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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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2
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Léonard J, Kim S, Kwan J, Segura P, Grusdt F, Repellin C, Goldman N, Greiner M. Realization of a fractional quantum Hall state with ultracold atoms. Nature 2023; 619:495-499. [PMID: 37344594 DOI: 10.1038/s41586-023-06122-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2022] [Accepted: 04/24/2023] [Indexed: 06/23/2023]
Abstract
Strongly interacting topological matter1 exhibits fundamentally new phenomena with potential applications in quantum information technology2,3. Emblematic instances are fractional quantum Hall (FQH) states4, in which the interplay of a magnetic field and strong interactions gives rise to fractionally charged quasi-particles, long-ranged entanglement and anyonic exchange statistics. Progress in engineering synthetic magnetic fields5-21 has raised the hope to create these exotic states in controlled quantum systems. However, except for a recent Laughlin state of light22, preparing FQH states in engineered systems remains elusive. Here we realize a FQH state with ultracold atoms in an optical lattice. The state is a lattice version of a bosonic ν = 1/2 Laughlin state4,23 with two particles on 16 sites. This minimal system already captures many hallmark features of Laughlin-type FQH states24-28: we observe a suppression of two-body interactions, we find a distinctive vortex structure in the density correlations and we measure a fractional Hall conductivity of σH/σ0 = 0.6(2) by means of the bulk response to a magnetic perturbation. Furthermore, by tuning the magnetic field, we map out the transition point between the normal and the FQH regime through a spectroscopic investigation of the many-body gap. Our work provides a starting point for exploring highly entangled topological matter with ultracold atoms29-33.
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Affiliation(s)
- Julian Léonard
- Department of Physics, Harvard University, Cambridge, MA, USA.
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Vienna, Austria.
| | - Sooshin Kim
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Joyce Kwan
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Perrin Segura
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Fabian Grusdt
- Department of Physics and ASC, Ludwig-Maximilians-Universität München, Munich, Germany
- Munich Center for Quantum Science and Technology (MCQST), Munich, Germany
| | | | - Nathan Goldman
- Center for Nonlinear Phenomena and Complex Systems (CENOLI), Université Libre de Bruxelles, Brussels, Belgium
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA
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3
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Umucalılar RO, Iskin M. BCS Theory of Time-Reversal-Symmetric Hofstadter-Hubbard Model. PHYSICAL REVIEW LETTERS 2017; 119:085301. [PMID: 28952771 DOI: 10.1103/physrevlett.119.085301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2017] [Indexed: 06/07/2023]
Abstract
The competition between the length scales associated with the periodicity of a lattice potential and the cyclotron radius of a uniform magnetic field is known to have dramatic effects on the single-particle properties of a quantum particle, e.g., the fractal spectrum is known as the Hofstadter butterfly. Having this intricate competition in mind, we consider a two-component Fermi gas on a square optical lattice with opposite synthetic magnetic fields for the components, and study its effects on the many-body BCS-pairing phenomenon. By a careful addressing of the distinct superfluid transitions from the semimetal, quantum spin-Hall insulator, or normal phases, we explore the low-temperature phase diagrams of the model, displaying lobe structures that are reminiscent of the well-known Mott-insulator transitions of the Bose-Hubbard model.
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Affiliation(s)
- R O Umucalılar
- Department of Physics, Koç University, Rumelifeneri Yolu, 34450 Sarıyer, Istanbul, Turkey
- Department of Physics, Mimar Sinan Fine Arts University, 34380 Şişli, Istanbul, Turkey
| | - M Iskin
- Department of Physics, Koç University, Rumelifeneri Yolu, 34450 Sarıyer, Istanbul, Turkey
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4
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Asbóth JK, Alberti A. Spectral Flow and Global Topology of the Hofstadter Butterfly. PHYSICAL REVIEW LETTERS 2017; 118:216801. [PMID: 28598676 DOI: 10.1103/physrevlett.118.216801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2016] [Indexed: 06/07/2023]
Abstract
We study the relation between the global topology of the Hofstadter butterfly of a multiband insulator and the topological invariants of the underlying Hamiltonian. The global topology of the butterfly, i.e., the displacement of the energy gaps as the magnetic field is varied by one flux quantum, is determined by the spectral flow of energy eigenstates crossing gaps as the field is tuned. We find that for each gap this spectral flow is equal to the topological invariant of the gap, i.e., the net number of edge modes traversing the gap. For periodically driven systems, our results apply to the spectrum of quasienergies. In this case, the spectral flow of the sum of all the quasienergies gives directly the Rudner-Lindner-Berg-Levin invariant that characterizes the topological phases of a periodically driven system.
