The DOI matches its Crossref record; 268 of the 273 references it cites were found in a registry or an index.
Topological bands for ultracold atoms
Open accessAbstract
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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“atomic gases enjoy an extraordinary level of cleanness and control at the microscopic level, which permits a quantitative comparison with ab initio theoretical calculations.”
From How to exploit driving and dissipation to stabilize and manipulate quantum many-body states (2025) · cites this paper as [4]
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Items 201–268 of 268
Segev, M. (2019) · Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) · doi:10.1109/cleoe-eqec.2019.8871460 · Cited by 74
Revealing the Topology of Quasicrystals with a Diffraction Experiment
Dareau, A., Levy, E., Aguilera, M. B., Bouganne, R., Akkermans, É., Gerbier, F., & Beugnon, J. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.215304 · Cited by 72
Dynamics of interacting fermions under spin–orbit coupling in an optical lattice clock
Bromley, S. L., Kolkowitz, S., Bothwell, T., Kedar, D., Safavi-Naini, A., Wall, M. L., Salomon, C., Rey, A. M., & Ye, J. (2018) · Nature Physics · doi:10.1038/s41567-017-0029-0 · Cited by 71
Topological States in a One-Dimensional Fermi Gas with Attractive Interaction
Ruhman, J., Berg, E., & Altman, E. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.100401 · Cited by 70
Topological states in a microscopic model of interacting fermions
Lang, N., & Büchler, H. P. (2015) · Physical Review B · doi:10.1103/physrevb.92.041118 · Cited by 69
Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid
Hickey, C., Cincio, Ł., Papić, Z., & Paramekanti, A. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.137202 · Cited by 67
Mazza, L., Bermúdez, A., Goldman, N., Rizzi, M., Martin-delgado, M. A., & Lewenstein, M. (2012) · MPG.PuRe (Max Planck Society) · Cited by 66
Stability of a Floquet Bose-Einstein condensate in a one-dimensional optical lattice
Choudhury, S., & Mueller, E. J. (2014) · Physical Review A · doi:10.1103/physreva.90.013621 · Cited by 64
Parametric Instability Rates in Periodically Driven Band Systems
Lellouch, S., Bukov, M., Demler, E., & Goldman, N. (2017) · Physical Review X · doi:10.1103/physrevx.7.021015 · Cited by 64
Topological degeneracy and pairing in a one-dimensional gas of spinless fermions
Ruhman, J., & Altman, E. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.96.085133 · Cited by 64
Condensed ground states of frustrated Bose-Hubbard models
Möller, G., & Cooper, N. R. (2010) · Physical Review A · doi:10.1103/physreva.82.063625 · Cited by 63
Self-citationChiral currents in one-dimensional fractional quantum Hall states
Cornfeld, E., & Sela, E. (2015) · Physical Review B · doi:10.1103/physrevb.92.115446 · Cited by 63
Interaction-stabilized steady states in the driven O(N) model
Chandran, A., & Sondhi, S. L. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.174305 · Cited by 59
Topological Superfluid in a Fermi-Bose Mixture with a High Critical Temperature
Wu, Z., & Bruun, G. M. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.245302 · Cited by 57
Detecting topological invariants in chiral symmetric insulators via losses
Rakovszky, T., Asbóth, J. K., & Alberti, A. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.95.201407 · Cited by 56
Symmetry-protected topological Hopf insulator and its generalizations
Liu, C., Vafa, F., & Xu, C. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.95.161116 · Cited by 56
Realizing one-dimensional topological superfluids with ultracold atomic gases
Nascimbène, S. (2013) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/46/13/134005 · Cited by 55
Hall response and edge current dynamics in Chern insulators out of equilibrium
