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The present Chapter discusses methods by which topological Bloch bands can be prepared in cold-atom setups.
Single band motion of conduction electrons in a uniform magnetic field
Harper, P. G. 1955 · 1955
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Berry phase effects on electronic properties
Xiao, D., Chang, M.-C., and Niu, Q. 2010 · 1959
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Significance of electromagnetic potentials in quantum theory
Aharonov, Y., and Bohm, D. 1959 · 1959
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Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields
Hofstadter, D. R. 1976 · 1976
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Quantized Hall Conductance in a Two-Dimensional Periodic Potential
Thouless, D. J., Kohmoto, M., Nightingale, M. P., and den Nijs, M. 1982 · 1982
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Quantal phase factors accompanying adiabatic changes
Berry, M. V. 1984 · 1984
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Topological invariant and the quantization of the Hall conductance
Kohmoto, M. 1985 · 1985
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Quantum Mechanics
Cohen-Tannoudji, C., Diu, B., and Laloë, F. 1991 · 1991
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Gauge Structures in Atom-Laser Interaction: Bloch Oscillations in a Dark Lattice
Dum, R., and Olshanii, M. 1996 · 1996
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Vortex formation in a stirred Bose-Einstein condensate
Madison, K. W., Chevy, F., Wohlleben, W., and Dalibard, J. 2000 · 2000
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Observation of vortex lattices in Bose-Einstein condensates
Abo-Shaeer, J. R., Raman, C., and Vogels, J. M. andKetterle, W. 2001 · 2001
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Particle Number Fractionalization of an Atomic Fermi-Dirac Gas in an Optical Lattice
Ruostekoski, J., Dunne, G. V, and Javanainen, J. 2002 · 2002
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Vortex Nucleation in Bose-Einstein Condensates in an Oblate, Purely Magnetic Potential
Hodby, E., Hechenblaikner, G., Hopkins, S. A., Marago, O. M., and Foot, C. J. 2002 · 2002
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Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms
Jaksch, D., and Zoller, P. 2003 · 2003
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Effective Hamiltonians for periodically driven systems
Rahav, S., Gilary, I., and Fishman, S. 2003 · 2003
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Artificial electromagnetism for neutral atoms: Escher staircase and Laughlin liquids
Mueller, E. 2004 · 2004
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Experimental studies of equilibrium vortex properties in a Bose-condensed gas
Coddington, I., Haljan, P. C., Engels, P., Schweikhard, V., Tung, S., and Cornell, E. A. 2004 · 2004
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Rapidly Rotating Bose-Einstein Condensates in and near the Lowest Landau Level
Schweikhard, V., Coddington, I., Engels, P., Mogendorff, V. P., and Cornell, E. A. 2004 · 2004
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Fractional Quantum Hall States of Atoms in Optical Lattices
Sorensen, A. S., Demler, E., and Lukin, M. D. 2005 · 2005
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Observation of Vortex Pinning in Bose-Einstein Condensates
Tung, S., Schweikhard, V., and Cornell, E. A. 2006 · 2006
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High-Field Fractional Quantum Hall Effect in Optical Lattices
Palmer, R. N., and Jaksch, D. 2006 · 2006
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AC-induced superfluidity
Eckardt, A., and Holthaus, M. 2007 · 2007
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Excitation of a d-Density Wave in an Optical Lattice with Driven Tunneling
Hemmerich, A., and Morais Smith, C. 2007 · 2007
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Many-body physics with ultracold gases
Bloch, I., Dalibard, J., and Zwerger, W. 2008 · 2008
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Rapidly rotating atomic gases
Cooper, N. R. 2008 · 2008
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Rotating trapped Bose-Einstein condensates
Fetter, A. L. 2009 · 2009
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Synthetic magnetic fields for ultracold neutral atoms
Lin, Y.-J., Compton, R. L., Jiménez-García, K., Porto, J. V., and Spielman, I. B. 2009 · 2009
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Composite Fermion Theory for Bosonic Quantum Hall States on Lattices
Möller, G., and Cooper, N. R. 2009 · 2009
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Gauge fields for ultracold atoms in optical superlattices
Gerbier, F., and Dalibard, J. 2010 · 2010
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Artificial staggered magnetic field for ultracold atoms in optical lattices
Lim, L.-K., Hemmerich, A., and Morais Smith, C. 2010 · 2010
Cited alongside, same era.
