Researching | Real-time measurement of non-Hermitian Landau–Zener tunneling near band crossings

Advanced Photonics, Volume. 7, Issue 3, 036002(2025)

Real-time measurement of non-Hermitian Landau–Zener tunneling near band crossings

Lange Zhao^1、†, Shulin Wang^1,2, Chengzhi Qin¹, Bing Wang^1、*, Han Ye¹, Weiwei Liu¹, Stefano Longhi^3,4、*, and Peixiang Lu^1,5、*

Author Affiliations

¹Huazhong University of Science and Technology, Wuhan National Laboratory for Optoelectronics and School of Physics, Wuhan, China

²Southeast University, School of Physics, Nanjing, China

³Politecnico di Milano, Dipartimento di Fisica, Milano, Italy

⁴Instituto de Fisica Interdisciplinary Sistemas Complejos, IFISC (UIB-CSIC), Palma de Mallorca, Spain

⁵Wuhan Institute of Technology, Hubei Key Laboratory of Optical Information and Pattern Recognition, Wuhan, China

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[1] C. Zener. Non-adiabatic crossing of energy levels. Proc. R. Soc. Lond. A, 137, 696-702(1932). https://doi.org/10.1098/rspa.1932.0165

[2] L. D. Landau. Theorie der Energieubertragung. II. Phys. Z. Sowjetunion, 2, 46(1932).

[3] N. V. Vitanov. Transition times in the Landau–Zener model. Phys. Rev. A, 59, 988-994(1999). https://doi.org/10.1103/PhysRevA.59.988

[4] O. V. Ivakhnenko, S. N. Shevchenko, F. Nori. Nonadiabatic Landau–Zener–Stückelberg–Majorana transitions, dynamics, and interference. Phys. Rep., 995, 1-89(2023). https://doi.org/10.1016/j.physrep.2022.10.002

[5] P. Voisin et al. Observation of the Wannier–Stark quantization in a semiconductor superlattice. Phys. Rev. Lett., 61, 1639-1642(1988). https://doi.org/10.1103/PhysRevLett.61.1639

[6] J. Feldmann et al. Optical investigation of Bloch oscillations in a semiconductor superlattice. Phys. Rev. B, 46, 7252-7255(1992). https://doi.org/10.1103/PhysRevB.46.7252

[7] S. R. Wilkinson et al. Observation of atomic Wannier–Stark ladders in an accelerating optical potential. Phys. Rev. Lett., 76, 4512-4515(1996). https://doi.org/10.1103/PhysRevLett.76.4512

[8] B. P. Anderson, M. A. Kasevich. Macroscopic quantum interference from atomic tunnel arrays. Science, 282, 1686-1689(1998). https://doi.org/10.1126/science.282.5394.1686

[9] W. D. Oliver et al. Mach–Zehnder interferometry in a strongly driven superconducting qubit. Science, 310, 1653-1657(2005). https://doi.org/10.1126/science.1119678

[10] M. Ghulinyan et al. Zener tunneling of light waves in an optical superlattice. Phys. Rev. Lett., 94, 127401(2005). https://doi.org/10.1103/PhysRevLett.94.127401

[11] H. Trompeter et al. Bloch oscillations and Zener tunneling in two-dimensional photonic lattices. Phys. Rev. Lett., 96, 053903(2006). https://doi.org/10.1103/PhysRevLett.96.053903

[12] H. Sanchis-Alepuz, Y. A. Kosevich, J. Sánchez-Dehesa. Acoustic analogue of electronic Bloch oscillations and resonant Zener tunneling in ultrasonic superlattices. Phys. Rev. Lett., 98, 134301(2007). https://doi.org/10.1103/PhysRevLett.98.134301

[13] E. H. Hauge, J. A. Støvneng. Tunneling times: a critical review. Rev. Mod. Phys., 61, 917-936(1989). https://doi.org/10.1103/RevModPhys.61.917

