The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling
Abstract
Here we propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one- and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k-space. Lastly, we compare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper-Hofstadter Hamiltonian, and obtain excellent agreement.
- Authors:
-
- Univ. of Zagreb, Zagreb (Croatia). Dept. of Physics
- Univ. of Zagreb, Zagreb (Croatia). Faculty of Textile Technology
- Univ. of Zagreb, Zagreb (Croatia). Dept. of Physics; Max Planck Instit. for the Physics of Complex Systems, Dresden (Germany)
- Univ. of Zagreb, Sisak (Croatia). Faculty of Metallurgy
- Massachusetts Instit. of Technology (MIT), Cambridge, MA (United States). Dept. of Physics
- Publication Date:
- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Energy Frontier Research Centers (EFRC) (United States). Solid-State Solar-Thermal Energy Conversion Center (S3TEC)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); UKF; US Army Research Office
- OSTI Identifier:
- 1315269
- Grant/Contract Number:
- SC0001299; FG02-09ER46577; 5/13; W911NF-13-D-0001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- New Journal of Physics
- Additional Journal Information:
- Journal Volume: 17; Journal Issue: 12; Journal ID: ISSN 1367-2630
- Publisher:
- IOP Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; synthetic magnetic fields; photonic lattices; topological effects; conical diffraction; topological insulators; magnetic-field; neutral atoms; solitons
Citation Formats
Dubček, Tena, Lelas, Karlo, Jukić, Dario, Pezer, Robert, Soljačić, Marin, and Buljan, Hrvoje. The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling. United States: N. p., 2015.
Web. doi:10.1088/1367-2630/17/12/125002.
Dubček, Tena, Lelas, Karlo, Jukić, Dario, Pezer, Robert, Soljačić, Marin, & Buljan, Hrvoje. The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling. United States. https://doi.org/10.1088/1367-2630/17/12/125002
Dubček, Tena, Lelas, Karlo, Jukić, Dario, Pezer, Robert, Soljačić, Marin, and Buljan, Hrvoje. Mon .
"The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling". United States. https://doi.org/10.1088/1367-2630/17/12/125002. https://www.osti.gov/servlets/purl/1315269.
@article{osti_1315269,
title = {The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling},
author = {Dubček, Tena and Lelas, Karlo and Jukić, Dario and Pezer, Robert and Soljačić, Marin and Buljan, Hrvoje},
abstractNote = {Here we propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one- and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k-space. Lastly, we compare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper-Hofstadter Hamiltonian, and obtain excellent agreement.},
doi = {10.1088/1367-2630/17/12/125002},
journal = {New Journal of Physics},
number = 12,
volume = 17,
place = {United States},
year = {Mon Dec 07 00:00:00 EST 2015},
month = {Mon Dec 07 00:00:00 EST 2015}
}
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Works referenced in this record:
Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
journal, January 2008
- Haldane, F. D. M.; Raghu, S.
- Physical Review Letters, Vol. 100, Issue 1
Analogs of quantum-Hall-effect edge states in photonic crystals
journal, September 2008
- Raghu, S.; Haldane, F. D. M.
- Physical Review A, Vol. 78, Issue 3
Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
journal, January 2008
- Wang, Zheng; Chong, Y. D.; Joannopoulos, John D.
- Physical Review Letters, Vol. 100, Issue 1
Observation of unidirectional backscattering-immune topological electromagnetic states
journal, October 2009
- Wang, Zheng; Chong, Yidong; Joannopoulos, J. D.
- Nature, Vol. 461, Issue 7265
Photonic Floquet topological insulators
journal, April 2013
- Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan
- Nature, Vol. 496, Issue 7444
Imaging topological edge states in silicon photonics
journal, October 2013
- Hafezi, M.; Mittal, S.; Fan, J.
- Nature Photonics, Vol. 7, Issue 12
Robust optical delay lines with topological protection
journal, August 2011
- Hafezi, Mohammad; Demler, Eugene A.; Lukin, Mikhail D.
- Nature Physics, Vol. 7, Issue 11
Artificial gauge field for photons in coupled cavity arrays
journal, October 2011
- Umucalılar, R. O.; Carusotto, I.
