Revealing the missing dimension at an exceptional point


The radiation of electromagnetic and mechanical waves depends not only on the intrinsic properties of the emitter but also on the surrounding environment. This principle has laid the foundation for the development of lasers, quantum optics, sonar, musical instruments and other fields related to wave–matter interaction. In the conventional wisdom, the environment is defined exclusively by its eigenstates, and an emitter radiates into and interacts with these eigenstates. Here we show experimentally that this scenario breaks down at a non-Hermitian degeneracy known as an exceptional point. We find a chirality-reversal phenomenon in a ring cavity where the radiation field reveals the missing dimension of the Hilbert space, known as the Jordan vector. This phenomenon demonstrates that the radiation field of an emitter can become fully decoupled from the eigenstates of its environment. The generality of this striking phenomenon in wave–matter interaction is experimentally confirmed in both electromagnetic and acoustic systems. Our finding transforms the fundamental understanding of light–matter interaction and wave–matter interaction in general, and enriches the intriguing physics of exceptional points.

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Fig. 1: Chirality-reversal radiation at an exceptional point.
Fig. 2: Experimental results of chirality-reversal radiation.
Fig. 3: Chirality-reversal vortex radiation from a single emitter.
Fig. 4: Position- and frequency-dependent chirality of single-emitter radiation inside the exceptional point cavity.
Fig. 5: Experimental demonstrations of the chirality-reversal phenomenon in an acoustic wave system.
Fig. 6: Chirality evolution in the passive acoustic PT-symmetric system.

Data availability

The data represented in Figs. 2–6 are available as Source Data. All other data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.


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This work is supported by NSFC under project Nos. 11774014, 91950115, 11574012 and 61521004, Beijing Natural Science Foundation (Z180011) and the National Key R&D Programme of China (2018YFA0704401). J.Z. is supported by the Early Career Scheme of Hong Kong RGC (grant no. PolyU 252081/15E) and the National Natural Science Foundation of China (grant no. 11774297). L.G. is supported by NSF under grant no. PHY-1847240. L.L. is supported by the National Key R&D Programme of China under grant nos 2017YFA0303800 and 2016YFA0302400 and by NSFC under project no. 11721404. R.-J.L. is supported by NSFC under project no. 11974415. X.-F.Z. acknowledges financial support from the National Natural Science Foundation of China (grant nos 11674119, 11690030 and 11690032) and the Bird Nest Plan of HUST.

Author information




R.-M.M. conceived the concept and supervised the project. H.-Z.C., X.-Y.W. and R.-M.M. performed the coupled-mode equation analysis and conducted the electromagnetic simulation. H.-Y.L., Y.-B.L., R.-J.L., L.L. and R.-M.M. carried out the microwave experiments. H.-Y.L. and R.-M.M. did the data analysis of the microwave experiment. J.Z. and R.-M.M. initiated the acoustic experiment. T.L., H.-Z.C. and X.-F.Z. performed the simulation and designed the acoustic experiment. T.L., Z.-M.G., S.-J.L. and H.G. conducted the acoustic experiments. T.L., X.Z. and R.-M.M. did the data analysis of the acoustic experiment. J.Z. supervised the acoustic experiment. L.G. performed the Green function and Jordan vector analysis. R.-M.M., H.-Z.C., L.G., T.L., J.Z., X.-Y.W. and S.Z. wrote the manuscript.

Corresponding authors

Correspondence to Li Ge or Jie Zhu or Ren-Min Ma.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Andrea Alu, Nicolas Bachelard, Romain Fleury and Stefan Rotter for their contribution to the peer review of this work.

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Supplementary information


The three-dimensional radiation fields of the coalesced eigenstates of a ring cavity operating close to an exceptional point, and a dipole emitter inside a ring cavity operating close to an exceptional point.

Supplementary Information

Supplementary Figs. 1–16 and Sections 1–11.

Supplementary Video

The three-dimensional radiation fields of the coalesced eigenstates of a ring cavity operating close to an exceptional point, and a dipole emitter inside a ring cavity operating close to an exceptional point.

Source data

Source Data Fig. 2

The data corresponding to the graphs in Fig. 2.

Source Data Fig. 3

The data corresponding to the graphs in Fig. 3.

Source Data Fig. 4

The data corresponding to the graphs in Fig. 4.

Source Data Fig. 5

The data corresponding to the graphs in Fig. 5.

Source Data Fig. 6

The data corresponding to the graphs in Fig. 6.

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Chen, H., Liu, T., Luan, H. et al. Revealing the missing dimension at an exceptional point. Nat. Phys. 16, 571–578 (2020).

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