Figure 1

(Color online) (a) Schematic depiction of an adsorbed $\mathrm{Rb}$ atom on a conducting substrate (not to scale). The adatom in part relinquishes its valence electron to the substrate, leaving a positively charged ion bound to the substrate with a negative image charge in the substrate. The typical adatom-image charge separation is $\sim 5\mathrm{\AA }$. Electric field plates are added to the setup to enhance the effect of ionized adsorbates. The applied electric field may be oriented in either direction to add constructively or destructively to the surface dipolar field. (b) Roughly elliptical footprint of adsorbates following deposition of a number of elongated condensates, producing large electric field gradients near the surface.Reuse & Permissions

Figure 2

(Color online) Typical potential experienced by a condensate magnetically trapped near a surface. The dotted line is the sum of the harmonic magnetic trapping potential and the Casimir-Polder potential, and the solid curve includes the calculated electric potential from $\sim {10}^7\mathrm{Rb}$ atoms adsorbed on a conducting surface in a pattern $\sim 4\mu \mathrm{m}\times 150\mu \mathrm{m}$. The hatched region is the region occupied by a typical condensate at equilibrium.Reuse & Permissions

Figure 3

(Color online) Surface-based electric field as a function of atoms stuck to the surface. $\mathrm{Si}$ $(∎)$ and $\mathrm{Ti}$ $(▵)$ substrates exhibit similar behavior, roughly linearly increasing with adsorbate number, while the glass substrate $(●)$ shows only a small effect of adsorbates. The distance between the center of the magnetic trap and the surface is fixed to $10\mu \mathrm{m}$. Vertical error bars denote statistical errors only and do not represent systematic uncertainties, notably uncertainties in $E_{\mathrm{app}}$ and in the power law of $E_{\mathrm{surf}}$. The inset shows a typical plot of frequency versus applied voltage before $(●)$ and after $(◻)$ one condensate has been deposited on $\mathrm{Ti}$ $({\nu }_o=216.5\mathrm{Hz})$. There is a measurable effect from the atoms of only one condensate adsorbing. The lines are weighted fits to extract the frequency shift per applied voltage.Reuse & Permissions

Figure 4

(Color online) Frequency shift as a function distance between the magnetic trap center and the surface, after a large number of adsorbates $(>2\times {10}^7)$ had accumulated on the surface. $\mathrm{Si}$ $(∎)$ and $\mathrm{Ti}$ $(▵)$ substrates exhibit similar behavior. Solid lines are fits giving powers of $1∕r^{2.3}$ for the electric field near $\mathrm{Si}$ and $1∕r^{2.0}$ for $\mathrm{Ti}$, according to the pointlike approximate frequency shift method. These powers are consistent with a highly elongated, quasi-one-dimensional distribution of dipoles.Reuse & Permissions

Figure 5

(Color online) (a) Absorption image of a condensate undergoing dipolar oscillations near $\mathrm{Si}$. The curvature along the axial direction (long axis) is due to an inhomogeneous distribution of adatoms, which results in different radial trap frequencies along the axial direction. For imaging, the condensate is expanded radially by a factor of about 5. (b) Axial (parallel to the surface) spatial profile of trap frequency for a condensate near a $\mathrm{Si}$ substrate with no applied field after a large number of atoms have adhered to the surface. The three lines represent magnetic trap centers $19.7\mu \mathrm{m}$ (solid), $9.8\mu \mathrm{m}$ (dotted), and $9.1\mu \mathrm{m}$ (dashed) from the surface. The sharp dip in frequency is indicative of a greater number of adatoms at that spatial location on the surface. One would expect a distribution of adatoms that mirrors the elliptical distribution of the deposited condensates, with an axial Thomas-Fermi radius of $\sim 150\mu \mathrm{m}$. However, the stronger attractive surface potential near the center of the condensate might further attract atoms to stick there, thus altering the expected distribution. The increased noise in the data is due to fitting rows of single pixels in an image rather than averaging over an entire condensate. This technique treats the transverse oscillation of each axial segment of the elongated condensate as independent from the adjacent segment, which involves the implicit assumption that the “stiffness” of the condensate does not impede the oscillations.Reuse & Permissions