The European Physical Journal D

, Volume 65, Issue 1–2, pp 177–187 | Cite as

On the role of the magnetic dipolar interaction in cold and ultracold collisions: numerical and analytical results for NH(3Σ) + NH(3Σ)

Regular Article Cold and ultracold molecules

Abstract

We present a detailed analysis of the role of the magnetic dipole-dipole interaction in cold and ultracold collisions. We focus on collisions between magnetically trapped NH molecules, but the theory is general for any two paramagnetic species for which the electronic spin and its space-fixed projection are (approximately) good quantum numbers. It is shown that dipolar spin relaxation is directly associated with magnetic-dipole induced avoided crossings that occur between different adiabatic potential curves. For a given collision energy and magnetic field strength, the cross-section contributions from different scattering channels depend strongly on whether or not the corresponding avoided crossings are energetically accessible. We find that the crossings become lower in energy as the magnetic field decreases, so that higher partial-wave scattering becomes increasingly important below a certain magnetic field strength. In addition, we derive analytical cross-section expressions for dipolar spin relaxation based on the Born approximation and distorted-wave Born approximation. The validity regions of these analytical expressions are determined by comparison with the NH + NH cross sections obtained from full coupled-channel calculations. We find that the Born approximation is accurate over a wide range of energies and field strengths, but breaks down at high energies and high magnetic fields. The analytical distorted-wave Born approximation gives more accurate results in the case of s-wave scattering, but shows some significant discrepancies for the higher partial-wave channels. We thus conclude that the Born approximation gives generally more meaningful results than the distorted-wave Born approximation at the collision energies and fields considered in this work.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002)ADSCrossRefGoogle Scholar
  2. 2.
    D. Jaksch, P. Zoller, Ann. Phys. 315, 52 (2005)ADSMATHCrossRefGoogle Scholar
  3. 3.
    A. Micheli, G.K. Brennen, P. Zoller, Nature Phys. 2, 341 (2006)ADSCrossRefGoogle Scholar
  4. 4.
    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    D. DeMille, Phys. Rev. Lett. 88, 067901 (2002)ADSCrossRefGoogle Scholar
  6. 6.
    S. Gulde, M. Riebe, G.P.T. Lancaster, C. Becher, J. Eschner, H. Häffner, F. Schmidt-Kaler, I.L. Chuang, R. Blatt, Nature 421, 48 (2003)ADSCrossRefGoogle Scholar
  7. 7.
    A. André, D. DeMille, J.M. Doyle, M.D. Lukin, S.E. Maxwell, P. Rabl, R.J. Schoelkopf, P. Zoller, Nature Phys. 2, 636 (2006)ADSCrossRefGoogle Scholar
  8. 8.
