Splitter engineering through optimizing topological adiababtic passage

Jia-Ning Zhang, Jin-Lei Wu, Cheng Lv, Jiabao Yao, Jie Song, Yong-Yuan Jiang

PDF(4620 KB)
PDF(4620 KB)
Front. Phys. ›› 2025, Vol. 20 ›› Issue (1) : 014206. DOI: 10.15302/frontphys.2025.014206
RESEARCH ARTICLE

Splitter engineering through optimizing topological adiababtic passage

Author information +
History +

Abstract

Topologically protected states are important in realizing robust optical behaviors that are quite insensitive to local defects or perturbations, which provide a promising solution for robust photonic integrations. Here, we propose to implement fast topological beam splitters and routers via the adiabatic passage of edge and interface states in the cross-linking configuration of Su–Schrieffer–Heeger (SSH) chains with interface defects. The channel state does not immerse into the band continuum during the adiabatic cycle, making the adiabatic restriction less stringent and the transport process more efficient. Based on the accelerated topological pumping, the beam splitters and routers exhibit improved robustness against losses of the system yet degraded resilience to fluctuation of coupling strengths and on-site energies compared with the conventional topological splitting and routing schemes. In addition, we confirm that the model demonstrates good scalability when the system size is varied. The simulation results of topological beam splitting in coupled waveguide arrays are in good consistency with theoretical analysis. This topological design provides a robust way to control photons, which may suggest further application of topological devices with unique properties and functionalities for integrated photonics.

Graphical abstract

Keywords

topological effects in photonic systems / Su−Schrieffer−Heeger / topological photonics / waveguides

Cite this article

Download citation ▾
Jia-Ning Zhang, Jin-Lei Wu, Cheng Lv, Jiabao Yao, Jie Song, Yong-Yuan Jiang. Splitter engineering through optimizing topological adiababtic passage. Front. Phys., 2025, 20(1): 014206 https://doi.org/10.15302/frontphys.2025.014206

