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Dynamically encircling an exceptional point for asymmetric mode switching


Physical systems with loss or gain have resonant modes that decay or grow exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, an ‘exceptional point’ occurs, giving rise to fascinating phenomena that defy our physical intuition1,2,3,4,5,6. Particularly intriguing behaviour is predicted to appear when an exceptional point is encircled sufficiently slowly7,8, such as a state-flip or the accumulation of a geometric phase9,10. The topological structure of exceptional points has been experimentally explored11,12,13, but a full dynamical encircling of such a point and the associated breakdown of adiabaticity14,15,16,17,18,19,20,21 have remained out of reach of measurement. Here we demonstrate that a dynamical encircling of an exceptional point is analogous to the scattering through a two-mode waveguide with suitably designed boundaries and losses. We present experimental results from a corresponding waveguide structure that steers incoming waves around an exceptional point during the transmission process. In this way, mode transitions are induced that transform this device into a robust and asymmetric switch between different waveguide modes. This work will enable the exploration of exceptional point physics in system control and state transfer schemes at the crossroads between fundamental research and practical applications.

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Figure 1: Mode evolution in the vicinity of an exceptional point.
Figure 2: Chiral transport in the presence of bulk absorption.
Figure 3: Microwave measurements.


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J.D., A.G. and S.R. are supported by the Austrian Science Fund (FWF) through project numbers SFB IR-ON F25-14, SFB-NextLite F49-P10 and I 1142- N27 (GePartWave). The computational results presented were achieved in part using the Vienna Scientific Cluster. A.A.M. is supported by the National Council for Scientific and Technological Development (CNPq) grant number 302351/2015-9 and by the FAPERJ grant number E-26/210.874/2014. J.B. and U.K. acknowledge ANR project number I 1142-N27 (GePartWave). F.L. acknowledges support by the FWF through SFB-F41 VI-COM. T.J.M. and P.R. are supported by the FWF through DK CoQuS W 1210, SFB FOQUS F40, START (grant number Y 591-N16), and project OPSOQI (316607) of the WWTF. N.M. acknowledges I-Core (the Israeli Excellence Center ‘Circle of Light’) and the Israel Science Foundation (grant numbers 298/11 and 1530/15) for their financial support.

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J.D., A.A.M., A.G., F.L., T.J.M., P.R., N.M., and S.R. developed the theoretical framework and performed numerical simulations. J.B., J.D. and U.K. designed the experiment. J.B. and U.K. were responsible for the experimental implementation, the data acquisition and its evaluation. All authors contributed to the analysis, interpretation and discussion of the theoretical and experimental findings, as well as to the preparation of the manuscript. The project was jointly supervised by A.A.M. and S.R. (theory) and by U.K. (experiment).

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Correspondence to Alexei A. Mailybaev, Ulrich Kuhl or Stefan Rotter.

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The authors declare no competing financial interests.

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Doppler, J., Mailybaev, A., Böhm, J. et al. Dynamically encircling an exceptional point for asymmetric mode switching. Nature 537, 76–79 (2016).

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