[14] K. Mullen et al. Time of Zener tunneling. Phys. Rev. Lett., 62, 2543-2546(1989). https://doi.org/10.1103/PhysRevLett.62.2543

[15] R. Landauer, T. Martin. Barrier interaction time in tunneling. Rev. Mod. Phys., 66, 217-228(1994). https://doi.org/10.1103/RevModPhys.66.217

[16] F. Dreisow et al. Bloch–Zener oscillations in binary superlattices. Phys. Rev. Lett., 102, 076802(2009). https://doi.org/10.1103/PhysRevLett.102.076802

[17] A. Zenesini et al. Time-resolved measurement of Landau–Zener tunneling in periodic potentials. Phys. Rev. Lett., 103, 090403(2009). https://doi.org/10.1103/PhysRevLett.103.090403

[18] C. M. Bender. Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys., 70, 947(2007). https://doi.org/10.1088/0034-4885/70/6/R03

[19] N. Moiseyev. Non-Hermitian Quantum Mechanics(2011).

[20] Y. Ashida, Z. Gong, M. Ueda. Non-Hermitian physics. Adv. Phys., 69, 249-435(2020). https://doi.org/10.1080/00018732.2021.1876991

[21] N. Bender et al. Wave-packet self-imaging and giant recombinations via stable Bloch–Zener oscillations in photonic lattices with local PT symmetry. Phys. Rev. A, 92, 041803(2015). https://doi.org/10.1103/PhysRevA.92.041803

[22] M. Wimmer et al. Observation of Bloch oscillations in complex PT-symmetric photonic lattices. Sci. Rep., 5, 17760(2015). https://doi.org/10.1038/srep17760

[23] Y. L. Xu et al. Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice. Nat. Commun., 7, 11319(2016). https://doi.org/10.1038/ncomms11319

[24] V. M. Akulin, W. P Schleich. Landau–Zener transition to a decaying level. Phys. Rev. A, 46, 4110-4113(1992). https://doi.org/10.1103/PhysRevA.46.4110

[25] N. V. Vitanov, S. Stenholm. Pulsed excitation of a transition to a decaying level. Phys. Rev. A, 55, 2982-2988(1997). https://doi.org/10.1103/PhysRevA.55.2982

[26] E. M. Graefe, H. J. Korsch. Crossing scenario for a nonlinear non-Hermitian two-level system. Czech. J. Phys., 56, 1007-1020(2006). https://doi.org/10.1007/s10582-006-0396-8

[27] K. Saito et al. Dissipative Landau–Zener transitions of a qubit: bath-specific and universal behavior. Phys. Rev. B, 75, 214308(2007). https://doi.org/10.1103/PhysRevB.75.214308

[28] B. T. Torosov, G. Della Valle, S. Longhi. Non-Hermitian shortcut to adiabaticity. Phys. Rev. A, 87, 052502(2013). https://doi.org/10.1103/PhysRevA.87.052502

[29] Y. Avishai, Y. B. Band. Landau–Zener problem with decay and dephasing. Phys. Rev. A, 90, 032116(2014). https://doi.org/10.1103/PhysRevA.90.032116

[30] B. T. Torosov, N. V. Vitanov. Pseudo-Hermitian Landau–Zener–Stückelberg–Majorana model. Phys. Rev. A, 96, 013845(2017). https://doi.org/10.1103/PhysRevA.96.013845

[31] Z.-Y. Ge et al. Topological band theory for non-Hermitian systems from the Dirac equation. Phys. Rev. B, 100, 054105(2019). https://doi.org/10.1103/PhysRevB.100.054105

[32] S. Longhi. Non-Bloch-band collapse and chiral Zener tunneling. Phys. Rev. Lett., 124, 066602(2020). https://doi.org/10.1103/PhysRevLett.124.066602

[33] R. Melanathuru, S. Malzard, E.-M. Graefe. Landau–Zener transitions through a pair of higher-order exceptional points. Phys. Rev. A, 106, 012208(2022). https://doi.org/10.1103/PhysRevA.106.012208