    B.L. Lev, E.R. Meyer, E.R. Hudson, B.C. Sawyer, J.L. Bohn, J. Ye, Phys. Rev. A 74, 061402 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    T.M. Fortier et al., Phys. Rev. Lett. 98, 070801 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    H.L. Bethlem, W. Ubachs, Faraday Discuss. 142, 25 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    M.R. Tarbutt, J.J. Hudson, B.E. Sauer, E.A. Hinds, Faraday Discuss. 142, 37 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    N. Poli, F. Wang, M.G. Tarallo, A. Alberti, M. Prevedelli, G.M. Tino, Phys. Rev. Lett. 106, 038501 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    S.Y.T. van de Meerakker, N. Vanhaecke, M.P.J. van der Loo, G.C. Groenenboom, G. Meijer, Phys. Rev. Lett. 95, 013003 (2005)ADSCrossRefGoogle Scholar
  14. 14.
    J.J. Gilijamse, S. Hoekstra, S.Y.T. van de Meerakker, G.C. Groenenboom, G. Meijer, Science 313, 1617 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    J.J. Gilijamse, S. Hoekstra, S.A. Meek, M. Metsälä, S.Y.T. van de Meerakker, G. Meijer, G.C. Groenenboom, J. Chem. Phys. 127, 221102 (2007)ADSCrossRefGoogle Scholar
  16. 16.
    W.C. Campbell, E. Tsikata, H.-I. Lu, L.D. van Buuren, J.M. Doyle, Phys. Rev. Lett. 98, 213001 (2007)ADSCrossRefGoogle Scholar
  17. 17.
    W.C. Campbell, G.C. Groenenboom, H.-I. Lu, E. Tsikata, J.M. Doyle, Phys. Rev. Lett. 100, 083003 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    B.C. Sawyer, B.K. Stuhl, D. Wang, M. Yeo, J. Ye, Phys. Rev. Lett. 101, 203203 (2008)ADSCrossRefGoogle Scholar
  19. 19.
    R.V. Krems, Phys. Chem. Chem. Phys. 10, 4079 (2008)CrossRefGoogle Scholar
  20. 20.
    W.C. Campbell, T.V. Tscherbul, H.-I. Lu, E. Tsikata, R.V. Krems, J.M. Doyle, Phys. Rev. Lett. 102, 013003 (2009)ADSCrossRefGoogle Scholar
  21. 21.
    L. Scharfenberg, J. Kłos, P.J. Dagdigian, M.H. Alexander, G. Meijer, S.Y.T. van de Meerakker, Phys. Chem. Chem. Phys. 12, 10660 (2010)CrossRefGoogle Scholar
  22. 22.
    S. Ospelkaus, K.K. Ni, D. Wang, M.H.G. de Miranda, B. Neyenhuis, G. Quéméner, P.S. Julienne, J.L. Bohn, D.S. Jin, J. Ye, Science 327, 853 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, E.A. Cornell, Science 269, 198 (1995)ADSCrossRefGoogle Scholar
  24. 24.
    K.B. Davis, M.-O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995)ADSCrossRefGoogle Scholar
  25. 25.
    E.S. Shuman, J.F. Barry, D. DeMille, Nature 467, 820 (2010)ADSCrossRefGoogle Scholar
  26. 26.
    K.M. Jones, E. Tiesinga, P.D. Lett, P.S. Julienne, Rev. Mod. Phys. 78, 483 (2006)ADSCrossRefGoogle Scholar
  27. 27.
    T. Köhler, K. Góral, P.S. Julienne, Rev. Mod. Phys. 78, 1311 (2006)ADSCrossRefGoogle Scholar
  28. 28.
    H.L. Bethlem, G. Meijer, Int. Rev. Phys. Chem. 22, 73 (2003)CrossRefGoogle Scholar
  29. 29.
    E. Narevicius, A. Libson, C.G. Parthey, I. Chavez, J. Narevicius, U. Even, M.G. Raizen, Phys. Rev. A 77, 051401 (2008)ADSCrossRefGoogle Scholar
  30. 30.
    T. Rieger, T. Junglen, S.A. Rangwala, P.W.H. Pinkse, G. Rempe, Phys. Rev. Lett. 95, 173002 (2005)ADSCrossRefGoogle Scholar
  31. 31.
    J.D. Weinstein, R. deCarvalho, T. Guillet, B. Friedrich, J.M. Doyle, Nature 395, 148 (1998)ADSCrossRefGoogle Scholar
  32. 32.
    P. Soldán, P.S. Żuchowski, J.M. Hutson, Faraday Discuss. 142, 191 (2009)ADSCrossRefGoogle Scholar
  33. 33.
