Electromagnetically induced moiré optical lattices in a coherent atomic gas
Zhiming Chen, Xiuye Liu, Jianhua Zeng
Electromagnetically induced moiré optical lattices in a coherent atomic gas
Electromagnetically induced optical (or photonic) lattices via atomic coherence in atomic ensembles have recently received great theoretical and experimental interest. We here conceive a way to generate electromagnetically induced moiré optical lattices — a twisted periodic pattern when two identical periodic patterns (lattices) are overlapped in a twisted angle (θ) — in a three-level coherent atomic gas working under electromagnetically induced transparency. We show that, changing the twisted angle and relative strength between the two constitutive sublattices, the moiré Bloch bands that are extremely flattened can always appear, resembling the typical flat-band and moiré physics found in other contexts. Dynamics of light propagation in the induced periodic structures demonstrating the unique linear localization and delocalization properties are also revealed. Our scheme can be implemented in a Rubidium atomic medium, where the predicted moiré optical lattices and flattened bands are naturally observable.
electromagnetically induced transparency / moiré optical lattices / extremely flat bands / light propagation / coherent atomic gas
[1] |
Y. S. Kivshar and G. P. Agrawal , Optical Solitons: From Fibers to Photonic Crystals, San Diego: Academic Press, 2003
|
[2] |
J. D. Joannopoulos , S. G. Johnson , J. N. Winn , and R. D. Meade , Photonic Crystals: Molding the Flow of Light, 2nd Ed., Princeton: Princeton University Press, 2011
|
[3] |
O. Morsch and M. Oberthaler , Dynamics of Bose–Einstein condensates in optical lattices, Rev. Mod. Phys. 78 (1), 179 (2006)
CrossRef
ADS
Google scholar
|
[4] |
I. L. Garanovich , S. Longhi , A. A. Sukhorukov , and Y. S. Kivshar , Light propagation and localization in modulated photonic lattices and waveguides, Phys. Rep. 518 (1-2), 1 (2012)
CrossRef
ADS
Google scholar
|
[5] |
Y. V. Kartashov , G. E. Astrakharchik , B. A. Malomed , and L. Torner , Frontiers in multidimensional self-trapping of nonlinear fields and matter, Nat. Rev. Phys. 1 (3), 185 (2019)
CrossRef
ADS
Google scholar
|
[6] |
L. Zeng and J. Zeng , Gap-type dark localized modes in a Bose–Einstein condensate with optical lattices, Adv. Photonics 1 (4), 046004 (2019)
CrossRef
ADS
Google scholar
|
[7] |
L. Zeng and J. Zeng , Preventing critical collapse of higherorder solitons by tailoring unconventional optical diffraction and nonlinearities, Commun. Phys. 3 (1), 26 (2020)
CrossRef
ADS
Google scholar
|
[8] |
J. Shi and J. Zeng , Self-trapped spatially localized states in combined linear-nonlinear periodic potentials, Front. Phys. 15 (1), 12602 (2020)
CrossRef
ADS
Google scholar
|
[9] |
Y. Y. Zheng , S. T. Chen , Z. P. Huang , S. X. Dai , B. Liu , Y. Y. Li , and S. R. Wang , Quantum droplets in two-dimensional optical lattices, Front. Phys. 16 (2), 22501 (2021)
CrossRef
ADS
Google scholar
|
[10] |
J. Li and J. Zeng , Dark matter-wave gap solitons in dense ultracold atoms trapped by a one-dimensional optical lattice, Phys. Rev. A 103 (1), 013320 (2021)
CrossRef
ADS
Google scholar
|
[11] |
J. Chen and J. Zeng , Dark matter-wave gap solitons of Bose–Einstein condensates trapped in optical lattices with competing cubic-quintic nonlinearities, Chaos Solitons Fractals 150, 111149 (2021)
CrossRef
ADS
Google scholar
|
[12] |
Y. Zhang , Z. Wu , M. R. Belić , H. Zheng , Z. Wang , M. Xiao , and Y. Zhang , Photonic floquet topological insulators in atomic ensembles, Laser Photon. Rev. 9 (3), 331 (2015)