- Physical Review A, Vol. 84, Issue 4
Realizing effective magnetic field for photons by controlling the phase of dynamic modulation
journal, October 2012
- Fang, Kejie; Yu, Zongfu; Fan, Shanhui
- Nature Photonics, Vol. 6, Issue 11
Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures
journal, December 2012
- Rechtsman, Mikael C.; Zeuner, Julia M.; Tünnermann, Andreas
- Nature Photonics, Vol. 7, Issue 2
Hofstadter butterflies in nonlinear Harper lattices, and their optical realizations
journal, May 2010
- Manela, Ofer; Segev, Mordechai; Christodoulides, Demetrios N.
- New Journal of Physics, Vol. 12, Issue 5
Topological States and Adiabatic Pumping in Quasicrystals
journal, September 2012
- Kraus, Yaacov E.; Lahini, Yoav; Ringel, Zohar
- Physical Review Letters, Vol. 109, Issue 10
Photonic topological insulators
journal, December 2012
- Khanikaev, Alexander B.; Hossein Mousavi, S.; Tse, Wang-Kong
- Nature Materials, Vol. 12, Issue 3
Weyl points and line nodes in gyroid photonic crystals
journal, March 2013
- Lu, Ling; Fu, Liang; Joannopoulos, John D.
- Nature Photonics, Vol. 7, Issue 4
Topological photonics
journal, October 2014
- Lu, Ling; Joannopoulos, John D.; Soljačić, Marin
- Nature Photonics, Vol. 8, Issue 11
Colloquium : Artificial gauge potentials for neutral atoms
journal, November 2011
- Dalibard, Jean; Gerbier, Fabrice; Juzeliūnas, Gediminas
- Reviews of Modern Physics, Vol. 83, Issue 4
Light-induced gauge fields for ultracold atoms
journal, November 2014
- Goldman, N.; Juzeliūnas, G.; Öhberg, P.
- Reports on Progress in Physics, Vol. 77, Issue 12
Colloquium: Topological insulators
journal, November 2010
- Hasan, M. Z.; Kane, C. L.
- Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067
Observation of Discrete Solitons in Optically Induced Real Time Waveguide Arrays
journal, January 2003
- Fleischer, Jason W.; Carmon, Tal; Segev, Mordechai
- Physical Review Letters, Vol. 90, Issue 2
Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices
journal, March 2003
- Fleischer, Jason W.; Segev, Mordechai; Efremidis, Nikolaos K.
- Nature, Vol. 422, Issue 6928
Spatial solitons in optically induced gratings
journal, January 2003
- Neshev, Dragomir; Ostrovskaya, Elena; Kivshar, Yuri
- Optics Letters, Vol. 28, Issue 9
Spatial photonics in nonlinear waveguide arrays
journal, January 2005
- Fleischer, Jason W.; Bartal, Guy; Cohen, Oren
- Optics Express, Vol. 13, Issue 6
Conical Diffraction and Gap Solitons in Honeycomb Photonic Lattices
journal, March 2007
- Peleg, Or; Bartal, Guy; Freedman, Barak
- Physical Review Letters, Vol. 98, Issue 10
Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering
journal, September 2009
- Guinea, F.; Katsnelson, M. I.; Geim, A. K.
- Nature Physics, Vol. 6, Issue 1
Inhibition of Light Tunneling in Waveguide Arrays
journal, April 2009
- Szameit, A.; Kartashov, Y. V.; Dreisow, F.
- Physical Review Letters, Vol. 102, Issue 15
Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike
journal, February 2004
- Berry, M. V.
- Journal of Optics A: Pure and Applied Optics, Vol. 6, Issue 4
Single Band Motion of Conduction Electrons in a Uniform Magnetic Field
journal, October 1955
- Harper, P. G.
- Proceedings of the Physical Society. Section A, Vol. 68, Issue 10
Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields
journal, September 1976
- Hofstadter, Douglas R.
- Physical Review B, Vol. 14, Issue 6
Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
journal, October 2013
- Miyake, Hirokazu; Siviloglou, Georgios A.; Kennedy, Colin J.
- Physical Review Letters, Vol. 111, Issue 18
Realization of the Hofstadter Hamiltonian with Ultracold Atoms in Optical Lattices
journal, October 2013
- Aidelsburger, M.; Atala, M.; Lohse, M.
- Physical Review Letters, Vol. 111, Issue 18
Creation of effective magnetic fields in optical lattices: the Hofstadter butterfly for cold neutral atoms
journal, January 2003
- Jaksch, D.; Zoller, P.
- New Journal of Physics, Vol. 5
Creating artificial magnetic fields for cold atoms by photon-assisted tunneling
journal, January 2011
- Kolovsky, A. R.
