Advertisement

van der Waals interaction of atoms in circular Rydberg states

  • Aleksandr A. Kamenski
  • Nikolay L. Manakov
  • Sergey N. Mokhnenko
  • Vitaly D. Ovsiannikov
  • Alisa A. Zenischeva
Regular Article

Abstract

Analytical expressions for the constants of resolution in powers of inverse interatomic distance 1∕R are determined for the energy of the long-range interaction between two atoms A and B in their circular Rydberg states of equal principal quantum numbers nA = nBn ≫ 1, maximal angular momenta and magnetic quantum numbers lA = lB = |mA| = |mB| = n − 1 in the case of arbitrary orientation of the interatomic axis relative the axis of the m-quantization. Coefficients of the odd-power terms CkRk are derived for k = 5, 7, 9 from the first-order perturbation theory (PT) for the interaction Hamiltonian. The constant C6 of the van der Waals interaction ΔEvdW = −C6R6, determined from the second-order PT, is resolved into irreducible components. The combinations of irreducible components determine coefficients at Legendre polynomials and/or cosine functions describing the dependence of C6 on the angle between the interatomic and quantization axes. The asymptotic dependence on the principal quantum number C6n12 is demonstrated analytically. Polynomials in powers of n are derived for extrapolation of calculated data to the case of arbitrary n. The transformation of attractive van der Waals force (C6 > 0) for low-energy states n < 6 into repulsive force (C6 < 0) for all higher-energy states of n ≥ 8 is demonstrated in numerical calculations.

Graphical abstract

Keywords

Quantum Optics 

References

  1. 1.
    K. Singer, M. Reetz-Lamour, T. Amthor, L.G. Marcassa, M. Weidemüeller, Phys. Rev. Lett. 93, 163001 (2004) ADSCrossRefGoogle Scholar
  2. 2.
    M. Saffman, T.G. Walker, K. Mölmer, Rev. Mol. Phys. 82, 2313 (2010) ADSCrossRefGoogle Scholar
  3. 3.
    P.A. Braun, V.N. Ostrovsky, N.V. Prudov, Phys. Rev. A 48, 941 (1993) ADSCrossRefGoogle Scholar
  4. 4.
    M.R. Flannery, D. Vrinceanu, V.N. Ostrovsky, J. Phys. B: At. Mol. Opt. Phys. 38, S279 (2005) ADSCrossRefGoogle Scholar
  5. 5.
    A.A. Kamenski, N.L. Manakov, S.N. Mokhnenko, V.D. Ovsiannikov, Phys. Rev. A 96, 032716 (2017) ADSCrossRefGoogle Scholar
  6. 6.
    A.A. Kamenski, S.N. Mokhnenko, V.D. Ovsiannikov, Eur. Phys. J. D 72, 28 (2018) ADSCrossRefGoogle Scholar
  7. 7.
    R.J. Le Roy, Can. J. Phys. 52, 246 (1974) ADSCrossRefGoogle Scholar
  8. 8.
    H.B.G. Casimir, D. Polder, Phys. Rev. 73, 360 (1948) ADSCrossRefGoogle Scholar
  9. 9.
    D.B. Tretyakov, V.M. Entin, E.A. Yakshina, I.I. Beterov, C. Andreeva, I.I. Ryabtsev, Phys. Rev. A 90, 041403(R) (2014) ADSCrossRefGoogle Scholar
  10. 10.
    D.A. Varshalovich, A.N. Moskalev, V.K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific Publishing, Singapore, 1988) Google Scholar
  11. 11.
    N.L. Manakov, V.D. Ovsiannikov, L.P. Rapoport, Phys. Rep. 141, 319 (1986) ADSCrossRefGoogle Scholar
  12. 12.
    N.L. Manakov, V.D. Ovsiannikov, V.N. Ostrovskiy, V.N. Yastrebkov, Opt. Spektr. 56, 222 (1984) Google Scholar
  13. 13.
    V.D. Ovsiannikov, A.A. Tarusin, A.A. Kamenski, Opt. Spectrosc. (Sov. Phys. Opt. Spektr.) 104, 181 (2008) Google Scholar
  14. 14.
    H. Bateman, A. Erdelyi, in Higher Transcendental Functions (McGraw-Hill Book Company, New York, 1953), Vol. 1 Google Scholar
  15. 15.
    I.L. Glukhov, S.N. Mokhnenko, E.A. Nikitina, V.D. Ovsiannikov, Eur. Phys. J. D 69, 1 (2015) ADSCrossRefGoogle Scholar
  16. 16.
    H.S. Bethe, E.E Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Springer, New-York, 1957) Google Scholar
  17. 17.
    D.P. Dewangan, Phys. Rep. 511, 1 (2012) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Aleksandr A. Kamenski
    • 1
  • Nikolay L. Manakov
    • 1
  • Sergey N. Mokhnenko
    • 1
  • Vitaly D. Ovsiannikov
    • 1
  • Alisa A. Zenischeva
    • 1
  1. 1.Department of PhysicsVoronezh State UniversityVoronezhRussia

Personalised recommendations