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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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Sun Y, Leykam D, Nenni S, Song D, Chen H, Chong YD, Chen Z. Observation of Valley Landau-Zener-Bloch Oscillations and Pseudospin Imbalance in Photonic Graphene. PHYSICAL REVIEW LETTERS 2018; 121:033904. [PMID: 30085826 DOI: 10.1103/physrevlett.121.033904] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2017] [Revised: 05/04/2018] [Indexed: 06/08/2023]
Abstract
We demonstrate intervalley Bloch oscillation (BO) and Landau-Zener tunneling (LZT) in an optically induced honeycomb lattice with a refractive-index gradient. Unlike previously observed BO in a gapped square lattice, we show nonadiabatic beam dynamics that are highly sensitive to the direction of the index gradient and the choice of the Dirac cones. In particular, a symmetry-preserving potential leads to nearly perfect LZT and coherent BO between the inequivalent valleys, whereas a symmetry-breaking potential generates asymmetric scattering, imperfect LZT, and valley-sensitive generation of vortices mediated by a pseudospin imbalance. This clearly indicates that, near the Dirac points, the transverse gradient does not always act as a simple scalar force, as commonly assumed, and the LZT probability is strongly affected by the sublattice symmetry as analyzed from an effective Landau-Zener Hamiltonian. Our results illustrate the anisotropic response of an otherwise isotropic Dirac platform to real-space potentials acting as strong driving fields, which may be useful for manipulation of pseudospin and valley degrees of freedom in graphenelike systems.
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Affiliation(s)
- Yong Sun
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Daniel Leykam
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34126, Republic of Korea
| | - Stephen Nenni
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
| | - Daohong Song
- MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Hong Chen
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Y D Chong
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
| | - Zhigang Chen
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
- MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
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Li T, Duca L, Reitter M, Grusdt F, Demler E, Endres M, Schleier-Smith M, Bloch I, Schneider U. Bloch state tomography using Wilson lines. Science 2016; 352:1094-7. [DOI: 10.1126/science.aad5812] [Citation(s) in RCA: 117] [Impact Index Per Article: 14.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2015] [Accepted: 04/15/2016] [Indexed: 11/02/2022]
Affiliation(s)
- Tracy Li
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
| | - Lucia Duca
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
| | - Martin Reitter
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
| | - Fabian Grusdt
- Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, Germany
- Graduate School Materials Science in Mainz, Gottlieb-Daimler-Strasse 47, 67663 Kaiserslautern, Germany
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Eugene Demler
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Manuel Endres
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | | | - Immanuel Bloch
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
| | - Ulrich Schneider
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK
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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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