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Physical Review A

Stability of a superconductive atom chip with persistent current

Christoph Hufnagel, T. Mukai, Fujio Shimizu

Published May 29, 2009• 32 citations

Abstract

The lifetime of $^{87}\text{R}\text{b}$ atoms trapped in a $\mathbsf{z}$ wire trap generated by a closed-circuit superconductive current on a ${\text{MgB}}_{2}$ strip is measured as a function of the distance between the atom and the strip. The lifetime is found to be longer than 10 s at a distance of $40\text{ }\ensuremath{\mu}\text{m}$. This value is an order of magnitude longer than the lifetime of a trap generated by a normal current at the same distance. However, it is many orders of magnitude shorter than the theoretical decay rate induced by the spin-flip transition caused by the fluctuation of the current. This shows that for a type-II superconductor the dominant trap loss mechanism is not the spin-flip transition caused by noise as with a normal current atom trap. An analysis of our measurement suggests that magnetic field distortion resulting from flux penetration into the superconductor leads to much faster decay.

DOI: 10.1103/physreva.79.053641

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The lifetime of

^{87}\text{R}\text{b}

atoms trapped in a

\mathbsf{z}

wire trap generated by a closed-circuit superconductive current on a

{\text{MgB}}_{2}

strip is measured as a function of the distance between the atom and the strip. The lifetime is found to be longer than 10 s at a distance of

40\text{ }\ensuremath{\mu}\text{m}

. This value is an order of magnitude longer than the lifetime of a trap generated by a normal current at the same distance. However, it is many orders of magnitude shorter than the theoretical decay rate induced by the spin-flip transition caused by the fluctuation of the current. This shows that for a type-II superconductor the dominant trap loss mechanism is not the spin-flip transition caused by noise as with a normal current atom trap. An analysis of our measurement suggests that magnetic field distortion resulting from flux penetration into the superconductor leads to much faster decay.

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.

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.

Magnetic traps for cold atoms have become a powerful tool in cold atom physics and condensed matter research. The traps on superconducting chips allow one to increase the trapped atom lifetime and coherence time by decreasing the thermal noise by several orders of magnitude compared to that of the typical normal-metal conductors. A thin superconducting film in the mixed state is, usually, the main element of such a chip. Using a finite element method to analyze thin film magnetization and transport current in type-II superconductivity, we study magnetic traps recently employed in experiments. The proposed approach allows us to predict important characteristics of the magnetic traps (their depth, shape, distance from the chip surface, etc) that are necessary when designing magnetic traps in cold atom experiments.

We study trapping of a cold atom by a single vortex line in an extreme type-II superconducting chip, allowing for pinning and friction. We evaluate the atom's spin flip rate and its dephasing due to the vortex fluctuations in equilibrium and find that they decay rapidly when the distance to the vortex exceeds the magnetic penetration length. We find that there are special spin orientations, depending on the spin location relative to the vortex, at which spin dephasing is considerably reduced while perpendicular directions have a reduced spin flip rate.

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.