A giant electro-optic effect using polarizable dark states


The electro-optic effect, where the refractive index of a medium is modified by an electric field, is of central importance in nonlinear optics, laser technology, quantum optics and optical communications. In general, electro-optic coefficients are very weak and a medium with a giant electro-optic coefficient could have profound implications for precision electrometry and nonlinear optics at the single-photon level. Here we propose and demonstrate a giant d.c. electro-optic effect on the basis of polarizable (Rydberg) dark states. When a medium is prepared in a dark state consisting of a superposition of ground and Rydberg energy levels, it becomes transparent and acquires a refractive index that is dependent on the energy of the highly polarizable Rydberg state. We demonstrate phase modulation of the light field in the Rydberg-dark-state medium and measure an electro-optic coefficient that is more than six orders of magnitude larger than in usual Kerr media.

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Figure 1: Principle of the giant electro-optic effect using polarizable dark states.
Figure 2: Effect of an external electric field on the transmission through the polarizable dark-state medium.
Figure 3: Measurement of the Kerr constant, B0.
Figure 4: Power spectrum of the signal light transmitted through the dark-state ensemble.


  1. 1

    Kerr, J. A new relation between electricity and light: Dielectric media birefrigent. Phil. Mag. 50, 337–348 (1875).

    Google Scholar 

  2. 2

    Yariv, A. Quantum Electronics 3rd edn, Ch. 14 (Wiley, 1988).

    Google Scholar 

  3. 3

    Boyd, R. W. Non-Linear Optics 2nd edn, Ch. 11 (Academic, 2003).

    Google Scholar 

  4. 4

    Spence, D. E., Kean, P. N. & Sibbett, W. 60-fsec pulse generation from a self-mode-locked Ti:sapphire laser. Opt. Lett. 16, 42–45 (1991).

    Google Scholar 

  5. 5

    Brabec, T. & Krausz, F. Intense few-cycle laser fields: Frontiers of nonlinear optics. Rev. Mod. Phys. 72, 545–591 (2000).

    Google Scholar 

  6. 6

    Boller, K.-J., Imamoğlu, A. & Harris, S. E. Observation of electromagnetically induced transparency. Phys. Rev. Lett. 66, 2593–2596 (1991).

    Google Scholar 

  7. 7

    Kasapi, A., Jain, M., Yin, G. Y. & Harris, S. E. Electromagnetically induced transparency: Propagation dynamics. Phys. Rev. Lett. 74, 2447–2450 (1995).

    Google Scholar 

  8. 8

    Fleischhauer, M., Imamoglu, A. & Marangos, J. P. Electromagnetically induced transparency: Optics in coherent media. Rev. Mod. Phys. 77, 633–673 (2005).

    Google Scholar 

  9. 9

    Harris, S. E., Field, J. E. & Imamoğlu, A. Nonlinear optical processes using electromagnetically induced transparency. Phys. Rev. Lett. 64, 1107–1110 (1990).

    Google Scholar 

  10. 10

    Schmidt, H. & Imamoğlu, A. Giant Kerr nonlinearities obtained by electromagnetically induced transparency. Opt. Lett. 21, 1936–1938 (1996).

    Google Scholar 

  11. 11

    Hau, L. V., Harris, S. E., Dutton, Z. & Behroozi, C. H. Light speed reduction to 17 m per second in an ultracold atomic gas. Nature 397, 594–598 (1999).

    Google Scholar 

  12. 12

    Kang, H. & Zhu, Y. Observation of large Kerr nonlinearity at low light intensities. Phys. Rev. Lett. 91, 093601 (2003).

    Google Scholar 

  13. 13

    Chuang, I. L. & Yamamoto, Y. Simple quantum computer. Phys. Rev. A 52, 3489–3496 (1995).

    Google Scholar 

  14. 14

    Shapiro, J. H. Single-photon Kerr nonlinearities do not help quantum computation. Phys. Rev. A 73, 062305 (2006).

    Google Scholar 

  15. 15

    Friedler, I., Petrosyan, D., Fleischhauer, M. & Kurizki, G. Long range interactions and entanglement of slow single-photon pulses. Phys. Rev. A 72, 043803 (2005).

    Google Scholar 

  16. 16

    Gallagher, T. F. Rydberg Atoms Ch. 2 (Cambridge Univ. Press, 1994).

    Google Scholar 

  17. 17

    Mohapatra, A. K., Jackson, T. R. & Adams, C. S. Coherent optical detection of highly excited Rydberg states using electromagnetically induced transparency. Phys. Rev. Lett. 98, 113003 (2007).

    Google Scholar 

  18. 18

    Mauger, S., Millen, J. & Jones, M. P. A. Spectroscopy of strontium Rydberg states using electromagnetically induced transparency. J. Phys. B 40, F319–F325 (2007).

