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Repulsive photons in a quantum nonlinear medium


The ability to control strongly interacting light quanta (photons) is of central importance in quantum science and engineering1,2,3,4,5. Recently it was shown that such strong interactions can be engineered in specially prepared quantum optical systems6,7,8,9,10. Here, we demonstrate a method for coherent control of strongly interacting photons, extending quantum nonlinear optics into the domain of repulsive photons. This is achieved by coherently coupling photons to several atomic states, including strongly interacting Rydberg levels in a cold Rubidium gas. Using this approach we demonstrate both repulsive and attractive interactions between individual photons and characterize them by the measured two- and three-photon correlation functions. For the repulsive case, we demonstrate signatures of interference and self ordering from three-photon measurements. These observations open a route to study strongly interacting dissipative systems and quantum matter composed of light such as a crystal of individual photons11,12.

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Fig. 1: Photon interaction engineering.
Fig. 2: Correlation functions showing repulsion and attraction.
Fig. 3: Repulsive interactions and phase.
Fig. 4: Three-photon correlations and onset of crystal-like behaviour.

Data availability

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


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We acknowledge helpful conversations with T. Pohl and C. Murray. We also acknowledge help with control electronics from Z. Zhang.

Author information

Authors and Affiliations



The experiment and analysis were carried out by S.H.C., A.V.V., W.X. and B.J. Theoretical modelling was performed by L.Z. and A.V.V. All work was supervised by M.D.L. and V.V. All authors discussed the results and contributed to the manuscript.

Corresponding authors

Correspondence to Mikhail D. Lukin or Vladan Vuletić.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

Supplementary Fig. 1 and discussion.

Source data

Source Data Fig. 2

Two-photon correlation measurements (amplitude and phase).

Source Data Fig. 3

Correlation and phase dependence over the two-photon detuning for repulsive interactions.

Source Data Fig. 4

Three-photon correlations and emergent phenomena.

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Cantu, S.H., Venkatramani, A.V., Xu, W. et al. Repulsive photons in a quantum nonlinear medium. Nat. Phys. 16, 921–925 (2020).

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