Observation of Vortex Nucleation in a Rotating Two-Dimensional Lattice of Bose-Einstein Condensates
Williams, R. A., Al-Assam, S., and Foot, C. J. 2010 · 2010
Cited alongside, same era.
Topological states in two-dimensional optical lattices
Stanescu, T. D., Galitski, V., and Das Sarma, S. 2010 · 2010
Cited alongside, same era.
Colloquium: Topological insulators
Hasan, M. Z., and Kane, C. L. 2010 · 2010
Cited alongside, same era.
Realistic Time-Reversal Invariant Topological Insulators with Neutral Atoms
Goldman, N., Satija, I., Nikolic, P., Bermudez, A., Martin-Delgado, M. A., Lewenstein, M., and Spielman, I. B. 2010 · 2010
Cited alongside, same era.
Wilson Fermions and Axion Electrodynamics in Optical Lattices
Coupled Ferromagnetic and Nematic Ordering of Fermions in an Optical Flux Lattice
Baur, S. K., and Cooper, N. R. 2012 · 2012
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Topological insulators and topological superconductors
Bernevig, B. A., and Hughes, T. L. 2013 · 2013
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Fractional quantum Hall physics in topological flat bands
Parameswaran, S. A., Roy, R., and Sondhi, S. L. 2013 · 2013
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Topological flat band models and fractional Chern insulators
Bergholz, E. J., and Liu, Z. 2013 · 2013
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Extracting the Chern Number from the Dynamics of a Fermi Gas: Implementing a Quantum Hall Bar for Cold Atoms
Dauphin, A., and Goldman, N. 2013 · 2013
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Measuring topology in a laser-coupled honeycomb lattice: from Chern insulators to topological semi-metals
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Bermudez, A., Mazza, L., Rizzi, M., Goldman, N., Lewenstein, M., and Martin-Delgado, M. A. 2010 · 2010
Cited alongside, same era.
Colloquium: Artificial gauge potentials for neutral atoms
Dalibard, J., Gerbier, F., Juzeliūnas, G., and Öhberg, P. 2011 · 2011
Cited alongside, same era.
Seeing Topological Order in Time-of-Flight Measurements
Alba, E., Fernandez-Gonzalvo, X., Mur-Petit, J., Pachos, J., and Garcia-Ripoll, J. 2011 · 2011
Cited alongside, same era.
Synthetic Gauge Fields for Vibrational Excitations of Trapped Ions
Bermudez, A., Schaetz, T., and Porras, D. 2011 · 2011
Cited alongside, same era.
Experimental Realization of Strong Effective Magnetic Fields in an Optical Lattice
Aidelsburger, M., Atala, M., Nascimbene, S., Trotzky, S., Chen, Y.-A., and Bloch, I. 2011 · 2011
Cited alongside, same era.
Creating artificial magnetic fields for cold atoms by photon-assisted tunneling
Kolovsky, A. R. 2011 · 2011
Cited alongside, same era.
Quantum Simulation of Frustrated Classical Magnetism in Triangular Optical Lattices
Struck, J., Ölschläger, C., Le Targat, R., Soltan-Panahi, P., Eckardt, A., Lewenstein, M., Windpassinger, P., and Sengstock, K. 2011 · 2011
Cited alongside, same era.