CrossRef
ADS
Google scholar
|
[13] |
F. Wen , H. Ye , X. Zhang , W. Wang , S. Li , H. Wang , Y. Zhang , and C. W. Qiu , Optically induced atomic lattice with tunable near-field and far-field diffraction patterns, Photon. Res. 5 (6), 676 (2017)
CrossRef
ADS
Google scholar
|
[14] |
F. Wen , X. Zhang , H. Ye , W. Wang , H. Wang , Y. Zhang , Z. Dai , and C. W. Qiu , Efficient and tunable photo-induced honeycomb lattice in an atomic ensemble, Laser Photon. Rev. 12 (9), 1800050 (2018)
CrossRef
ADS
Google scholar
|
[15] |
L. Zhao , Electromagnetically induced polarization grating, Sci. Rep. 8 (1), 3073 (2018)
CrossRef
ADS
Google scholar
|
[16] |
C. Hang , W. Li , and G. Huang , Nonlinear light diffraction by electromagnetically induced gratings with PT symmetry in a Rydberg atomic gas, Phys. Rev. A 100 (4), 043807 (2019)
CrossRef
ADS
Google scholar
|
[17] |
Z. Zhang , F. Li , G. Malpuech , Y. Zhang , O. Bleu , S. Koniakhin , C. Li , Y. Zhang , M. Xiao , and D. D. Solnyshkov , Particle-like behavior of topological defects in linear wave packets in photonic graphene, Phys. Rev. Lett. 122 (23), 233905 (2019)
CrossRef
ADS
Google scholar
|
[18] |
J. Yuan , C. Wu , L. Wang , G. Chen , and S. Jia , Observation of diffraction pattern in two-dimensional optically induced atomic lattice, Opt. Lett. 44 (17), 4123 (2019)
CrossRef
ADS
Google scholar
|
[19] |
H. Zhang , J. Yuan , S. Dong , C. Wu , and L. Wang , Observation of an electromagnetically induced grating in cold 85Rb atoms, Appl. Sci. (Basel) 10 (17), 5740 (2020)
CrossRef
ADS
Google scholar
|
[20] |
Z. Zhang , R. Wang , Y. Zhang , Y. V. Kartashov , F. Li , H. Zhong , H. Guan , K. Gao , F. Li , Y. Zhang , and M. Xiao , Observation of edge solitons in photonic graphene, Nat. Commun. 11 (1), 1902 (2020)
CrossRef
ADS
Google scholar
|
[21] |
Z. Zhang , Y. Shen , S. Ning , S. Liang , Y. Feng , C. Li , Y. Zhang , and M. Xiao , Transport of light in a moving photonic lattice via atomic coherence, Opt. Lett. 46 (17), 4096 (2021)
CrossRef
ADS
Google scholar
|
[22] |
S. Ning , J. Lu , S. Liang , Y. Feng , C. Li , Z. Zhang , and Y. Zhang , Talbot effect of an electromagnetically induced square photonic lattice assisted by a spatial light modulator, Opt. Lett. 46 (19), 5035 (2021)
CrossRef
ADS
Google scholar
|
[23] |
Z. Shi and G. Huang , Selection and cloning of periodic optical patterns with a cold Rydberg atomic gas, Opt. Lett. 46 (21), 5344 (2021)
CrossRef
ADS
Google scholar
|
[24] |
M. Fleischhauer , A. Imamoğlu , and J. P. Marangos , Electromagnetically induced transparency: Optics in coherent media, Rev. Mod. Phys. 77 (2), 633 (2005)
CrossRef
ADS
Google scholar
|
[25] |
M. Fleischhauer and M. D. Lukin , Dark-state polaritons in electromagnetically induced transparency, Phys. Rev. Lett. 84 (22), 5094 (2000)
CrossRef
ADS
Google scholar
|
[26] |
C. Liu , Z. Dutton , C. H. Behroozi , and L. V. Hau , Observation of coherent optical information storage in an atomic medium using halted light pulses, Nature 409 (6819), 490 (2001)
CrossRef
ADS
Google scholar
|
[27] |
M. D. Lukin and A. Imamoğlu , Controlling photons using electromagnetically induced transparency, Nature 413 (6853), 273 (2001)
CrossRef
ADS
Google scholar
|
[28] |
A. André and M. D. Lukin , Manipulating light pulses via dynamically controlled photonic band gap, Phys. Rev. Lett. 89 (14), 143602 (2002)
CrossRef
ADS
Google scholar
|
[29] |
C. Hang , G. Huang , and V. V. Konotop, PT symmetry with a system of three-level atoms, Phys. Rev. Lett. 110 (8), 083604 (2013)
CrossRef
ADS
Google scholar
|
[30] |