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Affiliation(s)
- János K Asbóth
- Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, H-1525 Budapest P.O. Box 49, Hungary
| | - Andrea Alberti
- Institut für Angewandte Physik, Universität Bonn, Wegelerstraße 8, D-53115 Bonn, Germany
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5
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Goldman N, Juzeliūnas G, Öhberg P, Spielman IB. Light-induced gauge fields for ultracold atoms. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2014; 77:126401. [PMID: 25422950 DOI: 10.1088/0034-4885/77/12/126401] [Citation(s) in RCA: 179] [Impact Index Per Article: 17.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle-the graviton-that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms 'feeling' laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials-both Abelian and non-Abelian-in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.
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Affiliation(s)
- N Goldman
- College de France, 11 place Marcelin Berthelot & Laboratoire Kastler Brossel, CNRS, UPMC, ENS, 24 rue Lhomond, 75005 Paris, France
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6
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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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7
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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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8
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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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9
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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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10
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Zhu SL, Wang ZD, Chan YH, Duan LM. Topological Bose-Mott insulators in a one-dimensional optical superlattice. PHYSICAL REVIEW LETTERS 2013; 110:075303. [PMID: 25166380 DOI: 10.1103/physrevlett.110.075303] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2012] [Indexed: 06/03/2023]
Abstract
We study topological properties of the Bose-Hubbard model with repulsive interactions in a one-dimensional optical superlattice. We find that the Mott insulator states of the single-component (two-component) Bose-Hubbard model under fractional fillings are topological insulators characterized by a nonzero charge (or spin) Chern number with nontrivial edge states. For ultracold atomic experiments, we show that the topological Chern number can be detected through measuring the density profiles of the bosonic atoms in a harmonic trap.
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Affiliation(s)
- Shi-Liang Zhu
- National Laboratory of Solid State Microstructures, Department of Physics, Nanjing University, Nanjing 210093, China and Laboratory of Quantum Information Technology and SPTE, South China Normal University, Guangzhou 510631, China and Department of Physics and Center of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Z-D Wang
- Department of Physics and Center of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Y-H Chan
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA and Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, China
| | - L-M Duan
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA and Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, China
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11
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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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12
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Islamoğlu S, Oktel MO, Gülseren O. The integer quantum Hall effect of a square lattice with an array of point defects. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:345501. [PMID: 22850432 DOI: 10.1088/0953-8984/24/34/345501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The electronic properties of a square lattice under an applied perpendicular magnetic field in the presence of impurities or vacancies are investigated by the tight-binding method including up to second nearest neighbor interactions. These imperfections result in new gaps and bands in the Hofstadter butterfly even when the second order interactions break the bipartite symmetry. In addition, the whole spectrum of the Hall conduction is obtained by the Kubo formula for the corresponding cases. The results are in accordance with the Thouless-Kohmoto-Nightingale-den Nijs integers when the Fermi energy lies in an energy gap. We find that the states due to the vacancies or impurities with small hopping constants are highly localized and do not contribute to the Hall conduction. However, the impurities with high hopping constants result in new Hall plateaus with constant conduction of σ(xy) =± e(2)/h, since high hopping constants increase the probability of an electron contributing to the conduction.
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Affiliation(s)
- S Islamoğlu
- Department of Physics, Bilkent University, 06800 Ankara, Turkey.
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13
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Goldman N, Beugnon J, Gerbier F. Detecting chiral edge states in the Hofstadter optical lattice. PHYSICAL REVIEW LETTERS 2012; 108:255303. [PMID: 23004616 DOI: 10.1103/physrevlett.108.255303] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2012] [Indexed: 06/01/2023]
Abstract
We propose a realistic scheme to detect topological edge states in an optical lattice subjected to a synthetic magnetic field, based on a generalization of Bragg spectroscopy sensitive to angular momentum. We demonstrate that using a well-designed laser probe, the Bragg spectra provide an unambiguous signature of the topological edge states that establishes their chiral nature. This signature is present for a variety of boundaries, from a hard wall to a smooth harmonic potential added on top of the optical lattice. Experimentally, the Bragg signal should be very weak. To make it detectable, we introduce a "shelving method," based on Raman transitions, which transfers angular momentum and changes the internal atomic state simultaneously. This scheme allows us to detect the weak signal from the selected edge states on a dark background, and drastically improves the detectivity. It also leads to the possibility to directly visualize the topological edge states, using in situ imaging, offering a unique and instructive view on topological insulating phases.
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Affiliation(s)
- Nathan Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, B-1050 Brussels, Belgium.
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14
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Lang LJ, Cai X, Chen S. Edge states and topological phases in one-dimensional optical superlattices. PHYSICAL REVIEW LETTERS 2012; 108:220401. [PMID: 23003578 DOI: 10.1103/physrevlett.108.220401] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2011] [Indexed: 06/01/2023]
Abstract
We show that one-dimensional quasiperiodic optical lattice systems can exhibit edge states and topological phases which are generally believed to appear in two-dimensional systems. When the Fermi energy lies in gaps, the Fermi system on the optical superlattice is a topological insulator characterized by a nonzero topological invariant. The topological nature can be revealed by observing the density profile of a trapped fermion system, which displays plateaus with their positions uniquely determined by the ration of wavelengths of the bichromatic optical lattice. The butterflylike spectrum of the superlattice system can be also determined from the finite-temperature density profiles of the trapped fermion system. This finding opens an alternative avenue to study the topological phases and Hofstadter-like spectrum in one-dimensional optical lattices.
