Atom chips in the real world: the effects of wire corrugation

Abstract

We present a detailed model describing the effects of wire corrugation on the trapping potential experienced by a cloud of atoms above a current carrying micro wire. We calculate the distortion of the current distribution due to corrugation and then derive the corresponding roughness in the magnetic field above the wire. Scaling laws are derived for the roughness as a function of height above a ribbon shaped wire. We also present experimental data on micro wire traps using cold atoms which complement some previously published measurements [11] and which demonstrate that wire corrugation can satisfactorily explain our observations of atom cloud fragmentation above electroplated gold wires. Finally, we present measurements of the corrugation of new wires fabricated by electron beam lithography and evaporation of gold. These wires appear to be substantially smoother than electroplated wires.PACS. 39.25.+k Atom manipulation (scanning probe microscopy, laser cooling, etc.) -03.75.Be Atom and neutron optics

The effect of self-affine fractal roughness of wires on atom chips

“…We see immediately that the dimensionless varianceṼ is approximately constant with distance, corresponding to a 1/d 4 variation in V that weakens when d y 0 . This result is consistent with experimental observations that the noise decreases with increasing distance from the wire [11,12,13]. All the dependence on ξ and α is contained inṼ , which is largest when d ≃ ξ (solid lines).…”

“…These experiments also require careful control over the noise of the surface. We note that if the distance to the surface becomes much less than the width of the wire, the corrugation of the surface [13] and imperfections of the bulk [33] may contribute significantly to the magnetic trap roughness.…”

“…In these cases where d ≃ y 0 ≫ ξ, the Hurst exponent is less important because it only affects the spectrum at frequencies above 1/ξ, which do not contribute significantly to the trap roughness. Naturally, if there is a second power-law regime at long wavelength, as in some wires [13], then the corresponding Hurst exponent significantly affects the magnetic trap roughness at that length scale.…”

“…In the following, we discuss the roughness of the magnetic atom traps produced when current flows through such a wire and we investigate how the field fluctuations vary with the Hurst exponent α and correlation length ξ. Wires made by electrodeposition into a thick photoresist mould have so far been much rougher. For example, the electroplated wire of [13] had σ ≃ 70 nm, α ≃ 0.5 and ξ ≃ 200 nm. Moreover, the spectrum of that wire exhibited a second power-law region with exponent −2.2 at wavelengths longer than 20 µm, indicating a second regime of correlated roughness.…”

“…(12) Let us take √ V max = 1 mG, for which the rms roughness in the potential corresponds to a temperature of 67 nK. We take κ ≃ 3 × 10 7 A m −3/2 [13,23], which is typical for gold wires on a Si/SiO 2 substrate. We further assume the values x 0 ≃ 1 µm, σ ≃ 3 nm, and ξ ≃ 20 nm, which are typical of our present wires, as discussed in section II.…”