    Google Scholar 

  19. 19

    Lukin, M. D. et al. Dipole blockade and quantum information processing in mesoscopic atomic ensembles. Phys. Rev. Lett. 87, 037901 (2001).

    Google Scholar 

  20. 20

    Jaksch, D. et al. Fast quantum gates for neutral atoms. Phys. Rev. Lett. 85, 2208–2211 (2000).

    Google Scholar 

  21. 21

    Tong, D. et al. Local blockade of Rydberg excitation in an ultracold gas. Phys. Rev. Lett. 93, 063001 (2004).

    Google Scholar 

  22. 22

    Singer, K., Reetz-Lamour, M., Amthor, T., Marcassa, L. G. & Weidemüller, M. Supression of excitation and spectral broadening induced by interactions in a cold gas of Rydberg atoms. Phys. Rev. Lett. 93, 163001 (2004).

    Google Scholar 

  23. 23

    Cubel Liebisch, T., Reinhard, A., Berman, P. R. & Raithel, G. Atom counting statistics in ensembles of interacting Rydberg atoms. Phys. Rev. Lett. 95, 253002 (2005).

    Google Scholar 

  24. 24

    Vogt, T. et al. Dipole blockade at Förster resonances in high resolution laser excitation of Rydberg states of cesium atoms. Phys. Rev. Lett. 97, 083003 (2006).

    Google Scholar 

  25. 25

    Heidemann, R. et al. Evidence for coherent collective Rydberg excitation in the strong blockade regime. Phys. Rev. Lett. 99, 163601 (2007).

    Google Scholar 

  26. 26

    Weatherill, K. J., Pritchard, J. D., Bason, M. G., Mohapatra, A. K. & Adams, C. S. Electromagnetically induced transparency of an interacting cold Rydberg ensemble. J. Phys. B (in the press); preprint at <http://arxiv.org/abs/0805.4327> (2008).

  27. 27

    Low, R. et al. Apparatus for excitation and detection of Rydberg atoms in quantum gases. Preprint at <http://arxiv.org/abs/0706.2639> (2007).

  28. 28

    Li, W., Mourachko, I., Noel, M. W. & Gallagher, T. F. Millimeter-wave spectroscopy of cold rubidium Rydberg atoms in magneto-optical trap: Quantum defects for the ns, np, and nd series. Phys. Rev. A 67, 052502 (2003).

    Google Scholar 

  29. 29

    Chen, Y.-F., Liu, Y.-C., Tsai, Z.-H., Wang, S.-H. & Yu, I. A. Beat-note interferometer for direct phase measurement of photonic information. Phys. Rev. A 72, 033812 (2005).

    Google Scholar 

  30. 30

    Li, Y. & Xiao, M. Transient properties of an electromagnetically induced transparency in three-level atoms. Opt. Lett. 20, 1489–1491 (1995).

    Google Scholar 

  31. 31

    Chen, H. X., Durrant, A. V., Marangos, J. P. & Vaccaro, J. A. Observation of transient electromagnetically induced transparency in rubidium Λ system. Phys. Rev. A 58, 1545–1548 (1998).

    Google Scholar 

  32. 32

    Shah, V., Knappe, S., Schwindt, P. D. D. & Kitching, J. Subpicotesla atomic magnetometry with a microfabricated vapour cell. Nature Photon. 1, 649–652 (2007).

    Google Scholar 

  33. 33

    Gea-Banacloche, J., Li, Y., Jin, S. & Xiao, M. Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment. Phys. Rev. A 51, 576–584 (1995).

    Google Scholar 

  34. 34

    Pearman, C. P. et al. Polarization spectroscopy of a closed atomic transition: Application to laser frequency locking. J. Phys. B 35, 5141–5151 (2002).

    Google Scholar 

  35. 35

    Inbar, E. & Arie, A. High sensitivity measurements of the Kerr constants in gases using a Fabry-Pèrot-based ellipsometer. Appl. Phys. B 70, 849–852 (2000).

    Google Scholar 

  36. 36

    Webber, M. J. (ed.) Handbook of Optical Materials Ch. 2,5 (CRC Press, 2003).

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We are grateful to E. Riis, T. Pfau, M. P. A. Jones, S. L. Cornish and I. G. Hughes for stimulating discussions, R. P. Abel for technical assistance and S. L. Cornish for loan of equipment. We thank the EPSRC for financial support.

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A.K.M. and C.S.A. contributed to project planning and data analysis, M.G.B., B.B., K.J.W. and A.K.M. contributed to experimental work, M.G.B., A.K.M. and C.S.A. contributed to theoretical modelling and all authors contributed to writing and editing the manuscript.

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Correspondence to Ashok K. Mohapatra or Charles S. Adams.

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Mohapatra, A., Bason, M., Butscher, B. et al. A giant electro-optic effect using polarizable dark states. Nature Phys 4, 890–894 (2008). https://doi.org/10.1038/nphys1091

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