    A.O.G. Wallis, J.M. Hutson, Phys. Rev. Lett. 103, 183201 (2009)ADSCrossRefGoogle Scholar
  34. 34.
    A.O.G. Wallis, E.J.J. Longdon, P.S. Żuchowski, J.M. Hutson, Eur. Phys. J. D (2011), DOI: 10.1140/epjd/ e2011-20025-4
  35. 35.
    P. Barletta, J. Tennyson, P.F. Barker, New J. Phys. 11, 055029 (2009)ADSCrossRefGoogle Scholar
  36. 36.
    P. Barletta, J. Tennyson, P.F. Barker, New J. Phys. 12, 113002 (2010)ADSCrossRefGoogle Scholar
  37. 37.
    A.V. Avdeenkov, J.L. Bohn, Phys. Rev. A 64, 052703 (2001)ADSCrossRefGoogle Scholar
  38. 38.
    L.M.C. Janssen, P.S. Żuchowski, A. van der Avoird, J.M. Hutson, G.C. Groenenboom, J. Chem. Phys. 134, 1124309 (2011)ADSGoogle Scholar
  39. 39.
    L.M.C. Janssen, P.S. Żuchowski, A. van der Avoird, G.C. Groenenboom, J.M. Hutson, Phys. Rev. A 83, 022713 (2011)ADSCrossRefGoogle Scholar
  40. 40.
    W. Ketterle, N.J. van Druten, Adv. Atom. Mol. Opt. Phys. 37, 181 (1996)Google Scholar
  41. 41.
    J.M. Gerton, C.A. Sackett, B.J. Frew, R.G. Hulet, Phys. Rev. A 59, 1514 (1999)ADSCrossRefGoogle Scholar
  42. 42.
    T.V. Tscherbul, J. Kłos, A. Dalgarno, B. Zygelman, Z. Pavlovic, M.T. Hummon, H.-I. Lu, E. Tsikata, J.M. Doyle, Phys. Rev. A 82, 042718 (2010)ADSCrossRefGoogle Scholar
  43. 43.
    S. Hensler, J. Werner, A. Griesmaier, P.O. Schmidt, A. Görlitz, T. Pfau, S. Giovanazzi, K. Rzażewski, Appl. Phys. B 77, 765 (2003)ADSCrossRefGoogle Scholar
  44. 44.
    M.T. Hummon, T.V. Tscherbul, J. Kłos, H.-I. Lu, E. Tsikata, W.C. Campbell, A. Dalgarno, J.M. Doyle, Phys. Rev. Lett. 106, 053201 (2011)ADSCrossRefGoogle Scholar
  45. 45.
    P.S. Żuchowski, J.M. Hutson, Phys. Chem. Chem. Phys. 13, 3669 (2011)CrossRefGoogle Scholar
  46. 46.
    R.V. Krems, A. Dalgarno, J. Chem. Phys. 120, 2296 (2004)ADSCrossRefGoogle Scholar
  47. 47.
    J.M. Hutson, S. Green, molscat computer code, version 14, distributed by Collaborative Computational Project No. 6 of the Engineering and Physical Sciences Research Council (UK, 1994)Google Scholar
  48. 48.
    M.L. González-Martínez, J.M. Hutson, Phys. Rev. A 75, 022702 (2007)ADSCrossRefGoogle Scholar
  49. 49.
    M.H. Alexander, D.E. Manolopoulos, J. Chem. Phys. 86, 2044 (1987)ADSCrossRefGoogle Scholar
  50. 50.
    A.J. Moerdijk, B.J. Verhaar, Phys. Rev. A 53, R19 (1996)ADSCrossRefGoogle Scholar
  51. 51.
    A.V. Avdeenkov, J.L. Bohn, Phys. Rev. A 71, 022706 (2005)ADSCrossRefGoogle Scholar
  52. 52.
    M. Kajita, Phys. Rev. A 74, 032710 (2006)ADSCrossRefGoogle Scholar
  53. 53.
    B. Zygelman, Phys. Rev. A 81, 032506 (2010)ADSCrossRefGoogle Scholar
  54. 54.
    A. Messiah, Quantum Mechanics (North Holland, Amsterdam, 1969)Google Scholar
  55. 55.
    M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), http://www.math.sfu.ca/˜cbm/aands
  56. 56.
    A. Volpi, J.L. Bohn, Phys. Rev. A 65, 052712 (2002)ADSCrossRefGoogle Scholar
  57. 57.
    T.V. Tscherbul, Y.V. Suleimanov, V. Aquilanti, R.V. Krems, New J. Phys. 11, 055021 (2009)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Institute for Molecules and MaterialsRadboud University NijmegenNijmegenThe Netherlands

Personalised recommendations