Z. Chen , Z. Bai , H. Li , C. Hang , and G. Huang , Storage and retrieval of (3+1)-dimensional weak-light bullets and vortices in a coherent atomic gas, Sci. Rep. 5 (1), 8211 (2015)
CrossRef
ADS
Google scholar
|
[31] |
D. Xu , Z. Chen , and G. Huang , Ultraslow weak-light solitons and their storage and retrieval in a kagome-structured hollowcore photonic crystal fiber, Opt. Express 25 (16), 19094 (2017)
CrossRef
ADS
Google scholar
|
[32] |
K. Zhang , Y. Liang , J. Lin , and H. Li , Controlling the stability of nonlinear optical modes via electromagnetically induced transparency, Phys. Rev. A 97 (2), 023844 (2018)
CrossRef
ADS
Google scholar
|
[33] |
Z. Chen , H. Xie , Q. Li , and G. Huang , Stern–Gerlach deflection of optical Thirring solitons in a coherent atomic system, Phys. Rev. A 100 (1), 013827 (2019)
CrossRef
ADS
Google scholar
|
[34] |
Z. Bai , W. Li , and G. Huang , Stable single light bullets and vortices and their active control in cold Rydberg gases, Optica 6 (3), 309 (2019)
CrossRef
ADS
Google scholar
|
[35] |
J. Ru , Z. Wu , Y. Zhang , F. Wen , and Y. Gu , Talbot effect in nonparaxial self-accelerating beams with electromagnetically induced transparency, Front. Phys. 15 (5), 52503 (2020)
CrossRef
ADS
Google scholar
|
[36] |
J. Tang , Y. Deng , and C. Lee , Tunable photon blockade with a single atom in a cavity under electromagnetically induced transparency, Photon. Res. 9 (7), 1226 (2021)
CrossRef
ADS
Google scholar
|
[37] |
Z. Chen and J. Zeng , Localized gap modes of coherently trapped atoms in an optical lattice, Opt. Express 29 (3), 3011 (2021)
CrossRef
ADS
Google scholar
|
[38] |
Z. Chen and J. Zeng , Two-dimensional optical gap solitons and vortices in a coherent atomic ensemble loaded on optical lattices, Commun. Nonlinear Sci. Numer. Simul. 102, 105911 (2021)
CrossRef
ADS
Google scholar
|
[39] |
P. Wang , Y. Zheng , X. Chen , C. Huang , Y. V. Kartashov , L. Torner , V. V. Konotop , and F. Ye , Localization and delocalization of light in photonic moiré lattices, Nature 577 (7788), 42 (2020)
CrossRef
ADS
Google scholar
|
[40] |
Q. Fu , P. Wang , C. Huang , Y. V. Kartashov , L. Torner , V. V. Konotop , and F. Ye , Optical soliton formation controlled by angle twisting in photonic moiré lattices, Nat. Photonics 14 (11), 663 (2020)
CrossRef
ADS
Google scholar
|
[41] |
D. A. Steck , Rubidium 87 D Line Data. http://steck.us/alkalidata (revision 2.2.2, 9 July 2021)
|
[42] |
C. Huang , F. Ye , X. Chen , Y. V. Kartashov , V. V. Konotop , and L. Torner , Localization-delocalization wavepacket transition in Pythagorean aperiodic potentials, Sci. Rep. 6 (1), 32546 (2016)
CrossRef
ADS
Google scholar
|
[43] |
X. R. Mao , Z. K. Shao , H. Y. Luan , S. L. Wang , and R. M. Ma , Magic-angle lasers in nanostructured moiré superlattice, Nat. Nanotechnol. 16 (10), 1099 (2021)
CrossRef
ADS
Google scholar
|
[44] |
A. González-Tudela and J. I. Cirac , Cold atoms in twistedbilayer optical potentials, Phys. Rev. A 100, 053604 (2019)
CrossRef
ADS
Google scholar
|
[45] |
T. Salamon , A. Celi , R. W. Chhajlany , I. Frérot , Maciej Lewenstein , L. Tarruell , and D. Rakshit , Simulating twistronics without a twist, Phys. Rev. Lett. 125, 030504 (2020)
CrossRef
ADS
Google scholar
|
[46] |
X.-W. Luo and C. Zhang , Spin-twisted optical lattices: Tunable flat bands and Larkin — Ovchinnikov superfluids, Phys. Rev. Lett. 126, 103201 (2021)
CrossRef
ADS
Google scholar
|
[47] |
Y. V. Kartashov , F. Ye , V. V. Konotop , and L. Torner , Multifrequency solitons in commensurate-incommensurate photonic moiré lattices. Phys. Rev. Lett. 127 (16), 163902 (2021)
CrossRef
ADS
Google scholar
|
/
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