Effect of magnetization inhomogeneity on magnetic microtraps for atoms

We report on the origin of fragmentation of ultracold atoms observed on a magnetic film atom chip. Radio frequency spectroscopy and optical imaging of the trapped atoms is used to characterize small spatial variations of the magnetic field near the film surface. Direct observations indicate the fragmentation is due to a corrugation of the magnetic potential caused by long range inhomogeneity in the film magnetization. A model which takes into account two-dimensional variations of the film magnetization is consistent with the observations.

Figure 1

(Color online) Schematic diagram of our permanent magnetic film atom chip. Long range inhomogeneity in the film magnetization leads to fragmentation of the trapped cloud of ultracold atoms when positioned near the surface.

Figure 2

Absorption images of the ${}^{87}\mathrm{Rb}$ atomic density in the magnetic microtrap located $y_0=67\mu \mathrm{m}$ below the magnetic film edge. The trap parameters are $B_{\text{bias}}=0.57\mathrm{mT}$, $B_0=82\mu \mathrm{T}$, and ${\omega }_r=2\pi \times 1070\mathrm{Hz}$. The initial cloud temperature is $T=10\mu \mathrm{K}$. As the rf cutoff ${\nu }_f$ is decreased, the structure of the potential is revealed, (a) ${\nu }_f=1238\mathrm{kHz}$, (b) ${\nu }_f=890\mathrm{kHz}$, (c) ${\nu }_f=766\mathrm{kHz}$, (d) ${\nu }_f=695\mathrm{kHz}$.

Figure 3

Magnetic field profiles $B_z\left(z\right)$ measured using spatially resolved rf spectroscopy (solid lines) for various distances $y_0$ below the magnetic film edge. The field offset $B_0$ and the effect of weak longitudinal confinement are subtracted and each profile has been offset by $40\mu \mathrm{T}$ for clarity. The dotted lines correspond to measurements of the magnetic film edge using a scanning magnetoresistance probe which measures the $B_y$ component of the corrugated magnetic field. The relative longitudinal offset between the two measurements is initially unknown and is adjusted for optimum agreement.

Figure 4

(Color online) Spectral density of the magnetic field variations for different distances from the film edge. The points represent experimental data with (squares) $y_0=115\mu \mathrm{m}$, (circles) $y_0=87\mu \mathrm{m}$, (triangles) $y_0=67\mu \mathrm{m}$, and (diamonds) $y_0=57\mu \mathrm{m}$. The vertical dashed lines correspond to the characteristic wave vectors $k=1∕390\mu {\mathrm{m}}^{-1}$ and $k=1∕170\mu {\mathrm{m}}^{-1}$ for the $y_0=115\mu \mathrm{m}$ and $y_0=57\mu \mathrm{m}$ data sets, respectively. The solid lines represent the expected noise due to white noise variations of the film magnetization given by Eq. (4).

Figure 5

Transverse absorption images and longitudinal absorption cross sections of trapped thermal clouds of atoms positioned (a) $y_0=50\mu \mathrm{m}$, $x_0=-100\mu \mathrm{m}$, below the nonmagnetic gold surface; (b) $y_0=50\mu \mathrm{m}$, $x=0\mu \mathrm{m}$, directly below the film edge; (c) $y_0=50\mu \mathrm{m}$, $x_0=100\mu \mathrm{m}$, below the magnetic film surface; and (d) $y_0=100\mu \mathrm{m}$, $x_0=0\mu \mathrm{m}$, below the film edge. The solid lines in the absorption images indicate the approximate position of the magnetic film. Each optical density cross section is offset by 1.5 for clarity.

Figure 6

(Color online) Behavior of the magnetic field roughness $B_{z,\mathrm{rms}}$ measured using rf spectroscopy of ultracold atoms (circles) and $B_{y,\mathrm{rms}}$ measured using a scanning magnetoresistive probe (triangles), as a function of distance from the film surface. The dashed line corresponds to the expected noise for a homogeneously magnetized film with a measured edge roughness of $50\mathrm{nm}$. The solid line is a fit to the results of rf spectroscopy using Eq. (5) with a characteristic feature size $d=5\mu \mathrm{m}$ and $\Delta M∕M_s\simeq 0.3$. The inset shows the predicted $x$ dependence of the field roughness away from the film edge for distances of $y_0=10\mu \mathrm{m}$ (dotted), $y_0=50\mu \mathrm{m}$ (dashed), and $y_0=100\mu \mathrm{m}$ (solid line).