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Spin-flip lifetimes in superconducting atom chips: Bardeen-Cooper-Schrieffer versus Eliashberg theory

Ulrich Hohenester, Asier Eiguren, Stefan Scheel, and E. A. Hinds
Phys. Rev. A 76, 033618 – Published 21 September 2007
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  • INTRODUCTION
  • THEORY OF SUPERCONDUCTIVITY
  • RESULTS FOR THE ATOM TRAPPING LIFETIME
  • SUMMARY
  • NOTES
  • ACKNOWLEDGEMENTS
  • APPENDICES
    • References

    Abstract

    We investigate theoretically the magnetic spin-flip transitions of neutral atoms trapped near a superconducting slab. Our calculations are based on a quantum-theoretical treatment of electromagnetic radiation near dielectric and metallic bodies. Specific results are given for rubidium atoms near a niobium superconductor. At the low frequencies typical of atomic transitions, we find that BCS theory greatly overestimates coherence effects, which are much less pronounced when quasiparticle lifetime effects are included through Eliashberg theory. At 4.2K, the typical atomic spin lifetime is found to be larger than 1000s, even for atom-superconductor distances of one 1μm. This constitutes a large enhancement in comparison with normal metals.

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    • Received 2 July 2007

    DOI:https://doi.org/10.1103/PhysRevA.76.033618

    ©2007 American Physical Society

    Authors & Affiliations

    Ulrich Hohenester1,*, Asier Eiguren1, Stefan Scheel2, and E. A. Hinds2

    • 1Institut für Physik, Karl-Franzens-Universität Graz, Universitätsplatz 5, 8010 Graz, Austria
    • 2Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom

    • *ulrich.hohenester@uni-graz.at

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    Issue

    Vol. 76, Iss. 3 — September 2007

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    • Figure 1
      Figure 1
      (Color online) Schematic geometrical setup. A plane metallic or superconducting slab lies parallel to the (x,y) plane. The atom with magnetic moment μ indicted by the arrow is located in vacuum at a distance z from the surface. The atom suffers spontaneous or thermally stimulated magnetic spin-flip transitions, as indicated by G0 and G, thereby becoming more weakly trapped and eventually lost. Johnson current noise ⟨jj⟩ within the penetration depth λ contributes to magnetic-field fluctuations at the position of the atom.Reuse & Permissions
    • Figure 2
      Figure 2
      (Color online) Temperature dependence of (a) real part σ′(ωA) and (b) imaginary part σ″(ωA) of the optical conductivity, normalized to the normal-state conductivity σ0. ωA=2π×500kHz is the atomic spin-flip frequency, and Tc=9.2K is the superconductor transition temperature. The different lines correspond to the results for the two-fluid model (dashed line), using δ0=16μm and λL(0)=35nm, BCS theory (solid line), and Eliashberg theory (symbols) for three elastic impurity scattering rates γ.Reuse & Permissions
    • Figure 3
      Figure 3
      (Color online) σ′(ω) at 4.2K as a function of frequency for three elastic scattering rates γ, as computed within the framework of Eliashberg theory. The peak at zero frequency is attributed to the condensate, and the peak at 1THz to the breaking of Cooper pairs. In the inset we show that the condensate peak saturates at low frequencies.Reuse & Permissions
    • Figure 4
      Figure 4
      (Color online) Spin-flip lifetime τA of a trapped atom near a superconducting slab as a function of (a) temperature (for 10μm atom-surface distance) and (b) distance (at 4.2K). The smallest distance in (b) is 1μm (with τA≈5000s for γ=1meV∕ℏ). For the calculation of τA we use Eq. (13) and the optical conductivity computed within Eliashberg theory for different elastic scattering rates γ. The atomic transition frequency is fixed at 500kHz throughout. The dashed lines correspond to calculations performed with the two-fluid model and the parameters given in Ref. 25 (London length λL=35nm).Reuse & Permissions
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