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Observation of PT-symmetric quantum interference

Nature Photonics volume 13, pages 883–887 (2019)Cite this article

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Abstract

A common wisdom in quantum mechanics is that the Hamiltonian has to be Hermitian in order to ensure a real eigenvalue spectrum. Yet, parity–time (PT)-symmetric Hamiltonians are sufficient for real eigenvalues and therefore constitute a complex extension of quantum mechanics beyond the constraints of Hermiticity. However, as only single-particle or classical wave physics has been exploited so far, an experimental demonstration of the true quantum nature of PT symmetry has been elusive. In our work, we demonstrate two-particle quantum interference in a PT-symmetric system. We employ integrated photonic waveguides to reveal that the quantum dynamics of indistinguishable photons shows strongly counterintuitive features. To substantiate our experimental data, we analytically solve the quantum master equation using Lie algebra methods. The ideas and results presented here pave the way for non-local PT-symmetric quantum mechanics as a novel building block for future quantum devices.

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Fig. 1: Combining photon correlations and PT symmetry.
Fig. 2: Analytical solution of the lossy directional coupler.
Fig. 3: Measurement of the intensity ratio for directional couplers at different propagation lengths.
Fig. 4: Measurement of the HOM dip for a set of PT-symmetric and corresponding Hermitian couplers.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. Bender, C. M. & Boettcher, S. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  2. Bender, C. M. PT Symmetry: In Quantum and Classical Physics (World Scientific Publishing, 2018).

  3. Bender, C. M., Brody, D. C. & Jones, H. F. Complex extension of quantum mechanics. Phys. Rev. Lett. 89, 270401 (2002).

    Article  MathSciNet  Google Scholar 

  4. Mostafazadeh, A. Pseudo-Hermitian representation of quantum mechanics. Int. J. Geom. Methods Mod. Phys. 7, 1191–1306 (2010).

    Article  MathSciNet  Google Scholar 

  5. Brody, D. C. Consistency of PT-symmetric quantum mechanics. J. Phys. A 49, 10LT03 (2016).

    Article  MathSciNet  Google Scholar 

  6. El-Ganainy, R. et al. Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).

    Article  Google Scholar 

  7. Dorey, P., Dunning, C. & Tateo, R. Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics. J. Phys. A 34, 5679–5704 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  8. Rüter, C. E. et al. Observation of parity–time symmetry in optics. Nat. Phys. 6, 192–195 (2010).

    Article  Google Scholar 

  9. Ching, E. S. C. et al. Quasinormal-mode expansion for waves in open systems. Rev. Mod. Phys. 70, 1545–1554 (1998).

    Article  ADS  Google Scholar 

  10. Berry, M. V. Mode degeneracies and the Petermann excess-noise factor. J. Mod. Phys. 50, 63–81 (2003).

    ADS  MATH  Google Scholar 

  11. Brody, D. C. Biorthogonal quantum mechanics. J. Phys. A 47, 035305 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  12. Gangaraj, S. A. H. & Monticone, F. Topological waveguiding near an exceptional point: defect-immune, slow-light and loss-immune propagation. Phys. Rev. Lett. 121, 093901 (2018).

    Article  ADS  Google Scholar 

  13. Heiss, W. D. & Steeb, W.-H. Avoided level crossing and Riemann sheet structure. J. Math. Phys. 32, 3003–3007 (1991).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  15. Milburn, T. J. et al. General description of quasiadiabatic dynamical phenomena near exceptional points. Phys. Rev. A 92, 052124 (2015).

    Article  ADS  Google Scholar 

  16. Miri, M.-A. & Alu, A. Exceptional points in optics and photonics. Science 363, eaar7709 (2019).

    Article  MathSciNet  Google Scholar 

  17. Eichelkraut, T. et al. Mobility transition from ballistic to diffusive transport in non-Hermitian lattices. Nat. Commun. 4, 2533 (2013).

    Article  ADS  Google Scholar 

  18. Musslimani, Z., Makris, K., El Ganainy, R. & Christodoulides, D. Optical solitons in PT periodic potentials. Phys. Rev. Lett. 100, 030402 (2008).

    Article  ADS  Google Scholar 

  19. Feng, L., Wong, Z. J., Ma, R. M., Wang, Y. & Zhang, X. Single-mode laser by parity–time symmetry breaking. Science 346, 972–975 (2014).

    Article  ADS  Google Scholar 

  20. Zeuner, J. M. et al. Observation of a topological transition in the bulk of a non-Hermitian system. Phys. Rev. Lett. 115, 040402 (2015).

    Article  ADS  Google Scholar 

  21. Weimann, S. et al. Topologically protected bound states in photonic PT-symmetric crystals. Nat. Mater. 16, 433–438 (2017).

