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Tunable pseudo-magnetic fields for polaritons in strained metasurfaces

Abstract

Pseudo-magnetic fields generated in artificially strained lattices have enabled the emulation of exotic phenomena once thought to be exclusive to charged particles. However, they have so far failed to emulate the tunability of real magnetic fields because they are determined solely by the engineered strain configuration, rendering them fixed by design. Here, we unveil a universal mechanism to tune pseudo-magnetic fields for polaritons supported by a strained honeycomb metasurface composed of interacting dipole emitters/antennas. Without altering the strain configuration, we show that the pseudo-magnetic field strength can be tuned by modifying the surrounding electromagnetic environment via an enclosing cavity waveguide, which modifies the nature of the dipole–dipole interactions. Owing to the competition between short-range Coulomb interactions and long-range photon-mediated interactions, the pseudo-magnetic field can be entirely switched off at a critical cavity width, without removing the strain. Consequently, by varying only the cavity width, we demonstrate a tunable Lorentz-like force that can be switched on/off and a collapse and revival of polariton Landau levels. Unlocking this tunable pseudo-magnetism poses new intriguing questions beyond the paradigm of conventional tight-binding physics.

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Fig. 1: Cavity-tunable dipole–dipole interactions.
Fig. 2: Cavity-tunable pseudo-gauge potentials.
Fig. 3: Cavity-tunable Lorentz-like force and cyclotron orbits.
Fig. 4: Cavity-induced collapse and revival of polariton Landau levels.

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All relevant data are available from the corresponding authors on reasonable request.

References

  1. Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nat. Phys. 7, 907–912 (2011).

    Article  Google Scholar 

  2. Umucalilar, R. O. & Carusotto, I. Artificial gauge field for photons in coupled cavity arrays. Phys. Rev. A 84, 043804 (2011).

    ADS  Article  Google Scholar 

  3. Fang, K., Yu, Z. & Fan, S. Photonic Aharonov-Bohm effect based on dynamic modulation. Phys. Rev. Lett. 108, 153901 (2012).

    ADS  Article  Google Scholar 

  4. Fang, K., Yu, Z. & Fan, S. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation. Nat. Photon. 6, 782–787 (2012).

    ADS  Article  Google Scholar 

  5. Fang, K. & Fan, S. Controlling the flow of light using the inhomogeneous effective gauge field that emerges from dynamic modulation. Phys. Rev. Lett. 111, 203901 (2013).

    ADS  Article  Google Scholar 

  6. Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. M. Imaging topological edge states in silicon photonics. Nat. Photon. 7, 1001–1005 (2013).

    ADS  Article  Google Scholar 

  7. Lin, Q. & Fan, S. Light guiding by effective gauge field for photons. Phys. Rev. X 4, 031031 (2014).

    Google Scholar 

  8. Tzuang, L. D., Fang, K., Nussenzveig, P., Fan, S. & Lipson, M. Non-reciprocal phase shift induced by an effective magnetic flux for light. Nat. Photon. 8, 701–705 (2014).

    ADS  Article  Google Scholar 

  9. Liu, F. & Li, J. Gauge field optics with anisotropic media. Phys. Rev. Lett. 114, 103902 (2015).

    ADS  Article  Google Scholar 

  10. Schine, N., Ryou, A., Gromov, A., Sommer, A. & Simon, J. Synthetic Landau levels for photons. Nature 534, 671–675 (2016).

    ADS  Article  Google Scholar 

  11. Schomerus, H. & Halpern, N. Y. Parity anomaly and Landau-level lasing in strained photonic honeycomb lattices. Phys. Rev. Lett. 110, 013903 (2013).

    ADS  Article  Google Scholar 

  12. Rechtsman, M. C. et al. Strain-induced pseudo-magnetic field and photonic Landau levels in dielectric structures. Nat. Photon. 7, 153–158 (2013).

    ADS  Article  Google Scholar 

  13. Abbaszadeh, H., Souslov, A., Paulose, J., Schomerus, H. & Vitelli, V. Sonic Landau levels and synthetic gauge fields in mechanical metamaterials. Phys. Rev. Lett. 119, 195502 (2017).

    ADS  Article  Google Scholar 

  14. Brendel, C., Peano, V., Painter, O. J. & Marquardt, F. Pseudo-magnetic fields for sound at the nanoscale. Proc. Natl Acad. Sci. USA 114, 3390–3395 (2017).

    ADS  Article  Google Scholar 

  15. Yang, Z., Gao, F., Yang, Y. & Baile, Z. Strain-induced gauge field and Landau levels in acoustic structures. Phys. Rev. Lett. 118, 194301 (2017).

    ADS  Article  Google Scholar 

  16. Wen, X. et al. Acoustic Landau quantization and quantum-Hall-like edge states. Nat. Phys. 15, 352–356 (2019).

    Article  Google Scholar 

  17. Jia, H. et al. Observation of chiral zero mode in inhomogeneous three-dimensional Weyl metamaterials. Science 363, 6423 (2019).

    MathSciNet  Article  Google Scholar 

  18. Peri, V., Serra-Garcia, M., Ilan, R. & Huber, S. D. Axial-field-induced chiral channels in an acoustic Weyl system. Nat. Phys. 15, 357–361 (2019).

    Article  Google Scholar 

  19. Guinea, F., Katsnelson, M. I. & Geim, A. K. Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering. Nat. Phys. 6, 30–33 (2009).

    Article  Google Scholar 

  20. Levy, N. et al. Strain-induced pseudo-magnetic fields greater than 300 Tesla in graphene nanobubbles. Science 329, 544–547 (2010).

