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Cooperative Phenomena

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Cooperative Optical Non-Linearity in a Blockaded Rydberg Ensemble

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Abstract

In the previous chapter the atom-light interaction for a single atom was assumed to describe the behaviour of a macroscopic sample, calculating the susceptibility of a uniform gas with density \(\rho \) using the single atom density matrix. This description is valid providing the atoms are both independent and identical. In some circumstances the atoms behave independently but the overall response of the system depends on the sum over all atoms. This is known as collective behaviour. An example is spin-echo, where each atom dephases at a different rate but reversing the phase leads to a restoration of the initial state, resulting in a collective emission.

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Notes

  1. 1.

    Comparison of \(\fancyscript{H}_{\mathrm{ dd} }\) to \(D_{12}\) in Eq. (9) of [6] yields \(D_{12}\equiv 2\,{\mathrm{ i} }\fancyscript{H}_{\mathrm{ dd} }/\hbar \Gamma \).

  2. 2.

    The Hadamard product defines element-wise multiplication of matrices \(A\) and \(B\) such that \([A\circ B]_{i,j}=[A]_{i,j}\cdot [B]_{i,j}\) (see e.g.[39], p. 205).

References

  1. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (CUP, Cambridge, 2008)

    Google Scholar 

  2. J.D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 1999)

    Google Scholar 

  3. M. Born, E. Wolf, Principles of Optics (CUP, Cambridge, 1999)

    Google Scholar 

  4. R. Loudon, The Quantum Theory of Light, 3rd edn. (OUP, Oxford, 2008)

    Google Scholar 

  5. R.H. Dicke, Coherence in spontaneous radiation processes. Phys. Rev. 93(1), 99 (1954)

    Article  ADS  MATH  Google Scholar 

  6. I.E. Protsenko, Superradiance of trapped atoms. J. Russ. Laser Res. 27(5), 414 (2006)

    Article  Google Scholar 

  7. R.G. DeVoe, R.G. Brewer, Observation of superradiant and subradiant spontaneous emission of two trapped ions. Phys. Rev. Lett. 76(12), 2049 (1996)

    Article  ADS  Google Scholar 

  8. R.H. Lehmberg, Radiation from an \(N\)-atom system. I. General formalism. Phys. Rev. A 2(3), 883 (1970)

    Article  ADS  Google Scholar 

  9. N.E. Rehler, J.H. Eberly, Superradiance. Phys. Rev. A 3(5), 1735 (1971)

    Article  ADS  Google Scholar 

  10. M. Gross, S. Haroche, Superradiance: an essay on the theory of collective spontaneous emission. Phys. Rep. 93(5), 301 (1982)

    Article  ADS  Google Scholar 

  11. J.O. Day, E. Brekke, T.G. Walker, Dynamics of low-density ultracold Rydberg gases. Phys. Rev. A 77(5), 052712 (2008)

    Article  ADS  Google Scholar 

  12. N. Skribanowitz, I.P. Herman, J.C. MacGillivray, M.S. Feld, Observation of Dicke superradiance in optically pumped HF gas. Phys. Rev. Lett. 30(8), 309 (1973)

    Article  ADS  Google Scholar 

  13. M. Gross, C. Fabre, P. Pillet, S. Haroche, Observation of near-infrared Dicke superradiance on cascading transitions in atomic sodium. Phys. Rev. Lett. 36(17), 1035 (1976)

    Article  ADS  Google Scholar 

  14. F. Gounand, M. Hugon, P.R. Fournier, J. Berlande, Superradiant cascading effects in rubidium Rydberg levels. J. Phys. B 12(4), 547 (1979)

    Article  ADS  Google Scholar 

  15. T. Wang, S.F. Yelin, R. Côté, E.E. Eyler, S.M. Farooqi, P.L. Gould, M. Koštrun, D. Tong, D. Vrinceanu, Superradiance in ultracold Rydberg gases. Phys. Rev. A 75(3), 033802 (2007)