Caio, M. D., Cooper, N. R., & Bhaseen, M. J. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.94.155104 · Cited by 55
Self-citationOptical flux lattices for two-photon dressed states
Cooper, N. R., & Dalibard, J. (2011) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/95/66004 · Cited by 54
Self-citationChiral bosonic phases on the Haldane honeycomb lattice
Vasić, I., Petrescu, A., Hur, K. L., & Hofstetter, W. (2015) · Physical Review B · doi:10.1103/physrevb.91.094502 · Cited by 54
Universal Chiral Quasisteady States in Periodically Driven Many-Body Systems
Lindner, N. H., Berg, E., & Rudner, M. S. (2017) · Physical Review X · doi:10.1103/physrevx.7.011018 · Cited by 54
Population dynamics in a Floquet realization of the Harper-Hofstadter Hamiltonian
Bilitewski, T., & Cooper, N. R. (2015) · Physical Review A · doi:10.1103/physreva.91.063611 · Cited by 54
Self-citationAnnual Review of Cold Atoms and Molecules
Madison, K. W., Bongs, K., Carr, L. D., Rey, A. M., & Zhai, H. (2013) · Annual review of cold atoms and molecules · doi:10.1142/9100 · Cited by 53
Phase diagram for a Josephson network in a magnetic field
Straley, J. P., & Barnett, G. M. (1993) · Physical review. B, Condensed matter · doi:10.1103/physrevb.48.3309 · Cited by 51
Probe of Three-Dimensional Chiral Topological Insulators in an Optical Lattice
Wang, S.-T., Deng, D.-L., & Duan, L. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.033002 · Cited by 50
Geometry of Bloch states probed by Stückelberg interferometry
Lim, L.-K., Fuchs, J.-N., & Montambaux, G. (2015) · Physical Review A · doi:10.1103/physreva.92.063627 · Cited by 50
First-order topological phase transition of the Haldane-Hubbard model
Imriška, J., Wang, L., & Troyer, M. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.94.035109 · Cited by 48
Synthetic dimensions in the strong-coupling limit: Supersolids and pair superfluids
Bilitewski, T., & Cooper, N. R. (2016) · Physical Review A · doi:10.1103/physreva.94.023630 · Cited by 47
Self-citationBermúdez, A., & Porras, D. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/10/103021 · Cited by 45
Model Fractional Chern Insulators
Behrmann, J., Liu, Z., & Bergholtz, E. J. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.216802 · Cited by 45
Magnetic-order-driven topological transition in the Haldane-Hubbard model
Zheng, W., Shen, H., Wang, Z., & Zhai, H. (2015) · Physical Review B · doi:10.1103/physrevb.91.161107 · Cited by 44
Signatures of Fractional Exclusion Statistics in the Spectroscopy of Quantum Hall Droplets
Cooper, N. R., & Simon, S. H. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.106802 · Cited by 44
Self-citationDesigning Topological Bands in Reciprocal Space
Cooper, N. R., & Moessner, R. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.215302 · Cited by 43
Self-citationParametric Heating in a 2D Periodically Driven Bosonic System: Beyond the Weakly Interacting Regime
Boulier, T., Maslek, J., Bukov, M., Bracamontes, C., Magnan, E., Lellouch, S., Demler, E., Goldman, N., & Porto, J. V. (2019) · Physical Review X · doi:10.1103/physrevx.9.011047 · Cited by 42
Choudhury, S., & Mueller, E. J. (2015) · Physical Review A · doi:10.1103/physreva.91.023624 · Cited by 39
Bermúdez, A., & Porras, D. (2015) · Sussex Research Online (University of Sussex) · Cited by 39
Chiral bosonic Mott insulator on the frustrated triangular lattice
Zaletel, M. P., Parameswaran, S. A., Rüegg, A., & Altman, E. (2014) · Physical Review B · doi:10.1103/physrevb.89.155142 · Cited by 39
Reservoir-induced Thouless pumping and symmetry-protected topological order in open quantum chains
Linzner, D., Wawer, L., Grusdt, F., & Fleischhauer, M. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.94.201105 · Cited by 39
Bogoliubov theory of interacting bosons on a lattice in a synthetic magnetic field
Powell, S., Barnett, R., Sensarma, R., & Sarma, S. D. (2011) · Physical Review A · doi:10.1103/physreva.83.013612 · Cited by 37
