlattices. OPTICS LETTERS 2019; 44:2530-2533. [PMID: 31090724 DOI: 10.1364/ol.44.002530] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2019] [Accepted: 04/21/2019] [Indexed: 06/09/2023]
Abstract
One-dimensional superlattices with modulated coupling constants show rich topological properties and tunable edge states. Beyond the dimeric case, probing the topological properties of superlattices is a challenge. Here we suggest a rather general method of bulk probing topological invariants in waveguide superlattices based on spatial displacement of discretized beams. A judiciously tailored initial beam excitation of the lattice, corresponding to superposition of Wannier functions, provides a direct measure of the band gap topological numbers. For a quadrimeric superlattice, a simple bulk probing method, which avoids Wannier states, is proposed to discriminate the existence of zero-energy topological edge states from non-topological ones.
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12
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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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13
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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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14
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Cooper NR, Dalibard J, Spielman IB. Topological bands for ultracold atoms. REVIEWS OF MODERN PHYSICS 2019; 91:10.1103/revmodphys.91.015005. [PMID: 32189812 PMCID: PMC7079706 DOI: 10.1103/revmodphys.91.015005] [Citation(s) in RCA: 123] [Impact Index Per Article: 24.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
There have been significant recent advances in realizing band structures with geometrical and topological features in experiments on cold atomic gases. This review summarizes these developments, beginning with a summary of the key concepts of geometry and topology for Bloch bands. Descriptions are given of the different methods that have been used to generate these novel band structures for cold atoms and of the physical observables that have allowed their characterization. The focus is on the physical principles that underlie the different experimental approaches, providing a conceptual framework within which to view these developments. Also described is how specific experimental implementations can influence physical properties. Moving beyond single-particle effects, descriptions are given of the forms of interparticle interactions that emerge when atoms are subjected to these energy bands and of some of the many-body phases that may be sought in future experiments.
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Affiliation(s)
- N R Cooper
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - J Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 place Marcelin Berthelot, 75005, Paris, France
| | - I B Spielman
- Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA
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15
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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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16
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Jin L, Song Z. Incident Direction Independent Wave Propagation and Unidirectional Lasing. PHYSICAL REVIEW LETTERS 2018; 121:073901. [PMID: 30169058 DOI: 10.1103/physrevlett.121.073901] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2018] [Indexed: 06/08/2023]
Abstract
We propose an incident direction independent wave propagation generated by properly assembling different unidirectional destructive interferences (UDIs), which is a consequence of the appropriate match between synthetic magnetic fluxes and the incident wave vector. Single-direction lasing at spectral singularity is feasible without introducing nonlinearity. UDI allows unidirectional lasing and unidirectional perfect absorption; when they are combined in a parity-time-symmetric manner, the spectral singularities vanish with bounded reflections and transmissions. Furthermore, the simultaneous unidirectional lasing and perfect absorption for incidences from opposite directions is created. Our findings provide insights into light control and may shed light on the explorations of desirable functionality in fundamental research and practical applications.
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Affiliation(s)
- L Jin
- School of Physics, Nankai University, Tianjin 300071, China
| | - Z Song
- School of Physics, Nankai University, Tianjin 300071, China
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17
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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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18
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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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19
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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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20
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Jendrzejewski F, Eckel S, Tiecke TG, Juzeliūnas G, Campbell GK, Jiang L, Gorshkov AV. Subwavelength-width optical tunnel junctions for ultracold atoms. PHYSICAL REVIEW. A 2016; 94:10.1103/PhysRevA.94.063422. [PMID: 31098433 PMCID: PMC6515915 DOI: 10.1103/physreva.94.063422] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
We propose a method for creating far-field optical barrier potentials for ultracold atoms with widths that are narrower than the diffraction limit and can approach tens of nanometers. The reduced widths stem from the nonlinear atomic response to control fields that create spatially varying dark resonances. The subwavelength barrier is the result of the geometric scalar potential experienced by an atom prepared in such a spatially varying dark state. The performance of this technique, as well as its applications to the study of many-body physics and to the implementation of quantum-information protocols with ultracold atoms, are discussed, with a focus on the implementation of tunnel junctions.
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Affiliation(s)
- F Jendrzejewski
- Kirchhoff Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - S Eckel
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - T G Tiecke
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Facebook Inc., Connectivity Lab, 1 Hacker Way, Menlo Park, California 94025, USA
| | - G Juzeliūnas
- Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio Avenue 3, LT-10222 Vilnius, Lithuania
| | - G K Campbell
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Liang Jiang
- Departments of Applied Physics and Physics, Yale University, New Haven, Connecticut 06520, USA
| | - A V Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
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21
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Caio MD, Cooper NR, Bhaseen MJ. Quantum Quenches in Chern Insulators. PHYSICAL REVIEW LETTERS 2015; 115:236403. [PMID: 26684130 DOI: 10.1103/physrevlett.115.236403] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2015] [Indexed: 05/22/2023]
Abstract
We explore the nonequilibrium response of Chern insulators. Focusing on the Haldane model, we study the dynamics induced by quantum quenches between topological and nontopological phases. A notable feature is that the Chern number, calculated for an infinite system, is unchanged under the dynamics following such a quench. However, in finite geometries, the initial and final Hamiltonians are distinguished by the presence or absence of edge modes. We study the edge excitations and describe their impact on the experimentally observable edge currents and magnetization. We show that, following a quantum quench, the edge currents relax towards new equilibrium values, and that there is light-cone spreading of the currents into the interior of the sample.
