Potential roughness near lithographically fabricated atom chips

Potential roughness has been reported to severely impair experiments in magnetic microtraps. We show that these obstacles can be overcome as we measure disorder potentials that are reduced by two orders of magnitude near lithographically patterned high-quality gold layers on semiconductor atom chip substrates. The spectrum of the remaining field variations exhibits a favorable scaling. A detailed analysis of the magnetic field roughness of a $100\text{−}\mu \mathrm{m}$-wide wire shows that these potentials stem from minute variations of the current flow caused by local properties of the wire rather than merely from rough edges. A technique for further reduction of potential roughness by several orders of magnitude based on time-orbiting magnetic fields is outlined.

Figure 1

In situ absorption images of atom clouds positioned at a chip-surface distance of $\sim 5\mu \mathrm{m}$ above a current-carrying wire (cross section $3.1\times 10\mu {\mathrm{m}}^2$). Parts of the images do not fully represent the atom density distribution since the imaging light beam was obstructed by bonding wires (hatched regions). (a) Thermal atoms show no fragmentation. (b) BECs display a much higher sensitivity and residual disorder potentials cause a fragmentation of the cloud. (c) A longitudinal displacement of the BEC by tuning the trapping potential shows that the disorder potential is stable in position.

Figure 2

Distance $d$ of the BEC from the (mirror) chip surface as a function of wire current ($3.1\times 100\mu {\mathrm{m}}^2$ wire). Atoms near the surface produce a double image when illuminated by an inclined imaging beam as shown in the insets (a)–(c). The imaging beam together with the chip surface produces a fringe pattern that makes distance measurements less reliable for certain surface distances (b). For clouds closer than $\sim 5\mu \mathrm{m}$ from the surface, the two images merge (d). To determine $d$ also in these cases we use an extrapolation according to a best fit (solid line) with the exact bias field strength as the only fitting parameter. The fitting model takes the finite size of the wire into account.

Figure 3

Scanning electron microscope images of the chip wire surface (left) and edges (right). The grain sizes of less than $100\mathrm{nm}$ determine both the surface and edge roughness.

Figure 4

(Color online) Disorder potential profiles for various heights over a $10\text{−}\mu \mathrm{m}$-wide wire surface. For comparison with previously published data, the units are given in $\mu \mathrm{K}∕\mathrm{A}$ and not in the universal $\Delta B∕B$. Longitudinal profiles of the disorder potential for selected $h$ (given in $\mu \mathrm{m}$ in the legend). Each curve has been shifted by $10\mu \mathrm{K}∕\mathrm{A}$; the dotted lines represent the corresponding zero-potential level.

Figure 5

(Color online) Longitudinal potential profiles measured with BECs at a constant distance of $d=10\mu \mathrm{m}$ from the surface of the $100\text{−}\mu \mathrm{m}$-broad wire. The different traces were measured at different currents and are normalized to the corresponding trapping fields. The bias field (10, 20, and $30\mathrm{G}$; black dotted, solid green, and dashed red lines, respectively) was adapted in order to keep $d$ constant. The inset shows a histogram of the deviations of the curves. The width of the distribution $(\sigma \sim 8\times {10}^{-6})$ is similar to the shot-to-shot variations of different realizations of the same experiment with equal wire currents.

Figure 6

(Color online) Spectral power density of the potential roughness near the $100\text{−}\mu \mathrm{m}$-wide gold wire for four spatial frequencies, measured at a transverse confinement of ${\omega }_{\perp }\sim 2\pi \times 3\mathrm{kHz}$. The open symbols correspond to data where the detected signal is limited by the chemical potential $\mu$ of the BEC. For these data points the complete depth of the potential cannot be measured, and they were omitted in the analysis. The solid lines are best fits according to a local fluctuating current path model; the dashed lines show best fits to the model outlined in [45]. For both models the only fitting parameter is the strength of the current path fluctuation at the corresponding spatial frequency $k$.

Figure 7

(Color online) Potential roughness measurements $10\mu \mathrm{m}$ above the the $100\text{−}\mu \mathrm{m}$-wide gold wire. Top: False color potential map recontructed from many 1D quasi-BEC images. Bottom: Change of the spectral power density of the potential roughness over the width of the $100\text{−}\mu \mathrm{m}$-wide wire for four spatial frequencies. For most of the frequencies the distribution is flat, except for $k=1∕40\mu \mathrm{m}$, where an increase is apparent when the wire edge is approached. We interpret this as caused by specific local defects in the edge.

Figure 8

(Color online) Height dependence of the potential roughness in the center of the $100\text{−}\mu \mathrm{m}$-wide gold wire are compared to the potential roughness calculated from the current reconstructed from the measurement of the magnetic field at $10\mu \mathrm{m}$ above the the $100\mu \mathrm{m}$ wire. The potential power spectral density calculated from the reconstructed current and a $2\sigma$ band is compared to the measured data. The $2\sigma$ band is estimated from the $3\mathrm{nT}$ magnetic field resolution for a single-shot single-point measurement with $3.5\mu \mathrm{m}$ spatial resolution.

Figure 9

(Color online) Comparison of the analysis of our 2003/04 data [53] presented in this work with the most detailed analysis of a different atom chip: the experiments at Orsay [44].

Figure 10

(Color online) Comparison of all atom chip potential roughness measurements available to us. Most of the data are taken from the figures in the published literature and available Ph.D. theses. The color codes correspond different experimental groups, as indicated in the legend. Filled symbols denote rms values, data displayed as open symbols correspond to the peak-to-valley maximum height of the roughness. Sussex: data from a gold-coated wire [23]. Orsay: ○, show the data from an electroplated wire [24, 44], more recent data from an evaporated gold chip shown as ▿ (peak to valley). Tübingen: data from electroplated wires [50]. Melbourne: data from a permanent magnet atom chip [28]. MIT: data from electroplated wires [15]. Heidelberg (2003/04 data [53]): data from the $100\mu \mathrm{m}$ wire shown as ○; data from the $10\mu \mathrm{m}$ wire shown as ◇ [36]. Later data from different other evaporated gold chip wires are shown as follows: The highest ever observed roughness in our atom chips: a $10\mu \mathrm{m}$ wire from ◇ [51]: Recent data from three different wires used in [52] *. The lines show the limits of maximal roughness allowed to be able to reach the one-dimensional regime of $\mu <\hslash {\omega }_{\perp }$ for different wire widths.

Figure 11

(Color online) Reduction of the potential roughness on applying an oscillating rf near field. Left: Trap potential with original roughness. Right: Effective potential created by subtracting the Ioffe offset field and adding a rf field with 0.1 $\left(1\right)\mathrm{G}$ amplitude.