    Article  ADS  Google Scholar 

  22. Zhao, K. F., Schaden, M. Z. & Wu, Z. Enhanced magnetic resonance signal of spin-polarized Rb atoms near surfaces of coated cells. Phys. Rev. A 81, 042903 (2010).

    Article  ADS  Google Scholar 

  23. Chtchelkatchev, N. M., Golubov, A. A., Baturina, T. I. & Vinokur, V. M. Stimulation of the fluctuation superconductivity by PT symmetry. Phys. Rev. Lett. 109, 150405 (2012).

    Article  ADS  Google Scholar 

  24. Schindler, J., Li, A., Zheng, M. C., Ellis, F. M. & Kottos, T. Experimental study of active LRC circuits with PT symmetries. Phys. Rev. A. 84, 040101 (2011).

    Article  ADS  Google Scholar 

  25. Xiao, L. et al. Observation of topological edge states in parity–time-symmetric quantum walks. Nat. Phys. 13, 1117–1123 (2017).

    Article  Google Scholar 

  26. Hong, C. K., Ou, Z. Y. & Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044–2634 (1987).

    Article  ADS  Google Scholar 

  27. Rai, A., Das, S. & Agarwal, G. S. Quantum entanglement in coupled lossy waveguides. Opt. Express. 18, 6241–6251 (2010).

    Article  ADS  Google Scholar 

  28. El-Ganainy, R., Makris, K. G., Christodoulides, D. N. & Musslimani, Z. H. Theory of coupled optical PT-symmetric structures. Opt. Lett. 32, 2632–2634 (2007).

    Article  ADS  Google Scholar 

  29. Scheel, S. & Szameit, A. PT-symmetric photonic quantum systems with gain and loss do not exist. Europhys. Lett. 122, 34001 (2018).

    Article  ADS  Google Scholar 

  30. Ornigotti, M. & Szameit, A. Quasi PT-symmetry in passive photonic lattices. J. Opt. 16, 065501 (2014).

    Article  ADS  Google Scholar 

  31. Guo, A. et al. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103, 093902 (2009).

    Article  ADS  Google Scholar 

  32. Ban, M. Lie-algebra methods in quantum optics: the Liouville-space formulation. Phys. Rev. A 47, 5093–5119 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  33. Szameit, A. & Nolte, S. Discrete optics in femtosecond-laser-written photonic structures. J. Phys. B 43, 163001 (2010).

    Article  ADS  Google Scholar 

  34. Eichelkraut, T., Weimann, S., Stützer, S., Nolte, S. & Szameit, A. Radiation-loss management in modulated waveguides. Opt. Lett. 39, 6831–6834 (2014).

    Article  ADS  Google Scholar 

  35. Barnett, S., Jeffers, J., Gatti, A. & Loudon, R. Quantum optics of lossy beam splitters. Phys. Rev. A 57, 2134–2145 (1998).

    Article  ADS  Google Scholar 

  36. Vest, B. et al. Anti-coalescence of bosons on a lossy beam splitter. Science 356, 1373–1376 (2017).

    Article  ADS  Google Scholar 

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Acknowledgements

We acknowledge funding from the Deutsche Forschungsgemeinschaft (grants SCHE 612/6-1, SZ 276/9-2, SZ 276/12-1, BL 574/13-1, SZ 276/20-1 and SZ 276/21-1) and the Alfried Krupp von Bohlen und Halbach Foundation. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 800942. We also thank C. Otto for preparing the high-quality fused-silica samples used in all experiments presented here.

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Author notes

  1. These authors contributed equally: F. Klauck, L. Teuber.

Authors and Affiliations

  1. Institut für Physik, Universität Rostock, Rostock, Germany

    F. Klauck, L. Teuber, M. Heinrich, S. Scheel & A. Szameit

  2. Photonics Laboratory, Physics Unit, Tampere University, Tampere, Finland

    M. Ornigotti

Authors
  1. F. Klauck
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  2. L. Teuber
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  4. M. Heinrich
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  5. S. Scheel
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  6. A. Szameit
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Contributions

F.K. and A.S. developed the idea. L.T. worked out the theory. F.K. designed the samples and performed the experiments. F.K., L.T., M.H., A.S. and S.S. analysed and discussed the results. A.S. and S.S. supervised the project. All authors co-wrote the manuscript.

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Correspondence to A. Szameit.

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Klauck, F., Teuber, L., Ornigotti, M. et al. Observation of PT-symmetric quantum interference. Nat. Photonics 13, 883–887 (2019). https://doi.org/10.1038/s41566-019-0517-0

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