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

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Abstract

Up to this point, we have only alluded to the effect that the interactions between identical atoms have on the spectral properties. In many cases, these inter-particle interactions are negligible. However, if the atoms are separated by less than the transition wavelength \(\lambda \), resonant dipole-dipole interactions become important. In this chapter we explore the consequences of such interactions.

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Notes

  1. 1.

    The excited state linewidth for Rydberg atoms is very much narrower than for low lying excited states so that it is usually only the laser linewidth that is the limiting factor in the blockade mechanism.

References

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

    Article  ADS  Google Scholar 

  2. C. Hettich et al., Nanometer resolution and coherent optical dipole coupling of two individual molecules. Science 298, 385 (2002)

    Article  Google Scholar 

  3. J. Javanainen, J. Ruostekoski, Y. Li, S.-M. Yoo, Shifts of a resonance line in a dense atomic sample. Phys. Rev. Lett. 112, 113603 (2014)

    Article  ADS  Google Scholar 

  4. M. Fleischhauer, S. Yelin, Radiative atom–atom interactions in optically dense media: quantum corrections to the Lorentz–Lorenz formula. Phys. Rev. A 59, 2427 (1999)

    Article  ADS  Google Scholar 

  5. A.P. Thorne, Spectrophysics, 2nd edn. (Chapman and Hall, London, 1988)

    Book  Google Scholar 

  6. E. Lewis, Collisional relaxation of atomic excited states, line broadening and interatomic interactions. Phys. Rep. 58, 1 (1980)

    Article  ADS  Google Scholar 

  7. C.A. Brau, Modern Problems in Classical Electrodynamics (OUP, Oxford, 2004)

    Google Scholar 

  8. P. Siddons, C.S. Adams, C. Ge, I.G. Hughes, Absolute absorption on rubidium D lines: comparison between theory and experiment. J. Phys. B 41, 155004 (2008)

    Article  ADS  Google Scholar 

  9. M.J. Stephen, First-order dispersion forces. J. Chem. Phys. 40, 669 (1964)

    Article  ADS  Google Scholar 

  10. J.D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, Hoboken, 1999)

    MATH  Google Scholar 

  11. D.-W. Wang, Z.-H. Li, H. Zheng, S.-Y. Zhu, Time evolution, Lamb shift, and emission spectra of spontaneous emission of two identical atoms. Phys. Rev. A 81, 043819 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  13. B.H. Bransden, C.J. Joachain, Physics of atoms and molecules, 2nd edn. (Pearson Education, Harlow, 2003)

    Google Scholar 

  14. L. Weller, R.J. Bettles, P. Siddons, C.S. Adams, I.G. Hughes, Absolute absorption on the rubidium D1 line including resonant dipoledipole interactions. J. Phys. B 44, 195006 (2011)

    Article  ADS  Google Scholar 

  15. S.L. Kemp, I.G. Hughes, S.L. Cornish, An analytical model of off-resonant Faraday rotation in hot alkali metal vapours. J. Phys. B 44, 235004 (2011)

    Article  ADS  Google Scholar 

  16. L. Weller, T. Dalton, P. Siddons, C.S. Adams, I.G. Hughes, Measuring the Stokes parameters for light transmitted by a high-density rubidium vapour in large magnetic fields. J. Phys. B 45, 055001 (2012)

    Article  ADS  Google Scholar 

  17. L. Weller et al., Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen–Back regime. J. Phys. B 45, 215005 (2012)

    Article  ADS  Google Scholar 

  18. L. Weller et al., Optical isolator using an atomic vapor in the hyperfine Paschen–Back regime. Opt. Lett. 37, 3405 (2012)

    Article  ADS  Google Scholar 

  19. A. Reinhard, T. Liebisch, B. Knuffman, G. Raithel, Level shifts of rubidium Rydberg states due to binary interactions. Phys. Rev. A 75, 032712 (2007)

    Article  ADS  Google Scholar 

  20. R.W. Boyd, Nonlinear Optics, 3rd edn. (Academic Press, USA, 2008)

    Google Scholar 

  21. R. Friedberg, S.R. Hartmann, J.T. Manassah, Frequency shifts in emission and absorption by resonant systems ot two-level atoms. Phys. Rep. 7, 101 (1973)

    Article  ADS  Google Scholar 

  22. H.A. Lorentz, The Theory of Electrons (BG Teubner, Leipzig, 1909)

    Google Scholar 

  23. M. Born, E. Wolf, Principles of Optics, 7th edn. (CUP, Cambridge, 1999)

    Book  Google Scholar 

  24. S. Chandrasekhar, Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15, 1 (1943)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  25. H. Foley, The pressure broadening of spectral lines. Phys. Rev. 69, 616 (1946)

    Article  ADS  Google Scholar 

  26. A. Corney, Atomic and Laser Spectroscopy (OUP, Oxford, 1989)

    Google Scholar 

  27. J. Woerdman, F. Blok, M. Kristensen, C. Schrama, Multiperturber effects in the Faraday spectrum of Rb atoms immersed in a high-density Xe gas. Phys. Rev. A 53, 1183 (1996)

    Article  ADS  Google Scholar 

  28. V.A. Sautenkov, H. van Kampen, E. Eliel, J. Woerdman, Dipole–dipole broadened line shape in a partially excited dense atomic gas. Phys. Rev. Lett. 77, 3327 (1996)

    Article  ADS  Google Scholar 

  29. H. van Kampen et al., Observation of collisional modification of the Zeeman effect in a high-density atomic vapor. Phys. Rev. A 56, 310 (1997)