References

[1]
D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett. 49(6), 405 (1982)
CrossRef ADS Google scholar
[2]
S. Rachel, Interacting topological insulators: A review, Rep. Prog. Phys. 81(11), 116501 (2018)
CrossRef ADS Google scholar
[3]
C. K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88(3), 035005 (2016)
CrossRef ADS Google scholar
[4]
D. J. Thouless, Quantization of particle transport, Phys. Rev. B 27(10), 6083 (1983)
CrossRef ADS Google scholar
[5]
Q. Niu and D. J. Thouless, Quantised adiabatic charge transport in the presence of substrate disorder and many body interaction, J. Phys. Math. Gen. 17(12), 2453 (1984)
CrossRef ADS Google scholar
[6]
Y. E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, Topological states and adiabatic pumping in quasicrystals, Phys. Rev. Lett. 109(10), 106402 (2012)
CrossRef ADS Google scholar
[7]
M. Verbin, O. Zilberberg, Y. Lahini, Y. E. Kraus, and Y. Silberberg, Topological pumping over a photonic Fibonacci quasicrystal, Phys. Rev. B 91(6), 064201 (2015)
CrossRef ADS Google scholar
[8]
A. Bansil, H. Lin, and T. Das, Topological band theory, Rev. Mod. Phys. 88(2), 021004 (2016)
CrossRef ADS Google scholar
[9]
P. Narang, C. A. C. Garcia, and C. Felser, The topology of electronic band structures, Nat. Mater. 20, 293 (2021)
CrossRef ADS Google scholar
[10]
M. He, H. Sun, and Q. L. He, Topological insulator: Spintronics and quantum computations, Front. Phys. 14(4), 43401 (2019)
CrossRef ADS Google scholar
[11]
O. Breunig and Y. Ando, Opportunities in topological insulator devices, Nat. Rev. Phys. 4(3), 184 (2021)
CrossRef ADS Google scholar
[12]
F. Mei, G. Chen, L. Tian, S. L. Zhu, and S. Jia, Robust quantum state transfer via topological edge states in superconducting qubit chains, Phys. Rev. A 98(1), 012331 (2018)
CrossRef ADS Google scholar
[13]
S. Longhi, Topological pumping of edge states via adiabatic passage, Phys. Rev. B 99(15), 155150 (2019)
CrossRef ADS Google scholar
[14]
T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys. 91(1), 015006 (2019)
CrossRef ADS Google scholar
[15]
L. Lu, J. D. Joannopoulos, and M. Soljačić, Topological photonics, Nat. Photonics 8(11), 821 (2014)
CrossRef ADS Google scholar
[16]
W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene, Phys. Rev. Lett. 42(25), 1698 (1979)
CrossRef ADS Google scholar
[17]
E. J. Meier, F. A. An, and B. Gadway, Observation of the topological soliton state in the Su–Schrieffer–Heeger model, Nat. Commun. 7(1), 13986 (2016)
CrossRef ADS Google scholar
[18]
L. Qi, G. L. Wang, S. Liu, S. Zhang, and H. F. Wang, Engineering the topological state transfer and topological beam splitter in an even-sized Su–Schrieffer–Heeger chain, Phys. Rev. A 102(2), 022404 (2020)
CrossRef ADS Google scholar
[19]
L. Qi, Y. Xing, X. D. Zhao, S. Liu, S. Zhang, S. Hu, and H. F. Wang, Topological beam splitter via defect-induced edge channel in the Rice‒Mele model, Phys. Rev. B 103(8), 085129 (2021)
CrossRef ADS Google scholar
[20]
J. N. Zhang, J. X. Han, J. L. Wu, J. Song, and Y. Y. Jiang, Robust beam splitter with fast quantum state transfer through a topological interface, Front. Phys. 18(5), 51303 (2023)
CrossRef ADS Google scholar
[21]
J. N. Zhang, J. L. Wu, J. X. Han, S. Tang, J. Song, and Y. Y. Jiang, Small admixture of nonadiabaticity facilitating topologically protected splitters and routers via optimizing coupling engineering, Phys. Rev. B 109(9), 094303 (2024)
CrossRef ADS Google scholar
[22]
L. Qi, Y. Yan, Y. Xing, X. D. Zhao, S. Liu, W. X. Cui, X. Han, S. Zhang, and H. F. Wang, Topological router induced via long-range hopping in a Su–Schrieffer–Heeger chain, Phys. Rev. Res. 3(2), 023037 (2021)
CrossRef ADS Google scholar
[23]
L. N. Zheng, X. Yi, and H. F. Wang, Engineering a phase-robust topological router in a dimerized superconducting-circuit lattice with long-range hopping and chiral symmetry, Phys. Rev. Appl. 18(5), 054037 (2022)
CrossRef ADS Google scholar
[24]
L. N. Zheng, H. F. Wang, and X. Yi, Planar and tunable quantum state transfer in a splicing Y-junction Su–Schrieffer–Heeger chain, New J. Phys. 25(11), 113003 (2023)
CrossRef ADS Google scholar
[25]
H. Li, R. Yao, B. Zheng, S. An, M. Haerinia, J. Ding, C. S. Lee, H. Zhang, and W. Guo, Electrically tunable and reconfigurable topological edge state laser, Optics 3(2), 107 (2022)
CrossRef ADS Google scholar
[26]
M. S. Wei, M. J. Liao, C. Wang, C. Zhu, Y. Yang, and J. Xu, Topological laser with higher-order corner states in the 2-dimensional Su–Schrieffer–Heeger model, Opt. Express 31(3), 3427 (2023)
CrossRef ADS Google scholar
[27]
P. St-Jean, V. Goblot, E. Galopin, A. Lemaître, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, Lasing in topological edge states of a one-dimensional lattice, Nat. Photonics 11, 651 (2017)
CrossRef ADS Google scholar
[28]
M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Edgemode lasing in 1d topological active arrays, Phys. Rev. Lett. 120(11), 113901 (2018)
CrossRef ADS Google scholar
[29]
G. Harari, M. A. Bandres, Y. Lumer, M. C. Rechtsman, Y. D. Chong, M. Khajavikhan, D. N. Christodoulides, and M. Segev, Topological insulator laser: Theory, Science 359(6381), eaar4003 (2018)
CrossRef ADS Google scholar
[30]
F. M. D’Angelis, F. A. Pinheiro, D. Guery-Odelin, S. Longhi, and F. Impens, Fast and robust quantum state transfer in a topological Su–Schrieffer–Heeger chain with next-to-nearest-neighbor interactions, Phys. Rev. Res. 2(3), 033475 (2020)
CrossRef ADS Google scholar
[31]
I. Brouzos, I. Kiorpelidis, F. K. Diakonos, and G. Theocharis, Fast, robust, and amplified transfer of topological edge modes on a time-varying mechanical chain, Phys. Rev. B 102(17), 174312 (2020)
CrossRef ADS Google scholar
[32]
N. E. Palaiodimopoulos, I. Brouzos, F. K. Diakonos, and G. Theocharis, Fast and robust quantum state transfer via a topological chain, Phys. Rev. A 103(5), 052409 (2021)
CrossRef ADS Google scholar
[33]
C. Wu, W. Liu, Y. Jia, G. Chen, and F. Chen, Observation of topological pumping of a defect state in a Fock photonic lattice, Phys. Rev. A 107(3), 033501 (2023)
CrossRef ADS Google scholar
[34]
J. Yuan, C. Xu, H. Cai, and D. W. Wang, Gap-protected transfer of topological defect states in photonic lattices, APL Photonics 6(3), 030803 (2021)
CrossRef ADS Google scholar
[35]
M. P. J. Lavery, A. Dudley, A. Forbes, J. Courtial, and M. J. Padgett, Robust interferometer for the routing of light beams carrying orbital angular momentum, New J. Phys. 13(9), 093014 (2011)
CrossRef ADS Google scholar
[36]
W. Bogaerts, D. Pérez, J. Capmany, D. A. B. Miller, J. Poon, D. Englund, F. Morichetti, and A. Melloni, Programmable photonic circuits, Nature 586(7828), 207 (2020)
CrossRef ADS Google scholar
[37]
H. Oukraou, V. Coda, A. A. Rangelov, and G. Montemezzani, Broadband photonic transport between waveguides by adiabatic elimination, Phys. Rev. A 97(2), 023811 (2018)
CrossRef ADS Google scholar
[38]
T. Lunghi, F. Doutre, A. P. Rambu, M. Bellec, M. P. De Micheli, A. M. Apetrei, O. Alibart, N. Belabas, S. Tascu, and S. Tanzilli, Broadband integrated beam splitter using spatial adiabatic passage, Opt. Express 26(21), 27058 (2018)
CrossRef ADS Google scholar
[39]
A. K. Taras, A. Tuniz, M. A. Bajwa, V. Ng, J. M. Dawes, C. G. Poulton, and C. M. De Sterke, Shortcuts to adiabaticity in waveguide couplers – theory and implementation, Adv. Phys. X 6, 1894978 (2021)
CrossRef ADS Google scholar
[40]
Y. X. Lin, M. Younesi, H. P. Chung, H. K. Chiu, R. Geiss, Q. H. Tseng, F. Setzpfandt, T. Pertsch, and Y. H. Chen, Ultra-compact, broadband adiabatic passage optical couplers in thin-film lithium niobate on insulator waveguides, Opt. Express 29(17), 27362 (2021)
CrossRef ADS Google scholar
[41]