Creating topological interfaces and detecting chiral edge modes in a two-dimensional optical lattice
Goldman, N., Jotzu, G., Messer, M., Görg, F., Desbuquois, R., & Esslinger, T. (2016) · Physical Review A · doi:10.1103/physreva.94.043611 · Cited by 37
Quantized Currents and Topological Invariants for Electrons in Incommensurate Potentials
Kunz, H. (1986) · Physical Review Letters · doi:10.1103/physrevlett.57.1095 · Cited by 35
Topological order of mixed states in correlated quantum many-body systems
Grusdt, F. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.95.075106 · Cited by 34
Mazza, L., Aidelsburger, M., Tu, H.-H., Goldman, N., & Burrello, M. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/10/105001 · Cited by 30
Introduction to the physics of artificial gauge fieldsPreprint
Dalibard, J. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1504.05520 · Cited by 29
Self-citationClassification of mixed-state topology in one dimension
van Nieuwenburg, E., & Huber, S. D. (2014) · Physical Review B · doi:10.1103/physrevb.90.075141 · Cited by 28
Antiferromagnetic topological insulators in cold atomic gases
Essin, A. M., & Gurarie, V. (2012) · Physical Review B · doi:10.1103/physrevb.85.195116 · Cited by 28
Interband Heating Processes in a Periodically Driven Optical Lattice
Sträter, C., & Eckardt, A. (2016) · Zeitschrift für Naturforschung A · doi:10.1515/zna-2016-0129 · Cited by 27
Mean field study of the topological Haldane-Hubbard model of spin- 12 fermions
Arun, V., Sohal, R., Hickey, C., & Paramekanti, A. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.115110 · Cited by 26
Majorana Quasiparticles Protected by Z 2 Angular Momentum Conservation
Iemini, F., Mazza, L., Fallani, L., Zoller, P., Fazio, R., & Dalmonte, M. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.200404 · Cited by 26
Dauphin, A., Tran, D.-T., Lewenstein, M., & Goldman, N. (2017) · 2D Materials · doi:10.1088/2053-1583/aa6a3b · Cited by 26
Effects of Berry Curvature on the Collective Modes of Ultracold Gases
Price, H. M., & Cooper, N. R. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.220407 · Cited by 26
Self-citationMass and Chirality Inversion of a Dirac Cone Pair in Stückelberg Interferometry
Lim, L.-K., Fuchs, J.-N., & Montambaux, G. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.155302 · Cited by 25
Juzeliūnas, G., & Spielman, I. B. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/12/123022 · Cited by 25
Self-citationEdge excitations and topological order in a rotating Bose gas
Cazalilla, M. A., Barberán, N., & Cooper, N. R. (2005) · Physical Review B · doi:10.1103/physrevb.71.121303 · Cited by 25
Self-citationInteracting bosons in topological optical flux lattices
Sterdyniak, A., Bernevig, B. A., Cooper, N. R., & Regnault, N. (2015) · Physical Review B · doi:10.1103/physrevb.91.035115 · Cited by 24
Self-citationGrosfeld, E., Cooper, N. R., Stern, A., & Ilan, R. (2007) · Physical Review B · doi:10.1103/physrevb.76.104516 · Cited by 24
Self-citationTopological Superfluid and Majorana Zero Modes in Synthetic Dimension
Yan, Z., Wan, S., & Wang, Z. (2015) · Scientific Reports · doi:10.1038/srep15927 · Cited by 23
Edge mode dynamics of quenched topological wires
Sacramento, P. D. (2016) · Physical review. E · doi:10.1103/physreve.93.062117 · Cited by 23
Topological phase transitions in finite-size periodically driven translationally invariant systems
Yang, G., & Rigol, M. (2017) · Physical Review A · doi:10.1103/physreva.96.023610 · Cited by 23
Račiūnas, M., Žlabys, G., Eckardt, A., & Anisimovas, E. (2016) · Physical Review A · doi:10.1103/physreva.93.043618 · Cited by 18
Gauge matters: observing the vortex-nucleation transition in a Bose condensate
LeBlanc, L. J., Jiménez-García, K., Williams, R. A., Beeler, M. C., Phillips, W. D., & Spielman, I. B. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/6/065016 · Cited by 18