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Affiliation(s)
- M D Caio
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - N R Cooper
- T.C.M. Group, Cavendish Laboratory, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - M J Bhaseen
- Department of Physics, King's College London, Strand, London WC2R 2LS, United Kingdom
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22
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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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23
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Zhao J, Hu S, Zhang P. Symmetry-Protected Topological Phase in a One-Dimensional Correlated Bosonic Model with a Synthetic Spin-Orbit Coupling. PHYSICAL REVIEW LETTERS 2015; 115:195302. [PMID: 26588393 DOI: 10.1103/physrevlett.115.195302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2015] [Indexed: 06/05/2023]
Abstract
By performing large-scale density-matrix renormalization group simulations, we investigate a one-dimensional correlated bosonic lattice model with a synthetic spin-orbit coupling realized in recent experiments. In the insulating regime, this model exhibits a symmetry-protected topological phase. This symmetry-protected topological phase is stabilized by time-reversal symmetry and it is identified as a Haldane phase. We confirm our conclusions further by analyzing the entanglement spectrum. In addition, we find four conventional phases: a Mott insulating phase with no long range order, a ferromagnetic superfluid phase, a ferromagnetic insulating phase, and a density-wave phase.
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Affiliation(s)
- Jize Zhao
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
| | - Shijie Hu
- Department of Physics and Research Center Optimas, Technical University Kaiserslautern, 67663 Kaiserslautern, Germany
| | - Ping Zhang
- Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
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24
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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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25
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Quantum simulation of 2D topological physics in a 1D array of optical cavities. Nat Commun 2015; 6:7704. [PMID: 26145177 PMCID: PMC4506549 DOI: 10.1038/ncomms8704] [Citation(s) in RCA: 93] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2014] [Accepted: 06/01/2015] [Indexed: 11/14/2022] Open
Abstract
Orbital angular momentum of light is a fundamental optical degree of freedom characterized by unlimited number of available angular momentum states. Although this unique property has proved invaluable in diverse recent studies ranging from optical communication to quantum information, it has not been considered useful or even relevant for simulating nontrivial physics problems such as topological phenomena. Contrary to this misconception, we demonstrate the incredible value of orbital angular momentum of light for quantum simulation by showing theoretically how it allows to study a variety of important 2D topological physics in a 1D array of optical cavities. This application for orbital angular momentum of light not only reduces required physical resources but also increases feasible scale of simulation, and thus makes it possible to investigate important topics such as edge-state transport and topological phase transition in a small simulator ready for immediate experimental exploration. A wide variety of interesting phenomena arise in 2D systems subject to external gauge fields, but these are sometimes challenging to verify experimentally. Here the authors propose a setup to simulate 2D physics with a 1D arrangement of cavities, by exploiting the orbital angular momentum of trapped photons.
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26
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Dubček T, Kennedy CJ, Lu L, Ketterle W, Soljačić M, Buljan H. Weyl Points in Three-Dimensional Optical Lattices: Synthetic Magnetic Monopoles in Momentum Space. PHYSICAL REVIEW LETTERS 2015. [PMID: 26196624 DOI: 10.1103/physrevlett.114.225301] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
We show that a Hamiltonian with Weyl points can be realized for ultracold atoms using laser-assisted tunneling in three-dimensional optical lattices. Weyl points are synthetic magnetic monopoles that exhibit a robust, three-dimensional linear dispersion, identical to the energy-momentum relation for relativistic Weyl fermions, which are not yet discovered in particle physics. Weyl semimetals are a promising new avenue in condensed matter physics due to their unusual properties such as the topologically protected "Fermi arc" surface states. However, experiments on Weyl points are highly elusive. We show that this elusive goal is well within experimental reach with an extension of techniques recently used in ultracold gases.
