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Continuous transition between weak and ultrastrong coupling through exceptional points in carbon nanotube microcavity exciton–polaritons


Non-perturbative coupling of photons and excitons produces hybrid particles, exciton–polaritons, which have exhibited a variety of many-body phenomena in various microcavity systems. However, the vacuum Rabi splitting (VRS), which defines the strength of photon–exciton coupling, is usually a single constant for a given system. Here, we have developed a unique architecture in which excitons in an aligned single-chirality carbon nanotube film interact with cavity photons in polarization-dependent manners. The system reveals ultrastrong coupling (VRS up to 329 meV or a coupling-strength-to-transition-energy ratio of 13.3%) for polarization parallel to the nanotube axis, whereas VRS is absent for perpendicular polarization. Between these two extremes, VRS is continuously tunable through polarization rotation with exceptional points separating crossing and anticrossing. The points between exceptional points form equienergy arcs onto which the upper and lower polaritons coalesce. The demonstrated on-demand ultrastrong coupling provides ways to explore topological properties of polaritons and quantum technology applications.

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Fig. 1: Characterization of macroscopically aligned (6,5) SWCNTs and fabrication of SWCNT microcavity exciton–polariton devices.
Fig. 2: Anisotropic dispersions of microcavity exciton–polaritons in the E11 and E22 regions.
Fig. 3: Dispersions of SWCNT microcavity exciton–polaritons showing a continuous transition from the weak coupling to strong coupling regime with EPs.
Fig. 4: Evidence for collective ultrastrong light–matter coupling in aligned (6,5) films and determination of the E11 exciton oscillator strength and dipole moment.

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  1. Kimble, H. J. in Cavity Quantum Electrodynamics (ed. Berman, P. R.) 203–266 (Academic Press, Boston, 1994).

  2. Vasanelli, A., Todorov, Y. & Sirtori, C. Ultra-strong light–matter coupling and superradiance using dense electron gases. C. R. Phys. 17, 861–873 (2016).

    Article  ADS  Google Scholar 

  3. Günter, G. et al. Sub-cycle switch-on of ultrastrong light–matter interaction. Nature 458, 178–181 (2009).

    Article  ADS  Google Scholar 

  4. Törmä, P. & Barnes, W. L. Strong coupling between surface plasmon polaritons and emitters: a review. Rep. Prog. Phys. 78, 013901 (2015).

    Article  ADS  Google Scholar 

  5. Zhang, X., Zou, C.-L., Jiang, L. & Tang, H. X. Strongly coupled magnons and cavity microwave photons. Phys. Rev. Lett. 113, 156401 (2014).

    Article  ADS  Google Scholar 

  6. Yoshihara, F. et al. Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime. Nat. Phys. 13, 44–47 (2017).

    Article  Google Scholar 

  7. Casanova, J., Romero, G., Lizuain, I., Garc¡a-Ripoll, J. J. & Solano, E. Deep strong coupling regime of the Jaynes-Cummings model. Phys. Rev. Lett. 105, 263603 (2010).

    Article  ADS  Google Scholar 

  8. Ciuti, C., Bastard, G. & Carusotto, I. Quantum vacuum properties of the intersubband cavity polariton field. Phys. Rev. B 72, 115303 (2005).

    Article  ADS  Google Scholar 

  9. Ciuti, C. & Carusotto, I. Input-output theory of cavities in the ultrastrong coupling regime: the case of time-independent cavity parameters. Phys. Rev. A 74, 033811 (2006).

    Article  ADS  Google Scholar 

  10. Moore, G. T. Quantum theory of the electromagnetic field in a variable-length one-dimensional cavity. J. Math. Phys. 11, 2679–2691 (1970).

    Article  ADS  Google Scholar 

  11. Fulling, S. A. & Davies, P. C. W. Radiation from a moving mirror in two dimensional space-time: Conformal anomaly. Proc. R. Soc. London Ser. A 348, 393–414 (1976).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Kardar, M. & Golestanian, R. The “friction” of vacuum, and other fluctuation-induced forces. Rev. Mod. Phys. 71, 1233–1245 (1999).

    Article  ADS  Google Scholar 

  13. Stassi, R., Ridolfo, A., Di Stefano, O., Hartmann, M. J. & Savasta, S. Spontaneous conversion from virtual to real photons in the ultrastrong-coupling regime. Phys. Rev. Lett. 110, 243601 (2013).

    Article  ADS  Google Scholar 

  14. Ridolfo, A., Leib, M., Savasta, S. & Hartmann, M. J. Photon blockade in the ultrastrong coupling regime. Phys. Rev. Lett. 109, 193602 (2012).

    Article  ADS  Google Scholar 

  15. De Liberato, S. Light–matter decoupling in the deep strong coupling regime: the breakdown of the Purcell effect. Phys. Rev. Lett. 112, 016401 (2014).

    Article  ADS  Google Scholar 

  16. Hepp, K. & Lieb, E. H. On the superradiant phase transition for molecules in a quantized radiation field: the Dicke maser model. Ann. Phys. 76, 360–404 (1973).

    Article  ADS  MathSciNet  Google Scholar 

  17. Wang, Y. K. & Hioe, F. T. Phase transition in the Dicke model of superradiance. Phys. Rev. A 7, 831–836 (1973).

    Article  ADS  Google Scholar 

  18. Weisbuch, C., Nishioka, M., Ishikawa, A. & Arakawa, Y. Observation of the coupled exciton–photon mode splitting in a semiconductor quantum microcavity. Phys. Rev. Lett. 69, 3314–3317 (1992).