Self-citationDestruction of string order after a quantum quench
Strinati, M. C., Mazza, L., Endres, M., Rossini, D., & Fazio, R. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.94.024302 · Cited by 17
Correlated spin-flip tunneling in a Fermi lattice gas
Xu, W., Morong, W., Hui, H.-Y., Scarola, V. W., & DeMarco, B. (2018) · Physical Review A · doi:10.1103/physreva.98.023623 · Cited by 16
Adiabatic preparation of vortex lattices
Baur, S. K., & Cooper, N. R. (2013) · Physical Review A · doi:10.1103/physreva.88.033603 · Cited by 9
Self-citationQuantum simulations made easy planePreprint
Läuchli, A. M., & Moessner, R. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1504.04380 · Cited by 8
Degeneracy of Many-Body Quantum States in an Optical Lattice under a Uniform Magnetic Field
Zhang, J., Jian, C., Ye, F., & Zhai, H. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.155302 · Cited by 8
Correspondence between a shaken honeycomb lattice and the Haldane model
Modugno, M., & Pettini, G. (2017) · Physical Review A · doi:10.1103/physreva.96.053603 · Cited by 5
Entanglement-Spectrum Crossing and Momentum-Time Skyrmions in Quench Dynamics
Gong, Z., & Ueda, M. (2017) · Cited by 2
Flagged first, then by citations
5 of the 273 references couldn’t be matched to a known paper.
Research works printed but not linked: 5
- Ashcroft, N. W., 1976, Solid State Physics
- Asteria, L., 2019, Nat. Phys.
- Dalibard, J., 2016, Quantum Matter at Ultralow Temperatures
- Gardiner, Crispin, 2004, Quantum Noise
- 1990, The Quantum Hall Effect
Cited by
Sorted by citations
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Symmetry and Topology in Non-Hermitian Physics
Kawabata, K., Shiozaki, K., Ueda, M., & Sato, M. (2019) · Physical Review X · doi:10.1103/physrevx.9.041015 · Cited by 1,472
Band structure engineering and non-equilibrium dynamics in Floquet topological insulators
Rudner, M. S., & Lindner, N. H. (2020) · Nature Reviews Physics · doi:10.1038/s42254-020-0170-z · Cited by 715
Photonic quadrupole topological phases
Mittal, S., Orre, V. V., Zhu, G., Gorlach, M. A., Poddubny, A. N., & Hafezi, M. (2019) · Nature Photonics · doi:10.1038/s41566-019-0452-0 · Cited by 556
Tools for quantum simulation with ultracold atoms in optical lattices
Schäfer, F., Fukuhara, T., Sugawa, S., Takasu, Y., & Takahashi, Y. (2020) · Nature Reviews Physics · doi:10.1038/s42254-020-0195-3 · Cited by 488
Metadata
- Authors
- Cooper, N. R., Dalibard, J., & Spielman, I. B.
- Affiliations
- University of Cambridge (GB)
- Centre National de la Recherche Scientifique (FR)
- National Institute of Standards and Technology (US)
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2019-03-25
- Volume
- 91
- Issue
- 1
- Pages
- 015005
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- PMC
- PMC7079706
- OpenAlex
- W2790327112
- Cited by
- 940
- References
- 273
- Citations by year
- 2026: 74 · 2025: 113 · 2024: 104 · 2023: 139 · 2022: 140 · 2021: 156 · 2020: 136 · 2019: 68
- FWCI
- 54.96
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Reviews of Modern Physics (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (acceptedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- HAL (submittedVersion)
- arXiv (Cornell University)
- Funders
- Engineering and Physical Sciences Research Council (EP/K030094/1, EP/P009565/1)
- Simons Foundation
- H2020 European Research Council (UQUAM)
- Army Research Office (MURI)
- Air Force Office of Scientific Research (MURI)
- National Institute of Standards and Technology
- National Science Foundation (PFC)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Keywords
- topological band structure, ultracold atoms, cold atoms, Bloch bands, band structure engineering, interparticle interactions, many-body phases, topological phases
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