[34] B. Longstaff, E.-M. Graefe. Nonadiabatic transitions through exceptional points in the band structure of a PT-symmetric lattice. Phys. Rev. A, 100, 052119(2019). https://doi.org/10.1103/PhysRevA.100.052119

[35] X. Shen et al. Landau–Zener–Stückelberg interferometry in PT-symmetric non-Hermitian models. Phys. Rev. A, 100, 062514(2019). https://doi.org/10.1103/PhysRevA.100.062514

[36] J.-S. Pan, F. Wu. Nonadiabatic transitions in non-Hermitian PT-symmetric two-level systems. Phys. Rev. A, 109, 022245(2024). https://doi.org/10.1103/PhysRevA.109.022245

[37] M. V. Berry. Physics of non-Hermitian degeneracies. Czech. J. Phys., 54, 1039-1047(2004). https://doi.org/10.1023/B:CJOP.0000044002.05657.04

[38] W. D. Heiss. The physics of exceptional points. J. Phys. A: Math. Theor., 45, 444016(2012). https://doi.org/10.1088/1751-8113/45/44/444016

[39] M.-A. Miri, A. Alù. Exceptional points in optics and photonics. Science, 363, eaar7709(2019). https://doi.org/10.1126/science.aar7709

[40] Ş. K. Özdemir et al. Parity-time symmetry and exceptional points in photonics. Nat. Mater., 18, 783-798(2019). https://doi.org/10.1038/s41563-019-0304-9

[41] M. V. Berry, R. Uzdin. Slow non-Hermitian cycling: exact solutions and the Stokes phenomenon. J. Phys. A: Math. Theor., 44, 435303(2011). https://doi.org/10.1088/1751-8113/44/43/435303

[42] J. Doppler et al. Dynamically encircling an exceptional point for asymmetric mode switching. Nature, 537, 76-79(2016). https://doi.org/10.1038/nature18605

[43] J. Alexandre, C. M. Bender. Foldy-Wouthuysen transformation for non-Hermitian Hamiltonians. J. Phys. A: Math. Theor., 48, 185403(2015). https://doi.org/10.1088/1751-8113/48/18/185403

[44] S. Longhi. Non-Hermitian topological phase transitions in superlattices and the optical Dirac equation. Opt. Lett., 46, 4470-4473(2021). https://doi.org/10.1364/OL.440052

[45] A. Regensburger et al. Photon propagation in a discrete fiber network: an interplay of coherence and losses. Phys. Rev. Lett., 107, 233902(2011). https://doi.org/10.1103/PhysRevLett.107.233902

[46] A. Regensburger et al. Parity-time synthetic photonic lattices. Nature, 488, 167-171(2012). https://doi.org/10.1038/nature11298

[47] M. Wimmer et al. Experimental measurement of the Berry curvature from anomalous transport. Nat. Phys., 13, 545-550(2017). https://doi.org/10.1038/nphys4050

[48] S. Weidemann et al. Topological funneling of light. Science, 368, 311-314(2020). https://doi.org/10.1126/science.aaz8727

[49] M. Wimmer et al. Superfluidity of light and its breakdown in optical mesh lattices. Phys. Rev. Lett., 127, 163901(2021). https://doi.org/10.1103/PhysRevLett.127.163901

[50] S. Wang et al. High-order dynamic localization and tunable temporal cloaking in ac-electric-field driven synthetic lattices. Nat. Commun., 13, 7653(2022). https://doi.org/10.1038/s41467-022-35398-9

[51] S. Weidemann et al. Topological triple phase transition in non-Hermitian Floquet quasicrystals. Nature, 601, 354-359(2022). https://doi.org/10.1038/s41586-021-04253-0

[52] S. Wang et al. Photonic Floquet Landau–Zener tunneling and temporal beam splitters. Sci. Adv., 9, eadh0415(2023). https://doi.org/10.1126/sciadv.adh0415