A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, Topological optical waveguiding in silicon and the transition between topological and trivial defect states, Phys. Rev. Lett. 116(16), 163901 (2016)
CrossRef ADS Google scholar
[42]
X.T. HeE. T. LiangJ.J. YuanH.Y. QiuX.D. Chen F.L. ZhaoJ. W. Dong, A silicon-on-insulator slab for topological valley transport, Nat. Commun. 10(1), 872 (2019)
[43]
M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, and N. M. Litchinitser, Robust topologically protected transport in photonic crystals at telecommunication wavelengths, Nat. Nanotechnol. 14(1), 31 (2019)
CrossRef ADS Google scholar
[44]
B. Sun, F. Morozko, P. S. Salter, S. Moser, Z. Pong, R. B. Patel, I. A. Walmsley, M. Wang, A. Hazan, N. Barré, A. Jesacher, J. Fells, C. He, A. Katiyi, Z. N. Tian, A. Karabchevsky, and M. J. Booth, On-chip beam rotators, adiabatic mode converters, and waveplates through low-loss waveguides with variable crosssections, Light Sci. Appl. 11(1), 214 (2022)
CrossRef ADS Google scholar
[45]
T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Anomalous refraction and diffraction in discrete optical systems, Phys. Rev. Lett. 88(9), 093901 (2002)
CrossRef ADS Google scholar
[46]
M. J. Ablowitz and J. T. Cole, Nonlinear optical waveguide lattices: Asymptotic analysis, solitons, and topological insulators, Physica D 440, 133440 (2022)
CrossRef ADS Google scholar
[47]
Y. Zhao, Y. Chen, Z. S. Hou, B. Han, H. Fan, L. H. Lin, X. F. Ren, and H. B. Sun, Polarization-dependent Bloch oscillations in optical waveguides, Opt. Lett. 47(3), 617 (2022)
CrossRef ADS Google scholar
[48]
W. F. Zhang, X. Zhang, Y. V. Kartashov, X. Chen, and F. Ye, Bloch oscillations in arrays of helical waveguides, Phys. Rev. A 97(6), 063845 (2018)
CrossRef ADS Google scholar
[49]
W. Li, C. Qin, T. Han, H. Chen, B. Wang, and P. Lu, Bloch oscillations in photonic spectral lattices through phase-mismatched four-wave mixing, Opt. Lett. 44(22), 5430 (2019)
CrossRef ADS Google scholar
[50]
T. L. Silva, W. B. Cardoso, A. T. Avelar, and J. M. C. Malbouisson, Nonclassical properties and Anderson localization of quantum states in coupled waveguides, Phys. Rev. A 105(2), 023710 (2022)
CrossRef ADS Google scholar
[51]
Y. Yang, R. J. Chapman, B. Haylock, F. Lenzini, Y. N. Joglekar, M. Lobino, and A. Peruzzo, Programmable high-dimensional Hamiltonian in a photonic waveguide array, Nat. Commun. 15(1), 50 (2024)
CrossRef ADS Google scholar
[52]
K. Jin, Y. Li, F. Li, M. R. Belic, Y. Zhang, and Y. Zhang, Rabi oscillations of azimuthons in weakly nonlinear waveguides, Adv. Photonics 2(4), 046002 (2020)
CrossRef ADS Google scholar
[53]
J. Beierlein, E. Rozas, O. A. Egorov, M. Klaas, A. Yulin, H. Suchomel, T. H. Harder, M. Emmerling, M. D. Martın, I. A. Shelykh, C. Schneider, U. Peschel, L. Vina, S. Hofling, and S. Klembt, Propagative oscillations in co-directional polariton waveguide couplers, Phys. Rev. Lett. 126(7), 075302 (2021)
CrossRef ADS Google scholar
[54]
C. Jorg, G. Queralto, M. Kremer, G. Pelegrı, J. Schulz, A. Szameit, G. von Freymann, J. Mompart, and V. Ahufinger, Artificial gauge field switching using orbital angular momentum modes in optical waveguides, Light Sci. Appl. 9(1), 150 (2020)
CrossRef ADS Google scholar
[55]
Y. Lumer, M. A. Bandres, M. Heinrich, L. J. Maczewsky, H. Herzig-Sheinfux, A. Szameit, and M. Segev, Light guiding by artificial gauge fields, Nat. Photonics 13(5), 339 (2019)
CrossRef ADS Google scholar
[56]
K. Xu, F. Chen, H. Chen, M. Fang, Z. Huang, and Y. Yang, Waveguide channel splitting induced by artificial gauge fields, ACS Photonics 10(3), 632 (2023)
CrossRef ADS Google scholar
[57]
W. Song, T. Li, S. Wu, Z. Wang, C. Chen, Y. Chen, C. Huang, K. Qiu, S. Zhu, Y. Zou, and T. Li, Dispersionless coupling among optical waveguides by artificial gauge field, Phys. Rev. Lett. 129(5), 053901 (2022)
CrossRef ADS Google scholar
[58]
P. Zhou, T. Li, Y. Lin, L. Xia, L. Shen, X. Xu, T. Li, and Y. Zou, Artificial gauge field enabled low-crosstalk, broadband, half-wavelength pitched waveguide arrays, Laser Photonics Rev. 17(6), 2200944 (2023)
CrossRef ADS Google scholar
[59]
E. Lustig, S. Weimann, Y. Plotnik, Y. Lumer, M. A. Bandres, A. Szameit, and M. Segev, Photonic topological insulator in synthetic dimensions, Nature 567(7748), 356 (2019)
CrossRef ADS Google scholar
[60]
M. J. Ablowitz and J. T. Cole, Topological insulators in longitudinally driven waveguides: Lieb and kagome lattices, Phys. Rev. A 99(3), 033821 (2019)
CrossRef ADS Google scholar
[61]
T. Biesenthal, L. J. Maczewsky, Z. Yang, M. Kremer, M. Segev, A. Szameit, and M. Heinrich, Fractal photonic topological insulators, Science 376(6597), 1114 (2022)
CrossRef ADS Google scholar
[62]
S. Shen, Y. V. Kartashov, Y. Li, and Y. Zhang, Floquet edge solitons in modulated trimer waveguide arrays, Phys. Rev. Appl. 20(1), 014012 (2023)
CrossRef ADS Google scholar
[63]
S. K. Ivanov, Y. V. Kartashov, and V. V. Konotop, Floquet defect solitons, Opt. Lett. 46(21), 5364 (2021)
CrossRef ADS Google scholar
[64]
S. Mukherjee and M. C. Rechtsman, Observation of floquet solitons in a topological bandgap, Science 368(6493), 856 (2020)
CrossRef ADS Google scholar
[65]
J. Zurita, C. E. Creffield, and G. Platero, Fast quantum transfer mediated by topological domain walls, Quantum 7, 1043 (2023)
CrossRef ADS Google scholar
[66]
N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, Stimulated Raman adiabatic passage in physics, chemistry, and beyond, Rev. Mod. Phys. 89(1), 015006 (2017)
CrossRef ADS Google scholar
[67]
S. Tang, J. L. Wu, C. Lu, J. Song, and Y. Jiang, Functional acoustic metamaterial using shortcut to adiabatic passage in acoustic waveguide couplers, Phys. Rev. Appl. 18(1), 014038 (2022)
CrossRef ADS Google scholar
[68]
S. Tang, J. L. Wu, C. Lu, X. Wang, J. Song, and Y. Jiang, Acoustic wavelength selected metamaterials designed by reversed fractional stimulated Raman adiabatic passage, Phys. Rev. B 105(10), 104107 (2022)
CrossRef ADS Google scholar
[69]
S. Tang, J. L. Wu, C. Lu, J. Yao, Y. Pei, and Y. Jiang, Unidirectional beam splitting in acoustic metamaterial governed by double fractional stimulated Raman adiabatic passage, Appl. Phys. Lett. 122(21), 212201 (2023)
CrossRef ADS Google scholar
[70]
S. Tang, J. L. Wu, C. Lu, J. Yao, X. Wang, J. Song, and Y. Jiang, One-way acoustic beam splitting in spatial four-waveguide couplers designed by adiabatic passage, New J. Phys. 25(3), 033032 (2023)
CrossRef ADS Google scholar
[71]
J. L. Wu, S. Tang, Y. Wang, X. S. Wang, J. X. Han, C. Lu, J. Song, S. L. Su, Y. Xia, and Y. Y. Jiang, Unidirectional acoustic metamaterials based on nonadiabatic holonomic quantum transformations, Sci. China Phys. Mech. Astron. 65(2), 220311 (2022)
CrossRef ADS Google scholar
[72]
W. P. Huang, Coupled-mode theory for optical waveguides: An overview, J. Opt. Soc. Am. A 11(3), 963 (1994)
CrossRef ADS Google scholar
[73]
H. A. Haus and W. Huang, Coupled-mode theory, Proc. IEEE 79(10), 1505 (1991)
CrossRef ADS Google scholar
[74]
W. Liu, C. Wu, Y. Jia, S. Jia, G. Chen, and F. Chen, Observation of edge-to-edge topological transport in a photonic lattice, Phys. Rev. A 105(6), L061502 (2022)
CrossRef ADS Google scholar
[75]
L. Huang, Z. Tan, H. Zhong, and B. Zhu, Fast and robust quantum state transfer assisted by zero energy interface states in a splicing Su–Schrieffer–Heeger chain, Phys. Rev. A 106(2), 022419 (2022)
CrossRef ADS Google scholar

Declarations

The authors declare no competing interests and no conflicts.

Acknowledgements

The authors acknowledge the financial support by the National Natural Science Foundation of China (Grant Nos. 62075048 and 12304407) and China Postdoctoral Science Foundation (Grant Nos. 2023TQ0310 and GZC20232446).

RIGHTS & PERMISSIONS

2024 Higher Education Press
AI Summary AI Mindmap
PDF(4620 KB)

Accesses

Citations

Detail

Sections
Recommended

/