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Affiliation(s)
- Li-Jun Lang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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15
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Zhang X, Chen Y, Liu G, Wu W, Wen L, Liu W. Quantum information and many body physics with cold atoms. CHINESE SCIENCE BULLETIN-CHINESE 2012. [DOI: 10.1007/s11434-012-5095-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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16
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Goldman N, Satija I, Nikolic P, Bermudez A, Martin-Delgado MA, Lewenstein M, Spielman IB. Realistic time-reversal invariant topological insulators with neutral atoms. PHYSICAL REVIEW LETTERS 2010; 105:255302. [PMID: 21231599 DOI: 10.1103/physrevlett.105.255302] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2010] [Revised: 10/26/2010] [Indexed: 05/30/2023]
Abstract
We lay out an experiment to realize time-reversal invariant topological insulators in alkali atomic gases. We introduce an original method to synthesize a gauge field in the near field of an atom chip, which effectively mimics the effects of spin-orbit coupling and produces quantum spin-Hall states. We also propose a feasible scheme to engineer sharp boundaries where the hallmark edge states are localized. Our multiband system has a large parameter space exhibiting a variety of quantum phase transitions between topological and normal insulating phases. Because of their remarkable versatility, cold-atom systems are ideally suited to realize topological states of matter and drive the development of topological quantum computing.
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Affiliation(s)
- N Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, B-1050 Brussels, Belgium
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17
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Kapit E, Mueller E. Exact parent Hamiltonian for the quantum Hall states in a lattice. PHYSICAL REVIEW LETTERS 2010; 105:215303. [PMID: 21231318 DOI: 10.1103/physrevlett.105.215303] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2010] [Revised: 07/13/2010] [Indexed: 05/30/2023]
Abstract
We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.
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Affiliation(s)
- Eliot Kapit
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York, USA
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18
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Goldman N, Kubasiak A, Bermudez A, Gaspard P, Lewenstein M, Martin-Delgado MA. Non-Abelian optical lattices: anomalous quantum Hall effect and Dirac fermions. PHYSICAL REVIEW LETTERS 2009; 103:035301. [PMID: 19659289 DOI: 10.1103/physrevlett.103.035301] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2009] [Revised: 05/29/2009] [Indexed: 05/28/2023]
Abstract
We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac fermions with cold atoms experiments. In particular, we show that the underlying Minkowski space-time can also be modified, reaching anisotropic regimes where a remarkable anomalous quantum Hall effect and a squeezed Landau vacuum could be observed.
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Affiliation(s)
- N Goldman
- Center for Nonlinear Phenomena and Complex Systems-Université Libre de Bruxelles (U.L.B.), Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
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20
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Shao LB, Zhu SL, Sheng L, Xing DY, Wang ZD. Realizing and detecting the quantum Hall effect without landau levels by using ultracold atoms. PHYSICAL REVIEW LETTERS 2008; 101:246810. [PMID: 19113652 DOI: 10.1103/physrevlett.101.246810] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2008] [Indexed: 05/27/2023]
Abstract
We design an ingenious scheme to realize Haldane's quantum Hall model without Landau levels by using ultracold atoms trapped in an optical lattice. Three standing-wave laser beams are used to construct a wanted honeycomb lattice, where different on site energies in two sublattices required in the model can be implemented through tuning the phase of one laser beam. The staggered magnetic field is generated from the light-induced Berry phase. Moreover, we establish a relation between the Hall conductivity and the atomic density, enabling us to detect the Chern number with the typical density-profile-measurement technique.
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Affiliation(s)
- L B Shao
- Institute for Condensed Matter Physics and Department of Physics, South China Normal University, Guangzhou, China
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21
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Wu C. Orbital analogue of the quantum anomalous Hall effect in p-band systems. PHYSICAL REVIEW LETTERS 2008; 101:186807. [PMID: 18999852 DOI: 10.1103/physrevlett.101.186807] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2008] [Indexed: 05/27/2023]
Abstract
We investigate the topological insulating states of the p-band systems in optical lattices induced by the on site orbital angular momentum polarization, which exhibit gapless edge modes in the absence of Landau levels. This effect arises from the energy-level splitting between the on site p_{x}+ip_{y} and p_{x}-ip_{y} orbitals by rotating each optical lattice site around its own center. At large rotation angular velocities, this model naturally reduces to two copies of Haldane's quantum Hall model. The distribution of the Berry curvature in momentum space and the quantized Chern numbers are calculated. The experimental realization of this state is feasible.
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Affiliation(s)
- Congjun Wu
- Department of Physics, University of California, San Diego, California 92093, USA
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