The fundamental properties of light derive from its constituent particles—massless quanta (photons) that do not interact with one another1. However, it has long been known that the realization of coherent interactions between individual photons, akin to those associated with conventional massive particles, could enable a wide variety of novel scientific and engineering applications2,3. Here we demonstrate a quantum nonlinear medium inside which individual photons travel as massive particles with strong mutual attraction, such that the propagation of photon pairs is dominated by a two-photon bound state4,5,6,7. We achieve this through dispersive coupling of light to strongly interacting atoms in highly excited Rydberg states. We measure the dynamical evolution of the two-photon wavefunction using time-resolved quantum state tomography, and demonstrate a conditional phase shift8 exceeding one radian, resulting in polarization-entangled photon pairs. Particular applications of this technique include all-optical switching, deterministic photonic quantum logic and the generation of strongly correlated states of light9.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Scully, M. O. & Zubairy, M. S. Quantum Optics (Cambridge Univ. Press, 1997)
Milburn, G. J. Quantum optical Fredkin gate. Phys. Rev. Lett. 62, 2124–2127 (1989)
Imamoğlu, A. Schmidt, H. Woods, G. & Deutsch, M. Strongly interacting photons in a nonlinear cavity. Phys. Rev. Lett. 79, 1467–1470 (1997)
Deutsch, I. H., Chiao, R. Y. & Garrison, J. C. Diphotons in a nonlinear Fabry-Pérot resonator: bound states of interacting photons in an optical “quantum wire”. Phys. Rev. Lett. 69, 3627–3630 (1992)
Shen, J.-T. & Fan, S. Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system. Phys. Rev. Lett. 98, 153003 (2007)
Chang, D. E., Srensen, A. S., Demler, E. A. & Lukin, M. D. A single-photon transistor using nanoscale surface plasmons. Nature Phys. 3, 807–812 (2007)
Cheng, Z. & Kurizki, G. Optical “multiexcitons”: quantum gap solitons in nonlinear Bragg reflectors. Phys. Rev. Lett. 75, 3430–3433 (1995)
Turchette, Q. A., Hood, C., Lange, W., Mabuchi, H. & Kimble, H. Measurement of conditional phase shifts for quantum logic. Phys. Rev. Lett. 75, 4710–4713 (1995)
Chang, D. E. et al. Crystallization of strongly interacting photons in a nonlinear optical fibre. Nature Phys. 4, 884–889 (2008)
Fushman, I. et al. Controlled phase shifts with a single quantum dot. Science 320, 769–772 (2008)
Rauschenbeutel, A. et al. Coherent operation of a tunable quantum phase gate in cavity QED. Phys. Rev. Lett. 83, 5166–5169 (1999)
Kirchmair, G. et al. Observation of quantum state collapse and revival due to the single-photon Kerr effect. Nature 495, 205–209 (2013)
Saffman, M., Walker, T. G. & Mølmer, K. Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313–2363 (2010)
Gorshkov, A. V., Otterbach, J., Fleischhauer, M., Pohl, T. & Lukin, M. D. Photon-photon interactions via Rydberg blockade. Phys. Rev. Lett. 107, 133602 (2011)
Pritchard, J. D. et al. Cooperative atom-light interaction in a blockaded Rydberg ensemble. Phys. Rev. Lett. 105, 193603 (2010)
Maxwell, D. et al. Storage and control of optical photons using Rydberg polaritons. Phys. Rev. Lett. 110, 103001 (2013)
Dudin, Y. O. & Kuzmich, A. Strongly interacting Rydberg excitations of a cold atomic gas. Science 336, 887–889 (2012)
Petrosyan, D., Otterbach, J. & Fleischhauer, M. Electromagnetically induced transparency with Rydberg atoms. Phys. Rev. Lett. 107, 213601 (2011)
Peyronel, T. et al. Quantum nonlinear optics with single photons enabled by strongly interacting atoms. Nature 488, 57–60 (2012)
Parigi, V. et al. Observation and measurement of interaction-induced dispersive optical nonlinearities in an ensemble of cold Rydberg atoms. Phys. Rev. Lett. 109, 233602 (2012)
Kasapi, A., Jain, M., Yin, G. Y. & Harris, S. E. Electromagnetically induced transparency: propagation dynamics. Phys. Rev. Lett. 74, 2447–2450 (1995)
Venkataraman, V., Saha, K. & Gaeta, A. L. Phase modulation at the few-photon level for weak-nonlinearity-based quantum computing. Nature Photon. 7, 138–141 (2012)
Rajapakse, R. M., Bragdon, T., Rey, A. M., Calarco, T. & Yelin, S. F. Single-photon nonlinearities using arrays of cold polar molecules. Phys. Rev. A 80, 013810 (2009)
Drummond, P. D. & He, H. Optical mesons. Phys. Rev. A 56, R1107–R1109 (1997)
Lukin, M. D. et al. Dipole blockade and quantum information processing in mesoscopic atomic ensembles. Phys. Rev. Lett. 87, 037901 (2001)
Fleischhauer, M., Imamoglu, A. & Marangos, J. P. Electromagnetically induced transparency: optics in coherent media. Rev. Mod. Phys. 77, 633–673 (2005)
James, D. F. V., Kwiat, P. G., Munro, W. J. & White, A. G. Measurement of qubits. Phys. Rev. A 64, 052312 (2001)
Adamson, R. B. A., Shalm, L. K., Mitchell, M. W. & Steinberg, A. M. Multiparticle state tomography: hidden differences. Phys. Rev. Lett. 98, 043601 (2007)
Sevinçli, S., Henkel, N., Ates, C. & Pohl, T. Nonlocal nonlinear optics in cold Rydberg gases. Phys. Rev. Lett. 107, 153001 (2011)
Heidemann, R. et al. Evidence for coherent collective Rydberg excitation in the strong blockade regime. Phys. Rev. Lett. 99, 163601 (2007)
Chen, W. et al. All-optical switch and transistor gated by one stored photon. Science 341, 768–770 (2013)
We thank H. P. Büchler, T. Pohl, J. Otterbach, P. Strack, M. Gullans and S. Choi for discussions. This work was supported by the NSF, the CUA, DARPA and the AFOSR Quantum Memories MURI and the Packard Foundations. O.F. acknowledges support from the HQOC. A.V.G. and M.D.L. thank KITP for hospitality. A.V.G. acknowledges funding from the Lee A. DuBridge Foundation and the IQIM, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation.
The authors declare no competing financial interests.
About this article
Cite this article
Firstenberg, O., Peyronel, T., Liang, QY. et al. Attractive photons in a quantum nonlinear medium. Nature 502, 71–75 (2013). https://doi.org/10.1038/nature12512
Frontiers of Physics (2022)
Scientific Reports (2021)
A weakly-interacting many-body system of Rydberg polaritons based on electromagnetically induced transparency
Communications Physics (2021)
Correlating photons using the collective nonlinear response of atoms weakly coupled to an optical mode
Nature Photonics (2020)
Nature Physics (2020)