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arXiv:quant-ph/0403166 · Physical Review A

Thermal spin flips in atom chips

Per Kristian Rekdal, Stefan Scheel, P. L. Knight, Edward A. Hinds

Published Jul 28, 2004• 79 citations
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Abstract

We derive a general expression for the spin-flip rate of an atom trapped near an arbitrary dielectric body and we apply this theory to the case of a two-layer cylindrical metal wire. The spin-flip lifetimes we calculate are compared with those expected for an atom near a metallic slab and with those measured by Jones et al. above a two-layer wire [M.P.A. Jones, C.J. Vale, D. Sahagun, B.V. Hall, and E.A. Hinds, Phys. Rev. Lett. 91, 080401 (2003)]. We investigate how the lifetime depends on the skin depth of the material and on the scaling of the dimensions. This leads us to some conclusions about the design of integrated circuits for manipulating ultracold atoms (atom chips).

DOI
10.1103/physreva.70.013811

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We derive a general expression for the spin-flip rate of an atom trapped near an arbitrary dielectric body and we apply this theory to the case of a two-layer cylindrical metal wire. The spin-flip lifetimes we calculate are compared with those expected for an atom near a metallic slab and with those measured by Jones et al. above a two-layer wire [M.P.A. Jones, C.J. Vale, D. Sahagun, B.V. Hall, and E.A. Hinds, Phys. Rev. Lett. 91, 080401 (2003)]. We investigate how the lifetime depends on the skin depth of the material and on the scaling of the dimensions. This leads us to some conclusions about the design of integrated circuits for manipulating ultracold atoms (atom chips).
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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 4.2K4.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}4.2K, the typical atomic spin lifetime is found to be larger than 1000s1000\phantom{\rule{0.3em}{0ex}}\mathrm{s}1000s, even for atom-superconductor distances of one $1\phantom{\rule{0.3em}{0ex}}\mathrm{\ensuremath{\mu}}\mathrm{m}$. This constitutes a large enhancement in comparison with normal metals.
Using a consistent quantum-mechanical treatment for the electromagnetic radiation, we theoretically investigate the magnetic spin-flip scatterings of a neutral two-level atom trapped in the vicinity of a superconducting body. We derive a simple scaling law for the corresponding spin-flip lifetime for such an atom trapped near a superconducting thick slab. For temperatures below the superconducting transition temperature T_c, the lifetime is found to be enhanced by several orders of magnitude in comparison to the case of a normal conducting slab. At zero temperature the spin-flip lifetime is given by the unbounded free-space value.
We investigate the possibility of trapping ultracold 87Rb^{87}\mathrm{Rb}87Rb atoms near the outside of a metallic carbon nanotube, which we imagine using as a miniaturized current-carrying wire. We calculate atomic spin-flip lifetimes and compare the strength of the Casimir-Polder potential with the magnetic trapping potential. Our analysis indicates that the Casimir-Polder force is the dominant loss mechanism, and we compute the minimum distance to the carbon nanotube at which the atoms can be trapped to be larger than 100nm100\phantom{\rule{0.3em}{0ex}}\mathrm{nm}100nm.
We derive scaling laws for the spin decoherence of neutral atoms trapped near conducting and superconducting plane surfaces. A result for thin films sheds light on the measurement of Y. J. Lin, I. Teper, C. Chin, and V. Vuleti\ifmmode \acute{c}\else \'{c}\fi{} [Phys. Rev. Lett. 92, 050404 (2004)]. Our calculation is based on a quantum-theoretical treatment of electromagnetic radiation near metallic bodies [P. K. Rekdal, S. Scheel, P. L. Knight, and E. A. Hinds, Phys. Rev. A 70, 013811 (2004)]. We show that there is a critical atom-surface distance that maximizes the spin relaxation rate and we show how this depends on the skin depth and thickness of the metal surface. In the light of this impedance-matching effect we discuss the spin relaxation to be expected above a thin superconducting niobium layer.
We investigate theoretically the heating rate and spin flip lifetimes due to near-field noise for atoms trapped close to layered superconducting structures with the superconductor in the Meissner state. In particular, we compare the case of a gold layer deposited above a superconductor with the case of a bare superconductor. We study a niobium-based and a YBa 2 Cu 3 O 7 − x (YBCO)-based chip. For both niobium and YBCO chips at a temperature of 4.2 K, we find that the deposition of the gold layer can have a significant impact on the heating rate and spin flip lifetime, as a result of the increase of the near-field noise. At a chip temperature of 77 K, this effect is less pronounced for the YBCO chip.