    ADS  Article  Google Scholar 

  21. Low, T. & Guinea, F. Strain-induced pseudo-magnetic field for novel graphene electronics. Nano Lett. 10, 3551–3554 (2010).

    ADS  Article  Google Scholar 

  22. Chaves, A., Covaci, L., Rakhimov, K. U., Farias, G. A. & Peeters, F. M. Wave-packet dynamics and valley filter in strained graphene. Phys. Rev. B 82, 205430 (2010).

    ADS  Article  Google Scholar 

  23. de Juan, F., Cortijo, A., Vozmediano, M. A. H. & Cano, A. Aharonov-Bohm interferences from local deformations in graphene. Nat. Phys. 7, 810–815 (2011).

    Article  Google Scholar 

  24. Mann, C.-R., Sturges, T. J., Weick, G., Barnes, W. L. & Mariani, E. Manipulating type-I and type-II Dirac polaritons in cavity-embedded honeycomb metasurfaces. Nat. Commun. 9, 2194 (2018).

    ADS  Article  Google Scholar 

  25. Plotnik, Y. et al. Observation of unconventional edge states in ‘photonic graphene’. Nat. Mater. 13, 57–62 (2014).

    ADS  Article  Google Scholar 

  26. Bellec, M., Kuhl, U., Montambaux, G. & Mortessagne, F. Tight-binding couplings in microwave artificial graphene. Phys. Rev. B 88, 115437 (2013).

    ADS  Article  Google Scholar 

  27. Jacqmin, T. et al. Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons. Phys. Rev. Lett. 112, 116402 (2014).

    ADS  Article  Google Scholar 

  28. Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Brooks Cole, 1976).

  29. Landau, L. Diamagnetismus der metalle. Z. Phys. 64, 629–637 (1930).

    ADS  Article  Google Scholar 

  30. Svidzinsky, A. A., Chang, J.-T. & Scully, M. O. Cooperative spontaneous emission of N atoms: many-body eigenstates, the effect of virtual Lamb shift processes and analogy with radiation of N classical oscillators. Phys. Rev. A 81, 053821 (2010).

    ADS  Article  Google Scholar 

  31. Yuen-Zhou, J., Saikin, S. S., Yao, N. Y. & Aspuru-Guzik, A. Topologically protected excitons in porphyrin thin films. Nat. Mater. 13, 1026–1032 (2014).

    ADS  Article  Google Scholar 

  32. Yuen-Zhou, J. et al. Plexciton Dirac points and topological modes. Nat. Commun. 7, 11783 (2016).

    ADS  Article  Google Scholar 

  33. Bettles, R. J., Gardiner, S. A. & Adams, C. S. Enhanced optical cross section via collective coupling of atomic dipoles in a 2D array. Phys. Rev. Lett. 116, 103602 (2016).

    ADS  Article  Google Scholar 

  34. Shahmoon, E., Wild, D. S., Lukin, M. D. & Yelin, S. F. Cooperative resonances in light scattering from two-dimensional atomic arrays. Phys. Rev. Lett. 118, 113601 (2017).

    ADS  Article  Google Scholar 

  35. Bettles, R. J. et al. Topological properties of a dense atomic lattice gas. Phys. Rev. A 96, 041603 (2017).

    ADS  Article  Google Scholar 

  36. Perczel, J. et al. Topological quantum optics in two-dimensional atomic arrays. Phys. Rev. Lett. 119, 023603 (2017).

    ADS  Article  Google Scholar 

  37. González-Tudela, A., Hung, C.-L., Chang, D. E., Cirac, J. I. & Kimble, H. J. Subwavelength vacuum lattices and atom-atom interactions in two-dimensional photonic crystals. Nat. Photon. 9, 320–325 (2015).

    ADS  Article  Google Scholar 

  38. Bekenstein, R. et al. Quantum metasurfaces with atom arrays. Nat. Phys. 16, 676–681 (2020).

    Article  Google Scholar 

  39. Nikitin, A. Y., Guinea, F., García-Vidal, F. J. & Martín-Moreno, L. Fields radiated by a nanoemitter in a graphene sheet. Phys. Rev. B 84, 195446 (2011).

    ADS  Article  Google Scholar 

  40. Perczel, J., Borregaard, J., Chang, D. E., Yelin, S. F. & Lukin, M. D. Topological quantum optics using atom-like emitter arrays coupled to photonic crystals. Phys. Rev. Lett. 124, 083603 (2020).

    ADS  Article  Google Scholar 

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Acknowledgements

C.-R.M. acknowledges financial support from the Rank Prize Funds and the Engineering and Physical Sciences Research Council of the United Kingdom through the EPSRC Centre for Doctoral Training in Metamaterials (grant number EP/L015331/1). S.A.R.H. acknowledges financial support from a Royal Society TATA University Research Fellowship (grant number RPG-2016-186). E.M. acknowledges financial support from the Royal Society International Exchanges grant number IEC/R2/192166.

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C.-R.M. conceived the idea, developed the theory, performed the calculations and wrote the manuscript. S.A.R.H. contributed to the theoretical understanding. E.M. initiated the study, contributed to the theoretical understanding and supervised the project. All authors commented on the manuscript.

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Correspondence to Charlie-Ray Mann or Eros Mariani.

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The authors declare no competing interests.

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Supplementary Information

Supplementary Sections 1–7 and Figs. 1–9.

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Mann, CR., Horsley, S.A.R. & Mariani, E. Tunable pseudo-magnetic fields for polaritons in strained metasurfaces. Nat. Photonics 14, 669–674 (2020). https://doi.org/10.1038/s41566-020-0688-8

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