[53] H. Ye et al. Reconfigurable refraction manipulation at synthetic temporal interfaces with scalar and vector gauge potentials. Proc. Natl. Acad. Sci. U. S. A, 120, e2300860120(2023). https://doi.org/10.1073/pnas.2300860120

[54] C. Qin et al. Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials. Phys. Rev. Lett., 120, 133901(2018). https://doi.org/10.1103/PhysRevLett.120.133901

[55] A. Dutt et al. Experimental band structure spectroscopy along a synthetic dimension. Nat. Commun., 10, 3122(2019). https://doi.org/10.1038/s41467-019-11117-9

[56] K. Wang et al. Topological complex-energy braiding of non-Hermitian bands. Nature, 598, 59-64(2021). https://doi.org/10.1038/s41586-021-03848-x

[57] K. Wang et al. Generating arbitrary topological windings of a non-Hermitian band. Science, 371, 1240-1245(2021). https://doi.org/10.1126/science.abf6568

[58] F. Cardano et al. Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons. Nat. Commun., 8, 15516(2017). https://doi.org/10.1038/ncomms15516

[59] X. W. Luo et al. Synthetic-lattice enabled all-optical devices based on orbital angular momentum of light. Nat. Commun., 8, 16097(2017). https://doi.org/10.1038/ncomms16097

[60] L. Yuan et al. Synthetic dimension in photonics. Optica, 5, 1396-1405(2018). https://doi.org/10.1364/OPTICA.5.001396

[61] E. Lustig et al. Photonic topological insulator in synthetic dimensions. Nature, 567, 356-360(2019). https://doi.org/10.1038/s41586-019-0943-7

[62] M. Ehrhardt et al. A perspective on synthetic dimensions in photonics. Laser Photonics Rev., 17, 2200518(2023). https://doi.org/10.1002/lpor.202200518

[63] K. Fang, Z. Yu, S. Fan. Photonic Aharonov–Bohm effect based on dynamic modulation. Phys. Rev. Lett., 108, 153901(2012). https://doi.org/10.1103/PhysRevLett.108.153901

[64] Q. Lin, S. Fan. Light guiding by effective gauge field for photons. Phys. Rev. X, 4, 031031(2014). https://doi.org/10.1103/PhysRevX.4.031031

[65] S. Ibáñez, J. G. Muga. Adiabaticity condition for non-Hermitian Hamiltonians. Phys. Rev. A, 89, 033403(2014). https://doi.org/10.1103/PhysRevA.89.033403

[66] K. Kawabata et al. Symmetry and topology in non-Hermitian physics. Phys. Rev. X, 9, 041015(2019). https://doi.org/10.1103/PhysRevX.9.041015

[67] A. Steinfurth et al. Observation of photonic constant-intensity waves and induced transparency in tailored non-Hermitian lattices. Sci. Adv., 8, eabl7412(2022). https://doi.org/10.1126/sciadv.abl7412

[68] T. Eichelkraut et al. Mobility transition from ballistic to diffusive transport in non-Hermitian lattices. Nat. Commun., 4, 2533(2013). https://doi.org/10.1038/ncomms3533

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Lange Zhao, Shulin Wang, Chengzhi Qin, Bing Wang, Han Ye, Weiwei Liu, Stefano Longhi, Peixiang Lu, "Real-time measurement of non-Hermitian Landau–Zener tunneling near band crossings," Adv. Photon. 7, 036002 (2025)

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Paper Information

Category: Research Articles

Received: Sep. 29, 2024

Accepted: Feb. 27, 2025

Published Online: Apr. 14, 2025

The Author Email: Wang Bing (wangbing@hust.edu.cn), Longhi Stefano (stefano.longhi@polimi.it), Lu Peixiang (lupeixiang@hust.edu.cn)

DOI:10.1117/1.AP.7.3.036002

CSTR:32187.14.1.AP.7.3.036002

Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology