Cooperative Phenomena

Chapter
Part of the Springer Theses book series (Springer Theses)

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.

Keywords

Entangle State Single Atom Rydberg State Rydberg Atom Spontaneous Decay Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (CUP, Cambridge, 2008)Google Scholar
  2. 2.
    J.D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 1999)Google Scholar
  3. 3.
    M. Born, E. Wolf, Principles of Optics (CUP, Cambridge, 1999)Google Scholar
  4. 4.
    R. Loudon, The Quantum Theory of Light, 3rd edn. (OUP, Oxford, 2008)Google Scholar
  5. 5.
    R.H. Dicke, Coherence in spontaneous radiation processes. Phys. Rev. 93(1), 99 (1954)ADSMATHCrossRefGoogle Scholar
  6. 6.
    I.E. Protsenko, Superradiance of trapped atoms. J. Russ. Laser Res. 27(5), 414 (2006)CrossRefGoogle Scholar
  7. 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)ADSCrossRefGoogle Scholar
  8. 8.
    R.H. Lehmberg, Radiation from an \(N\)-atom system. I. General formalism. Phys. Rev. A 2(3), 883 (1970)ADSCrossRefGoogle Scholar
  9. 9.
    N.E. Rehler, J.H. Eberly, Superradiance. Phys. Rev. A 3(5), 1735 (1971)ADSCrossRefGoogle Scholar
  10. 10.
    M. Gross, S. Haroche, Superradiance: an essay on the theory of collective spontaneous emission. Phys. Rep. 93(5), 301 (1982)ADSCrossRefGoogle Scholar
  11. 11.
    J.O. Day, E. Brekke, T.G. Walker, Dynamics of low-density ultracold Rydberg gases. Phys. Rev. A 77(5), 052712 (2008)ADSCrossRefGoogle Scholar
  12. 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)ADSCrossRefGoogle Scholar
  13. 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)ADSCrossRefGoogle Scholar
  14. 14.
    F. Gounand, M. Hugon, P.R. Fournier, J. Berlande, Superradiant cascading effects in rubidium Rydberg levels. J. Phys. B 12(4), 547 (1979)ADSCrossRefGoogle Scholar
  15. 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)ADSCrossRefGoogle Scholar
  16. 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)ADSCrossRefGoogle Scholar
  17. 17.
    D. Jaksch, J.I. Cirac, P. Zoller, Fast quantum gates for neutral atoms. Phys. Rev. Lett. 85(10), 2208 (2000)ADSCrossRefGoogle Scholar
  18. 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)CrossRefGoogle Scholar
  19. 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)CrossRefGoogle Scholar
  20. 20.
    I.E. Mazets, G. Kurizki, Multiatom cooperative emission following single-photon absorption: Dicke-state dynamics. J. Phys. B 40(6), F105 (2007)ADSCrossRefGoogle Scholar
  21. 21.
    L.H. Pedersen, K. Mølmer, Few qubit atom-light interfaces with collective encoding. Phys. Rev. A 79(1), 012320 (2009)ADSCrossRefGoogle Scholar
  22. 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)ADSCrossRefGoogle Scholar
  23. 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)ADSCrossRefGoogle Scholar
  24. 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)ADSCrossRefGoogle Scholar
  25. 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)ADSCrossRefGoogle Scholar
  26. 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)ADSCrossRefGoogle Scholar
  27. 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)ADSCrossRefGoogle Scholar
  28. 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. 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)ADSCrossRefGoogle Scholar
  30. 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)ADSCrossRefGoogle Scholar
  31. 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. 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)ADSCrossRefGoogle Scholar
  33. 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)CrossRefGoogle Scholar
  34. 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)CrossRefGoogle Scholar
  35. 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)ADSCrossRefGoogle Scholar
  36. 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)ADSCrossRefGoogle Scholar
  37. 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)ADSCrossRefGoogle Scholar
  38. 38.
    E. Shahmoon, G. Kurizki, M. Fleischhauer, D. Petrosyan, Strongly interacting photons in hollow-core waveguides. Phys. Rev. A 83, 033806 (2011)ADSCrossRefGoogle Scholar
  39. 39.
    G.B. Arfken, Mathematical Methods for Physicists, 3rd edn (Academic Press, New York, 1985)Google Scholar
  40. 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)ADSCrossRefGoogle Scholar
  41. 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)ADSCrossRefGoogle Scholar
  42. 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)ADSCrossRefGoogle Scholar
  43. 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)ADSCrossRefGoogle Scholar
  44. 44.
    C. Ates, S. Sevinçli, T. Pohl, Electromagnetically induced transparency in strongly interacting Rydberg gases. Phys. Rev. A 83(4), 041802 (2011)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Durham UniversityDurhamUK

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