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arXiv:0707.0238 · Physical Review A

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

Ulrich Hohenester, Asier Eiguren, Stefan Scheel, Edward A. Hinds

Published Sep 21, 2007• 51 citations
arXivHTMLPDF

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 $4.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the typical atomic spin lifetime is found to be larger than $1000\phantom{\rule{0.3em}{0ex}}\mathrm{s}$, 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.

DOI
10.1103/physreva.76.033618

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Comment on `Spin Decoherence in Superconducting Atom Chips'

Stefan Scheel, E. A. Hinds, P. L. Knight

We comment on a recent paper [Phys. Rev. Lett. 97, 070401 (2006): quant-ph/0603229] concerning rubidium atoms trapped near a superconducting niobium surface at ~4K. This seeks to calculate the rate of atomic spin flips induced by thermal magnetic noise. We point out that the calculation is in error by a large factor because it is based on the two-fluid model of superconductivity. This model gives a poor description of electromagnetic dissipation just below the critical temperature because it cannot incorporate the case II coherences of a fuller quantum theory.

arXiv:quant-ph/0610095•Oct 12, 2006•0 citations
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\ensuremathμm1\phantom{\rule{0.3em}{0ex}}\mathrm{\ensuremath{\mu}}\mathrm{m}1\ensuremathμm. 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 Tc, 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.
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 study the photon emission due to a magnetic spin-flip transition of a two-level atom in the vicinity of a dielectric body such as a normal conducting metal or a superconductor. For temperatures below the transition temperature Tc{T}_{c}Tc​ of a superconductor, the corresponding spin-flip lifetime is boosted by several orders of magnitude as compared to the case of a normal conducting body. Numerical results of an exact formulation are also compared to a previously derived approximative analytical expression for the spin-flip lifetime, and we find excellent agreement. We present results on how the spin-flip lifetime depends on the temperature TTT of a superconducting body as well as its thickness HHH. Finally, we study how nonmagnetic impurities as well as possible Eliashberg strong-coupling effects influence the spin-flip rate. It is found that nonmagnetic impurities as well as strong-coupling effects have no dramatic impact on the spin-flip lifetime.
We study theoretically the lifetime of magnetically trapped atoms in the close vicinity of a type-II superconducting surface, in the context of superconducting atom-chips. We account for the magnetic noise created at the cloud position by the vortices present in the superconductor and give specific results for our experiment which uses a niobium film. Our main result is that atom losses are dominated by the presence of vortices. They remain however dramatically smaller than in equivalent room-temperature atom-chip setups using normal metals.
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.
We comment on a recent paper [Phys. Rev. Lett. 97, 070401 (2006): quant-ph/0603229] concerning rubidium atoms trapped near a superconducting niobium surface at ~4K. This seeks to calculate the rate of atomic spin flips induced by thermal magnetic noise. We point out that the calculation is in error by a large factor because it is based on the two-fluid model of superconductivity. This model gives a poor description of electromagnetic dissipation just below the critical temperature because it cannot incorporate the case II coherences of a fuller quantum theory.