    Article  ADS  Google Scholar 

  16. M.D. Lukin, M. Fleischhauer, R. Cote, L.M. Duan, D. Jaksch, J.I. Cirac, P. Zoller, Dipole blockade and quantum information processing in mesoscopic atomic ensembles. Phys. Rev. Lett. 87(3), 037901 (2001)

    Article  ADS  Google Scholar 

  17. D. Jaksch, J.I. Cirac, P. Zoller, Fast quantum gates for neutral atoms. Phys. Rev. Lett. 85(10), 2208 (2000)

    Article  ADS  Google Scholar 

  18. D. Møller, L.B. Madsen, K. Mølmer, Quantum gates and multiparticle entanglement by Rydberg excitation blockade and adiabatic passage. Phys. Rev. Lett. 100(17), 170504 (2008)

    Article  Google Scholar 

  19. M. Müller, I. Lesanovsky, H. Weimer, H.P. Büchler, P. Zoller, Mesoscopic Rydberg gate based on electromagnetically induced transparency. Phys. Rev. Lett. 102(17), 170502 (2009)

    Article  Google Scholar 

  20. I.E. Mazets, G. Kurizki, Multiatom cooperative emission following single-photon absorption: Dicke-state dynamics. J. Phys. B 40(6), F105 (2007)

    Article  ADS  Google Scholar 

  21. L.H. Pedersen, K. Mølmer, Few qubit atom-light interfaces with collective encoding. Phys. Rev. A 79(1), 012320 (2009)

    Article  ADS  Google Scholar 

  22. D. Tong, S.M. Farooqi, J. Stanojevic, S. Krishnan, Y.P. Zhang, R. Côté, E.E. Eyler, P.L. Gould, Local blockade of Rydberg excitation in an ultracold gas. Phys. Rev. Lett. 93(6), 063001 (2004)

    Article  ADS  Google Scholar 

  23. K. Singer, M. Reetz-Lamour, T. Amthor, L.G. Marcassa, M. Weidemüller, Suppression of excitation and spectral broadening induced by interactions in a cold gas of Rydberg atoms. Phys. Rev. Lett. 93(16), 163001 (2004)

    Article  ADS  Google Scholar 

  24. K. Afrousheh, P. Bohlouli-Zanjani, D. Vagale, A. Mugford, M. Fedorov, J.D.D. Martin, Spectroscopic observation of resonant electric dipole–dipole interactions between cold Rydberg atoms. Phys. Rev. Lett. 93(23), 233001 (2004)

    Article  ADS  Google Scholar 

  25. T. Cubel Liebisch, A. Reinhard, P.R. Berman, G. Raithel, Atom counting statistics in ensembles of interacting Rydberg atoms. Phys. Rev. Lett. 95(25), 253002 (2005)

    Article  ADS  Google Scholar 

  26. T. Vogt, M. Viteau, J. Zhao, A. Chotia, D. Comparat, P. Pillet, Dipole blockade at Förster resonances in high resolution laser excitation of Rydberg states of cesium atoms. Phys. Rev. Lett. 97(8), 083003 (2006)

    Article  ADS  Google Scholar 

  27. T. Vogt, M. Viteau, A. Chotia, J. Zhao, D. Comparat, P. Pillet, Electric-field induced dipole blockade with Rydberg atoms. Phys. Rev. Lett. 99(7), 073002 (2007)

    Article  ADS  Google Scholar 

  28. C.S.E. van Ditzhuijzen, A.F. Koenderink, J.V. Hernández, F. Robicheaux, L.D. Noordam, H.B. van Linden van den Heuvell, Spatially resolved observation of dipole–dipole interaction between Rydberg atoms. Phys. Rev. Lett. 100(24), 243201 (2008)

    Google Scholar 

  29. R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Low, T. Pfau, Rydberg excitation of Bose–Einstein condensates. Phys. Rev. Lett. 100(3), 033601 (2008)

    Article  ADS  Google Scholar 

  30. R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Low, L. Santos, T. Pfau, Evidence for coherent collective Rydberg excitation in the strong blockade regime. Phys. Rev. Lett. 99(16), 163601 (2007)