    Article  ADS  Google Scholar 

  30. J.J. Maki, M.S. Malcuit, J.E. Sipe, R.W. Boyd, Linear and nonlinear optical measurements of the Lorentz local field. Phys. Rev. Lett. 67, 972 (1991)

    Article  ADS  Google Scholar 

  31. M.O. Scully, A.A. Svidzinsky, The effects of the N atom collective Lamb shift on single photon superradiance. Phys. Lett. A 373, 1283 (2009)

    Article  ADS  MATH  Google Scholar 

  32. R. Röhlsberger, K. Schlage, B. Sahoo, S. Couet, R. Rüffer, Collective Lamb shift in single-photon superradiance. Science 328, 1248 (2010)

    Article  ADS  Google Scholar 

  33. W. Lamb, R. Retherford, Fine structure of the hydrogen atom by a microwave method. Phys. Rev. 72, 241 (1947)

    Article  ADS  Google Scholar 

  34. R. Friedberg, J.T. Manassah, Analytic expressions for the initial cooperative decay rate and cooperative Lamb shift for a spherical sample of two-level atoms. Phys. Lett. A 374, 1648 (2010)

    Article  ADS  MATH  Google Scholar 

  35. R. Friedberg, J.T. Manassah, Initial cooperative decay rate and cooperative Lamb shift of resonant atoms in an infinite cylindrical geometry. Phys. Rev. A 84, 023839 (2011)

    Article  ADS  Google Scholar 

  36. M.O. Scully, Collective Lamb shift in single photon dicke superradiance. Phys. Rev. Lett. 102, 143601 (2009)

    Article  ADS  Google Scholar 

  37. T. Bienaimé, M. Petruzzo, D. Bigerni, N. Piovella, R. Kaiser, Atom and photon measurement in cooperative scattering by cold atoms. J. Mod. Opt. 58, 1942 (2011)

    Article  ADS  Google Scholar 

  38. T. Bienaimé, R. Bachelard, N. Piovella, R. Kaiser, Cooperativity in light scattering by cold atoms. Fortschr. Phys. 61, 377 (2013)

    Article  MathSciNet  Google Scholar 

  39. W.R. Garrett, R.C. Hart, J.E. Wray, I. Datskou, M.G. Payne, Large multiple collective line shifts observed in three-photon excitations of Xe. Phys. Rev. Lett. 64, 1717 (1990)

    Article  ADS  Google Scholar 

  40. R. Röhlsberger, The collective Lamb shift in nuclear \(\gamma \)-ray superradiance. J. Mod. Opt. 57, 1979 (2010)

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  44. S. Inouye, Superradiant rayleigh scattering from a Bose–Einstein condensate. Science 285, 571 (1999)

    Article  Google Scholar 

  45. T. Bienaimé, N. Piovella, R. Kaiser, Controlled Dicke subradiance from a large cloud of two-level systems. Phys. Rev. Lett. 108, 123602 (2012)

    Article  ADS  Google Scholar 

  46. M.O. Scully, E.S. Fry, C.H.R. Ooi, K. Wódkiewicz, Directed spontaneous emission from an extended ensemble of N atoms: timing is everything. Phys. Rev. Lett. 96, 010501 (2006)

    Article  ADS  Google Scholar 

  47. J.T. Manassah, Giant cooperative Lamb shift in a density-modulated slab of two-level atoms. Phys. Rev. A 374, 1985 (2010)

    MATH  Google Scholar 

  48. H. Li, V.A. Sautenkov, Y.V. Rostovtsev, M.O. Scully, Excitation dependence of resonance line self-broadening at different atomic densities. J. Phys. B 42, 065203 (2009)

    Article  ADS  Google Scholar 

  49. V.A. Sautenkov, Line shapes of atomic transitions in excited dense gas. Laser Phys. Lett. 8, 771 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  51. M. Saffman, T. Walker, K. Mølmer, Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313 (2010)

    Article  ADS  Google Scholar 

  52. R. Friedberg, S. Hartmann, J. Manassah, Mirrorless optical bistability condition. Phys. Rev. A 39, 3444 (1989)

    Article  ADS  Google Scholar 

  53. I.G. Hughes, T.P.A. Hase, Measurements and their Uncertainties: A Practical Guide to Modern Error Analysis (OUP, Oxford, 2010)

    Google Scholar 

  54. L. Barbier, M. Cheret, Energy pooling process in rubidium vapour. J. Phys. B 16, 3213 (1983)

    Article  ADS  Google Scholar 

  55. I. Hamdi et al., Laser spectroscopy with nanometric gas cells: distance dependence of atom surface interaction and collisions under confinement. Laser Phys. 15, 987 (2005)

    Google Scholar 

  56. C.M. Bowden, C.C. Sung, First- and second-order phase transitions in the Dicke model: relation to optical bistability. Phys. Rev. A 19, 2392 (1979)

    Article  ADS  Google Scholar 

  57. C. Carr, R. Ritter, K.J. Weatherill, C.S. Adams, Cooperative non-equilibrium phase transition in a dilute thermal atomic gas (2013), arxiv.org, 1302.6621, arXiv:1302.6621v1

  58. P. Ballin, E. Moufarej, I. Maurin, A. Laliotis, D. Bloch, Three-dimensional confinement of vapor in nanostructures for sub-Doppler optical resolution. Appl. Phys. Lett. 102, 231115 (2013)

    Article  ADS  Google Scholar 

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Correspondence to James Keaveney .

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Keaveney, J. (2014). Atom–Atom Interactions. In: Collective Atom–Light Interactions in Dense Atomic Vapours. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-07100-8_5

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