Goldman, N., Anisimovas, E., Gerbier, F., Öhberg, P., Spielman, I. B., and Juzeliūnas, G. 2013 · 2013
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Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
Aidelsburger, M., Atala, M., Lohse, M., Barreiro, J. T., Paredes, B., and Bloch, I. 2013 · 2013
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Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
Miyake, H., Siviloglou, G. A., Kennedy, C. J., Burton, W. C., and Ketterle, W. 2013 · 2013
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Comment on “Creating artificial magnetic fields for cold atoms by photon-assisted tunneling” by Kolovsky A. R
Creffield, C. E., and Sols, F. 2013 · 2013
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Engineering ising-XY spin-models in a triangular lattice using tunable artificial gauge fields
Struck, J., Weinberg, M., Ölschläger, C., Windpassinger, P., Simonet, J., Sengstock, K., Höppner, R., Hauke, P., Eckardt, A., Lewenstein, M., and Mathey, L. 2013 · 2013
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Reaching Fractional Quantum Hall States with Optical Flux Lattices
Cooper, N. R., and Dalibard, J. 2013 · 2013
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Interferometric Approach to Measuring Band Topology in 2D Optical Lattices
Abanin, D. A., Kitagawa, T., Bloch, I., and Demler, E. 2013 · 2013
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Direct imaging of topological edge states in cold-atom systems
Goldman, N., Dalibard, J., Dauphin, A., Gerbier, F., Lewenstein, M., Zoller, P., and Spielman, I. B. 2013 · 2013
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Realizing Fractional Chern Insulators in Dipolar Spin Systems
Yao, N. Y., Gorshkov, A. V., Laumann, C. R., Luchli, A. M., Ye, J., and Lukin, M. D. 2013 · 2013
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Light-induced gauge fields for ultracold atoms
Goldman, N., Juzeliūnas, G., Öhberg, P., and Spielman, I. B. 2014 · 2014
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Design of laser-coupled honeycomb optical lattices supporting Chern insulators
Anisimovas, E., Gerbier, F., Andrijauskas, T., and Goldman, N. 2014 · 2014
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Synthetic gauge fields in synthetic dimensions
Celi, A., Massignan, P., Ruseckas, J., Goldman, N., Spielman, I. B., Juzeliūnas, G., and Lewenstein, M. 2014 · 2014
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Periodically-driven quantum matter: the case of resonant modulations
Goldman, N., Dalibard, J., Aidelsburger, M., and Cooper, N. R. 2014 · 2014
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Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
Goldman, N., and Dalibard, J. 2014 · 2014
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Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
Bukov, M., D’Alessio, L., and Polkovnikov, A. 2014 · 2014
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Dynamic Optical Superlattices with Topological Bands
Baur, S. K., Schleier-Smith, M. H., and Cooper, N. R. 2014 · 2014
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Experimental realisation of the topological Haldane model
Jotzu, G., Messer, M., Desbuquois, R., Lebrat, M., Uehlinger, T., Greif, D., and Esslinger, T. 2014 · 2014
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Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the “parity anomaly”
Haldane, F. D. M. 1988 · 2015
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Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
Aidelsburger, M., Lohse, M., Schweizer, C., Atala, M., Barreiro, J. T., Nascimbene, S., Cooper, N. R., Bloch, I., and N., Goldman. 2015 · 2015
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Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
Mancini, M., Pagano, G., Cappellini, G., Livi, L., Rider, M., Catani, J., Sias, C., Zoller, P., Inguscio, M., Dalmonte, M., and Fallani, L. 2015 · 2015
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Visualizing edge states with an atomic Bose gas in the quantum Hall regime
Stuhl, B. K., Lu, H. I., Aycock, L. M., Genkina, D., and Spielman, I. B. 2015 · 2015
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An Aharonov-Bohm interferometer for determining Bloch band topology
Duca, L., Li, T., Reitter, M., Bloch, I., Schleier-Smith, M., and Schneider, U. 2015 · 2015
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Interacting bosons in topological optical flux lattices
Sterdyniak, A., Bernevig, B. Andrei, Cooper, Nigel R., and Regnault, N. 2015 · 2015
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