    Article  ADS  Google Scholar 

  31. U. Raitzsch, V. Bendkowsky, R. Heidemann, B. Butscher, R. Low, T. Pfau, Echo experiments in a strongly interacting Rydberg gas. Phys. Rev. Lett. 100(1), 013002 (2008)

    Google Scholar 

  32. M. Reetz-Lamour, T. Amthor, J. Deiglmayr, M. Weidemüller, Rabi oscillations and excitation trapping in the coherent excitation of a mesoscopic frozen Rydberg gas. Phys. Rev. Lett. 100(25), 253001 (2008)

    Article  ADS  Google Scholar 

  33. E. Urban, T.A. Johnson, T. Henage, L. Isenhower, D.D. Yavuz, T.G. Walker, M. Saffman, Observation of Rydberg blockade between two atoms. Nat. Phys. 5, 110 (2009)

    Article  Google Scholar 

  34. A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, P. Grangier, Observation of collective excitation of two individual atoms in the Rydberg blockade regime. Nat. Phys. 5, 115 (2009)

    Article  Google Scholar 

  35. T. Wilk, A. Gaëtan, C. Evellin, J. Wolters, Y. Miroshnychenko, P. Grangier, A. Browaeys, Entanglement of two individual neutral atoms using Rydberg blockade. Phys. Rev. Lett. 104(1), 010502 (2010)

    Article  ADS  Google Scholar 

  36. L. Isenhower, E. Urban, X.L. Zhang, A.T. Gill, T. Henage, T.A. Johnson, T.G. Walker, M. Saffman, Demonstration of a neutral atom controlled-NOT quantum gate. Phys. Rev. Lett. 104(1), 010503 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  38. E. Shahmoon, G. Kurizki, M. Fleischhauer, D. Petrosyan, Strongly interacting photons in hollow-core waveguides. Phys. Rev. A 83, 033806 (2011)

    Article  ADS  Google Scholar 

  39. G.B. Arfken, Mathematical Methods for Physicists, 3rd edn (Academic Press, New York, 1985)

    Google Scholar 

  40. M.P. Hehlen, H.U. Güdel, Q. Shu, J. Rai, S. Rai, S.C. Rand, Cooperative bistability in dense, excited atomic systems. Phys. Rev. Lett. 73(8), 1103 (1994)

    Article  ADS  Google Scholar 

  41. H. Weimer, R. Löw, T. Pfau, H.P. Büchler, Quantum critical behavior in strongly interacting Rydberg gases. Phys. Rev. Lett. 101(25), 250601 (2008)

    Article  ADS  Google Scholar 

  42. A. Chotia, M. Viteau, T. Vogt, D. Comparat, P. Pillet, Kinetic Monte Carlo modelling of dipole blockade in Rydberg excitation experiment. New J. Phys. 10, 045031 (2008)

    Article  ADS  Google Scholar 

  43. H. Schempp, G. Günter, C.S. Hofmann, C. Giese, S.D. Saliba, B.D. DePaola, T. Amthor, M. Weidemüller, S. Sevinçli, T. Pohl, Coherent population trapping with controlled interparticle interactions. Phys. Rev. Lett. 104(17), 173602 (2010)

    Article  ADS  Google Scholar 

  44. C. Ates, S. Sevinçli, T. Pohl, Electromagnetically induced transparency in strongly interacting Rydberg gases. Phys. Rev. A 83(4), 041802 (2011)

    Article  ADS  Google Scholar 

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  1. Durham University, Durham, UK

    Jonathan D. Pritchard

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  1. Jonathan D. Pritchard
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Correspondence to Jonathan D. Pritchard .

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Pritchard, J.D. (2012). Cooperative Phenomena. In: Cooperative Optical Non-Linearity in a Blockaded Rydberg Ensemble. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29712-0_5

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  • DOI: https://doi.org/10.1007/978-3-642-29712-0_5

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