Abstract
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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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.
References
Hartmann, M., Brandao, F. & Plenio, M. Strongly interacting polaritons in coupled arrays of cavities. Nat. Phys. 2, 849–855 (2006).
Greentree, A., Tahan, C., Cole, J. & Hollenberg, L. Quantum phase transitions of light. Nat. Phys. 2, 856–861 (2006).
Ma, R. et al. A dissipatively stabilized Mott insulator of photons. Nature 566, 51–57 (2019).
Clark, L. W. et al. Interacting Floquet polaritons. Nature 571, 532–536 (2010).
Giovannetti, V., Lloyd, S. & Maccone, L. Advances in quantum metrology. Nat. Photon. 5, 222–229 (2011).
Friedler, I., Petrosyan, D., Fleischhauer, M. & Kurizki, G. Long-range interactions and entanglement of slow single-photon pulses. Phys. Rev. A 72, 043803 (2005).
Birnbaum, K. M. et al. Photon blockade in an optical cavity with one trapped atom. Nature 436, 87–90 (2005).
Dudin, Y. O. & Kuzmich, A. Strongly interacting Rydberg excitations of a cold atomic gas. Science 336, 887–889 (2012).
Hacker, B., Welte, S., Rempe, G. & Ritter, S. A photon–photon quantum gate based on a single atom in an optical resonator. Nature 536, 193–196 (2016).
Busche, H. et al. Contactless nonlinear optics mediated by long-range Rydberg interactions. Nat. Phys. 13, 655–658 (2017).
Chang, D. et al. Crystallization of strongly interacting photons in a nonlinear optical fibre. Nat. Phys. 4, 884–889 (2008).
Otterbach, J., Moos, M., Muth, D. & Fleischhauer, M. Wigner crystallization of single photons in cold Rydberg ensembles. Phys. Rev. Lett. 111, 113001 (2013).
Liang, Q. Y. et al. Observation of three-photon bound states in a quantum nonlinear medium. Science 359, 783–786 (2018).
Firstenberg, O. et al. Attractive photons in a quantum nonlinear medium. Nature 502, 71–75 (2013).
Chang, D., Vuletic, V. & Lukin, M. Quantum nonlinear optics - photon by photon. Nat. Photon. 8, 685–694 (2014).
Lukin, M. D. et al. Dipole blockade and quantum information processing in mesoscopic atomic ensembles. Phys. Rev. Lett. 87, 037901 (2001).
Gorshkov, A. V., Otterbach, J., Fleischhauer, M., Pohl, T. & Lukin, M. D. Photon–photon interactions via Rydberg blockade. Phys. Rev. Lett. 107, 133602 (2011).
Peyronel, T. et al. Quantum nonlinear optics with single photons enabled by strongly interacting atoms. Nature 488, 57–60 (2012).
Stiesdal, N. et al. Observation of three-body correlations for photons coupled to a Rydberg superatom. Phys. Rev. Lett. 121, 103601 (2018).
Tiarks, D., Baur, S., Schneider, K., Dürr, S. & Rempe, G. Single-photon transistor using a Förster resonance. Phys. Rev. Lett. 113, 053602 (2014).
Gorniaczyk, H., Tresp, C., Schmidt, J., Fedder, H. & Hofferberth, S. Single-photon transistor mediated by interstate Rydberg interactions. Phys. Rev. Lett. 113, 053601 (2014).
Sommer, A., Büchler, H. P. & Simon, J. Quantum crystals and Laughlin droplets of cavity Rydberg polaritons. Preprint at https://arxiv.org/abs/1506.00341 (2015).
Bienias, P. et al. Scattering resonances and bound states for strongly interacting Rydberg polaritons. Phys. Rev. A 90, 053804 (2014).
Lukin, M. D., Yelin, S. F., Fleischhauer, M. & Scully, M. O. Quantum interference effects induced by interacting dark resonances. Phys. Rev. A 60, 3225–3228 (1999).
Mahmoudi, M., Fleischhaker, R., Sahrai, M. & Evers, J. Group velocity control in the ultraviolet domain via interacting dark-state resonances. J. Phys. B 41, 025504 (2008).
Duan, L. M., Cirac, I. & Zoller, P. Geometric manipulation of trapped ions for quantum computation. Science 292, 1695–1697 (2001).
Schauß, P. et al. Observation of spatially ordered structures in a two-dimensional Rydberg gas. Nature 491, 87–91 (2012).
Schauß, P. et al. Crystallization in Ising quantum magnets. Science 347, 1455–1458 (2015).
Nogrette, F. et al. Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries. Phys. Rev. X 4, 021034 (2014).
Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).
Acknowledgements
We acknowledge helpful conversations with T. Pohl and C. Murray. We also acknowledge help with control electronics from Z. Zhang.
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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.
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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). https://doi.org/10.1038/s41567-020-0917-6
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DOI: https://doi.org/10.1038/s41567-020-0917-6
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