- EPL (Europhysics Letters), Vol. 93, Issue 2
Vortex Formation in a Stirred Bose-Einstein Condensate
journal, January 2000
- Madison, K. W.; Chevy, F.; Wohlleben, W.
- Physical Review Letters, Vol. 84, Issue 5
Observation of Vortex Lattices in Bose-Einstein Condensates
journal, April 2001
- Abo-Shaeer, J. R.; Raman, C.; Vogels, J. M.
- Science, Vol. 292, Issue 5516
Synthetic magnetic fields for ultracold neutral atoms
journal, December 2009
- Lin, Y. -J.; Compton, R. L.; Jiménez-García, K.
- Nature, Vol. 462, Issue 7273
Tunable Gauge Potential for Neutral and Spinless Particles in Driven Optical Lattices
journal, May 2012
- Struck, J.; Ölschläger, C.; Weinberg, M.
- Physical Review Letters, Vol. 108, Issue 22
Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
journal, December 2014
- Aidelsburger, M.; Lohse, M.; Schweizer, C.
- Nature Physics, Vol. 11, Issue 2
Discretizing light behaviour in linear and nonlinear waveguide lattices
journal, August 2003
- Christodoulides, Demetrios N.; Lederer, Falk; Silberberg, Yaron
- Nature, Vol. 424, Issue 6950
Delocalization-enhanced Bloch oscillations and driven resonant tunneling in optical lattices for precision force measurements
journal, September 2012
- Tarallo, M. G.; Alberti, A.; Poli, N.
- Physical Review A, Vol. 86, Issue 3
Boundary force effects exerted on solitons in highly nonlocal nonlinear media
journal, December 2006
- Alfassi, Barak; Rotschild, Carmel; Manela, Ofer
- Optics Letters, Vol. 32, Issue 2
Four-dimensional photonic lattices and discrete tesseract solitons
journal, January 2013
- Jukić, D.; Buljan, H.
- Physical Review A, Vol. 87, Issue 1
Topological photonics
journal, October 2014
- Lu, Ling; Joannopoulos, John D.; Soljačić, Marin
- Nature Photonics, Vol. 8, Issue 11
Discrete solitons in photorefractive optically induced photonic lattices
journal, October 2002
- Efremidis, Nikos K.; Sears, Suzanne; Christodoulides, Demetrios N.
- Physical Review E, Vol. 66, Issue 4
Experimental Realization of Strong Effective Magnetic Fields in an Optical Lattice
journal, December 2011
- Aidelsburger, M.; Atala, M.; Nascimbène, S.
- Physical Review Letters, Vol. 107, Issue 25
Optical Analogues for Massless Dirac Particles and Conical Diffraction in One Dimension
journal, July 2012
- Zeuner, J. M.; Efremidis, N. K.; Keil, R.
- Physical Review Letters, Vol. 109, Issue 2
Artificial Gauge Field for Photons in Coupled Cavity Arrays
text, January 2011
- Umucalilar, R. O.; Carusotto, I.
- arXiv
Delocalization-enhanced Bloch oscillations and driven resonant tunneling in optical lattices for precision force measurements
text, January 2012
- Tarallo, M. G.; Alberti, A.; Poli, N.
- arXiv
Works referencing / citing this record:
PT symmetry in a fractional Schrödinger equation: PT symmetry in a fractional Schrödinger equation
journal, April 2016
- Zhang, Yiqi; Zhong, Hua; Belić, Milivoj R.
- Laser & Photonics Reviews, Vol. 10, Issue 3
Realization of uniform synthetic magnetic fields by periodically shaking an optical square lattice
journal, September 2016
- Creffield, C. E.; Pieplow, G.; Sols, F.
- New Journal of Physics, Vol. 18, Issue 9
Topological photonics
journal, March 2019
- Ozawa, Tomoki; Price, Hannah M.; Amo, Alberto
- Reviews of Modern Physics, Vol. 91, Issue 1
Constant intensity conical diffraction in discrete one-dimensional lattices with charge-conjugation symmetry
journal, December 2019
- Dehghani, Mojgan; Yuce, Cem; Kottos, Tsampikos
- Optics Letters, Vol. 45, Issue 1
Photonic topological phase transition on demand
journal, April 2019
- Kudyshev, Zhaxylyk A.; Kildishev, Alexander V.; Boltasseva, Alexandra
- Nanophotonics, Vol. 8, Issue 8
Realization of uniform synthetic magnetic fields by periodically shaking an optical square lattice
text, January 2016
- Creffield, C. E.; Pieplow, G.; Sols, F.
- arXiv