    Article  ADS  Google Scholar 

  19. Lidzey, D. G. et al. Strong exciton–photon coupling in an organic semiconductor microcavity. Nature 395, 53–55 (1998).

    Article  ADS  Google Scholar 

  20. Gambino, S. et al. Exploring light–matter interaction phenomena under ultrastrong coupling regime. ACS Photon. 1, 1042–1048 (2014).

    Article  Google Scholar 

  21. Liu, X. et al. Strong light–matter coupling in two-dimensional atomic crystals. Nat. Photon. 9, 30–34 (2015).

    Article  ADS  Google Scholar 

  22. Graf, A., Tropf, L., Zakharko, Y., Zaumseil, J. & Gather, M. C. Near-infrared exciton–polaritons in strongly coupled single-walled carbon nanotube microcavities. Nat. Commun. 7, 13078 (2016).

    Article  ADS  Google Scholar 

  23. Graf, A. et al. Electrical pumping and tuning of exciton–polaritons in carbon nanotube microcavities. Nat. Mater. 16, 911–917 (2017).

    Article  ADS  Google Scholar 

  24. Heiss, W. The physics of exceptional points. J. Phys. A 45, 444016 (2012).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Dembowski, C. et al. Experimental observation of the topological structure of exceptional points. Phys. Rev. Lett. 86, 787–790 (2001).

    Article  ADS  Google Scholar 

  26. Choi, Y. et al. Quasieigenstate coalescence in an atom-cavity quantum composite. Phys. Rev. Lett. 104, 153601 (2010).

    Article  ADS  Google Scholar 

  27. Zhen, B. et al. Spawning rings of exceptional points out of Dirac cones. Nature 525, 354–358 (2015).

    Article  ADS  Google Scholar 

  28. Gao, T. et al. Observation of non-Hermitian degeneracies in a chaotic exciton–polariton billiard. Nature 526, 554–558 (2015).

    Article  ADS  Google Scholar 

  29. Peng, B. et al. Chiral modes and directional lasing at exceptional points. Proc. Natl Acad. Sci. USA 113, 6845–6850 (2016).

    Article  ADS  Google Scholar 

  30. Peng, B. et al. Loss-induced suppression and revival of lasing. Science 346, 328–332 (2014).

    Article  ADS  Google Scholar 

  31. He, X. et al. Wafer-scale monodomain films of spontaneously aligned single-walled carbon nanotubes. Nat. Nanotech. 11, 633–638 (2016).

    Article  ADS  Google Scholar 

  32. Komatsu, N. et al. Modulation-doped multiple quantum wells of aligned single-wall carbon nanotubes. Adv. Func. Mater. 27, 1606022 (2017).

    Article  Google Scholar 

  33. Fagan, J. A. et al. Isolation of specific small-diameter single-wall carbon nanotube species via aqueous two-phase extraction. Adv. Mat. 26, 2800–2804 (2014).

    Article  Google Scholar 

  34. Dicke, R. H. Coherence in spontaneous radiation processes. Phys. Rev. 93, 99–110 (1954).

    Article  ADS  MATH  Google Scholar 

  35. Zhang, Q. et al. Collective non-perturbative coupling of 2D electrons with high-quality-factor terahertz cavity photons. Nat. Phys. 12, 1005–1011 (2016).

    Article  Google Scholar 

  36. Kéna-Cohen, S., Maier, S. A. & Bradley, D. D. C. Ultrastrongly coupled exciton–polaritons in metal-clad organic semiconductor microcavities. Adv. Opt. Mater. 1, 827–833 (2013).

    Article  Google Scholar 

  37. Brodbeck, S. et al. Experimental verification of the very strong coupling regime in a GaAs quantum well microcavity. Phys. Rev. Lett. 119, 027401 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  40. Riek, C. et al. Direct sampling of electric-field vacuum fluctuations. Science 350, 420–423 (2015).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. Benea-Chelmus, I.-C. Subcycle measurement of intensity correlations in the terahertz frequency range. Phys. Rev. A 93, 043812 (2016).

    Article  Google Scholar 

  42. Riek, C. et al. Subcycle quantum electrodynamics. Nature 541, 376–379 (2017).

    Article  ADS  Google Scholar 

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We thank D. Hagenmüller and J. Yuen-Zhou for useful discussion. This work was supported by the Department of Energy Basic Energy Sciences through grant no. DE-FG02-06ER46308 (optical spectroscopy experiments), the National Science Foundation through award no. ECCS-1708315 (device fabrication) and the Robert A. Welch Foundation through grant no. C-1509 (sample preparation). M.B. was supported by JST PRESTO (grant no. JPMJPR1767), KAKENHI (grant no. 26287087) and ImPACT Program of Council for Science, Technology and Innovation (Cabinet Office, Government of Japan).

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W.G. prepared the aligned SWCNT films, fabricated the devices and performed all measurements under the guidance of J.K. X.L. performed the transfer-matrix method simulations. M.B. developed the comprehensive theoretical model to explain the angular dependence of the coupling strength. All authors discussed the results and wrote the manuscript.

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Correspondence to Junichiro Kono.

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Gao, W., Li, X., Bamba, M. et al. Continuous transition between weak and ultrastrong coupling through exceptional points in carbon nanotube microcavity exciton–polaritons. Nature Photon 12, 362–367 (2018).

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