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Affiliation(s)
- Tena Dubček
- Department of Physics, University of Zagreb, Bijenička cesta 32, 10000 Zagreb, Croatia
| | - Colin J Kennedy
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Ling Lu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Wolfgang Ketterle
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Marin Soljačić
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Hrvoje Buljan
- Department of Physics, University of Zagreb, Bijenička cesta 32, 10000 Zagreb, Croatia
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27
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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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28
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Lim LK, Fuchs JN, Montambaux G. Mass and chirality inversion of a Dirac cone pair in Stückelberg interferometry. PHYSICAL REVIEW LETTERS 2014; 112:155302. [PMID: 24785046 DOI: 10.1103/physrevlett.112.155302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2013] [Indexed: 06/03/2023]
Abstract
We show that a Stückelberg interferometer made of two massive Dirac cones can reveal information on band eigenstates such as the chirality and mass sign of the cones. For a given spectrum with two gapped cones, we propose several low-energy Hamiltonians differing by their eigenstates properties. The corresponding interband transition probability is affected by such differences in its interference fringes being shifted by a new phase of geometrical origin. This phase can be a useful bulk probe for topological band structures realized with artificial crystals.
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Affiliation(s)
- Lih-King Lim
- Laboratoire de Physique des Solides, CNRS UMR 8502, Université Paris-Sud, 91405 Orsay, France and Laboratoire Charles Fabry, Institut d'Optique, CNRS, Université Paris-Sud, 2 avenue Augustin Fresnel, F-91127 Palaiseau cedex, France
| | - Jean-Noël Fuchs
- Laboratoire de Physique des Solides, CNRS UMR 8502, Université Paris-Sud, 91405 Orsay, France and Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre et Marie Curie, 4 place Jussieu, F-75252 Paris, France
| | - Gilles Montambaux
- Laboratoire de Physique des Solides, CNRS UMR 8502, Université Paris-Sud, 91405 Orsay, France
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29
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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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30
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Lababidi M, Satija II, Zhao E. Counter-propagating edge modes and topological phases of a kicked quantum Hall system. PHYSICAL REVIEW LETTERS 2014; 112:026805. [PMID: 24484039 DOI: 10.1103/physrevlett.112.026805] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2013] [Indexed: 06/03/2023]
Abstract
A periodically driven quantum Hall system in a fixed magnetic field is found to exhibit a series of phases featuring anomalous edge modes with the "wrong" chirality. This leads to pairs of counter-propagating chiral edge modes at each edge, in sharp contrast to stationary quantum Hall systems. We show that the pair of Floquet edge modes are protected by the chiral (sublattice) symmetry, and that they are robust against static disorder. The existence of distinctive phases with the same Chern and winding numbers but very different edge state spectra points to the important role played by symmetry in classifying topological properties of driven systems. We further explore the evolution of the edge states with driving using a simplified model, and discuss their experimental signatures.
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Affiliation(s)
- Mahmoud Lababidi
- School of Physics, Astronomy, and Computational Sciences, George Mason University, Fairfax, Virginia 22030, USA
| | - Indubala I Satija
- School of Physics, Astronomy, and Computational Sciences, George Mason University, Fairfax, Virginia 22030, USA
| | - Erhai Zhao
- School of Physics, Astronomy, and Computational Sciences, George Mason University, Fairfax, Virginia 22030, USA
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31
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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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32
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Aidelsburger M, Atala M, Lohse M, Barreiro JT, Paredes B, Bloch I. Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices. PHYSICAL REVIEW LETTERS 2013; 111:185301. [PMID: 24237530 DOI: 10.1103/physrevlett.111.185301] [Citation(s) in RCA: 231] [Impact Index Per Article: 21.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2013] [Indexed: 05/02/2023]
Abstract
We demonstrate the experimental implementation of an optical lattice that allows for the generation of large homogeneous and tunable artificial magnetic fields with ultracold atoms. Using laser-assisted tunneling in a tilted optical potential, we engineer spatially dependent complex tunneling amplitudes. Thereby, atoms hopping in the lattice accumulate a phase shift equivalent to the Aharonov-Bohm phase of charged particles in a magnetic field. We determine the local distribution of fluxes through the observation of cyclotron orbits of the atoms on lattice plaquettes, showing that the system is described by the Hofstadter model. Furthermore, we show that for two atomic spin states with opposite magnetic moments, our system naturally realizes the time-reversal-symmetric Hamiltonian underlying the quantum spin Hall effect; i.e., two different spin components experience opposite directions of the magnetic field.
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Affiliation(s)
- M Aidelsburger
- Fakultät für Physik, Ludwig-Maximilians-Universität, Schellingstrasse 4, 80799 München, Germany and Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
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33
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Longhi S. Zak phase of photons in optical waveguide lattices. OPTICS LETTERS 2013; 38:3716-3719. [PMID: 24081034 DOI: 10.1364/ol.38.003716] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Zak phase, that is, the Berry phase acquired during an adiabatic motion of a Bloch particle across the Brillouin zone, provides a measure of the topological invariant of Bloch bands in one-dimensional crystalline potentials. Here a photonic structure, based on engineered lattices of evanescently coupled optical waveguides, is proposed to detect Zak phase difference of photons undergoing Bloch oscillations in topologically distinct Bloch bands of dimerized superlattices.
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34
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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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35
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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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