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Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms
Open accessAbstract
We investigate the dynamics of neutral atoms in a 2D optical lattice which traps two distinct internal states of the atoms in different columns. Two Raman lasers are used to coherently transfer atoms from one internal state to the other, thereby causing hopping between the different columns. By adjusting the laser parameters appropriately we can induce a non-vanishing phase of particles moving along a closed path on the lattice. This phase is proportional to the enclosed area and we thus simulate a magnetic flux through the lattice. This set-up is described by a Hamiltonian identical to the one for electrons on a lattice subject to a magnetic field and thus allows us to study this equivalent situation under very well defined controllable conditions. We consider the limiting case of huge magnetic fields—which is not experimentally accessible for electrons in metals—where a fractal band structure, the Hofstadter butterfly, characterizes the system.
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“Control over this sign can be acquired by dynamical modulation of the lattice [16-21], Raman-assisted tunneling [22, 23] or embedding defects in infinite arrays [24].”
From Universal Sign Control of Coupling in Tight-Binding Lattices (2016) · cites this paper as [22]
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Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W., & Bloch, I. (2002) · Nature · doi:10.1038/415039a · Cited by 5,935
Raussendorf, R., & Briegel, H. J. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.5188 · Cited by 4,477
Cold Bosonic Atoms in Optical Lattices
Jaksch, D., Bruder, C., Cirac, J. I., Gardiner, C. W., & Zoller, P. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.3108 · Cited by 3,685
Self-citationEnergy levels and wave functions of Bloch electrons in rational and irrational magnetic fields
Hofstadter, D. R. (1976) · Physical Review B · doi:10.1103/physrevb.14.2239 · Cited by 3,495
Vortices in a Bose-Einstein Condensate
Matthews, M. R., Anderson, B. P., Haljan, P. C., Hall, D. S., Wieman, C., & Cornell, E. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.2498 · Cited by 1,842
Fast Quantum Gates for Neutral Atoms
Jaksch, D., Cirac, J. I., Zoller, P., Rolston, S. L., Côté, R., & Lukin, M. D. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.2208 · Cited by 1,540
Self-citationEntanglement of Atoms via Cold Controlled Collisions
Jaksch, D., Briegel, H.-J., Cirac, J. I., Gardiner, C. W., & Zoller, P. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.1975 · Cited by 795
Self-citationQuantum Logic Gates in Optical Lattices
Brennen, G. K., Caves, C. M., Jessen, P., & Deutsch, I. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.1060 · Cited by 659
The fractional quantum Hall effect
Stormer, H. L., Tsui, D. C., & Gossard, A. C. (1999) · Reviews of Modern Physics · doi:10.1103/revmodphys.71.s298 · Cited by 483
Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
Cooper, N. R., Wilkin, N. K., & Gunn, J. M. F. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.120405 · Cited by 456
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Ozawa, T., Price, H. M., Amo, A., Goldman, N., Hafezi, M., Lu, L., Rechtsman, M. C., Schuster, D., Simon, J., Zilberberg, O., et al. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015006 · Cited by 3,722
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Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
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Metadata
- Authors
- Jaksch, D., & Zoller, P.
- Affiliations
- Universität Innsbruck (AT)
- Venue
- New Journal of Physics
- Publisher
- IOP Publishing
- Published
- 2003-05-30
- Volume
- 5
- Pages
- 56-56
- ISSN
- 1367-2630 (ISSN-L)
- OpenAlex
- W2116365249
- Cited by
- 777
- References
- 20
- Citations by year
- 2026: 11 · 2025: 24 · 2024: 26 · 2023: 26 · 2022: 18 · 2021: 22 · 2020: 26 · 2019: 45 · 2018: 53 · 2017: 56 · 2016: 56 · 2015: 55 · 2014: 45 · 2013: 56 · 2012: 49
- FWCI
- 8.64
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- cc-by
- Locations
- New Journal of Physics (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- 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 › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Keywords
- Hofstadter butterfly, optical lattices, cold neutral atoms, effective magnetic field, Raman coupling, Aharonov-Bohm phase, two-dimensional lattice, ultracold atoms
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