Electric Field Cancellation on Quartz by Rb Adsorbate-Induced Negative Electron Affinity

We investigate the (0001) surface of single crystal quartz with a submonolayer of Rb adsorbates. Using Rydberg atom electromagnetically induced transparency, we investigate the electric fields resulting from Rb adsorbed on the quartz surface, and measure the activation energy of the Rb adsorbates. We show that the adsorbed Rb induces negative electron affinity (NEA) on the quartz surface. The NEA surface allows low energy electrons to bind to the surface and cancel the electric field from the Rb adsorbates. Our results will be important for integrating Rydberg atoms into hybrid quantum systems, as fundamental probes of atom-surface interactions, and for studies of 2D electron gases bound to surfaces.

Figure 1

(a) Stark shift for $81D_{5/2}$, $m_J=5/2$ and $1/2$ states in a 14.3 G magnetic field oriented perpendicular to the $E$ field. The inset shows the orientation of the electric and magnetic fields with respect to the quartz surface. (b) EIT spectra taken at two different positions $z=150\mu \mathrm{m}$ (upper) and $z=50\mu \mathrm{m}$ (lower) for $81D_{5/2}$ $m_J=1/2$ (left) and $m_J=5/2$ (right). The black points are pixel values of three averaged images, and the error bars are the standard deviation of the pixel values. The red lines are Lorentzian fits to the data. At $z=50\mu \mathrm{m}$ the $m_J=1/2$ state is broadened and shifted corresponding to an $E$ field of $0.02\mathrm{V}{\mathrm{cm}}^{-1}$. (c) In the limit of large numbers of Rydberg atoms $[\mathrm{Rb}(81D)]$, population the $E$ field is measured at distances of $\sim 20–800\mu \mathrm{m}$ from the quartz surface at $T_{\text{sub}}=79°\mathrm{C}$. Black points are taken from different pixels on a CCD camera. The error bars are the standard deviation of the measurement. The red line is a fit to Eq. (1), showing the inhomogeneity of the $E$ field. Our calculations indicate that the $E$ field at $z<200\mu \mathrm{m}$ is caused by the large spacing between the electrons.

Figure 2

(a) Level scheme for Rydberg EIT used in our experiments. ${\mathrm{\Delta }}_C$ is the coupling laser detuning. (b) A schematic of the experimental setup. Rb atoms are trapped in a mirror MOT, transferred into a magnetic trap, and transported to the surface. The probe and coupling beams for Rydberg EIT are overlapped and counterpropagate. The Rydberg EIT signal is observed by analyzing the absorption of the probe beam on a CCD camera. Heaters are placed outside of the vacuum to control the quartz temperature. The gold mirror is used to form the MOT. The heating block controls the temperature of the substrate. The $Z$ wire generates the magnetic trap. The aluminum nitride (AlN) mount insulates the $Z$ wire from the heating block.

Figure 3

The measured $E$ fields due to Rb adsorbates on the (0001) surface of quartz as a function temperature $T_{\text{sub}}$ at a distance of $500\mu \mathrm{m}$ from the surface. The $E$ fields are calculated by analyzing the frequency shifts of the EIT spectra. The black points are in the limit of low Rydberg atom production. The black line is a fit to the Langmuir isobar of Eq. (2), and yields a desorption activation energy of $E_a=0.66\pm 0.02\mathrm{eV}$. The red data points were taken with high Rydberg atom production. The red line is explained in the text. The horizontal error bars are due to the uncertainty in the temperature $T_{\mathrm{sub}}$. The vertical errors bars are the standard deviation of the experimental data. In the case of high- (low-) Rydberg atom production, the Rabi frequencies of the probe and coupling lasers are ${\mathrm{\Omega }}_p=2\pi \times 3.5(0.5)\mathrm{MHz}$ and ${\mathrm{\Omega }}_c=2\pi \times 4(4)\mathrm{MHz}$. Approximately 200 (10) electrons are produced during each experimental sequence, with a 10 (0.5) Hz average rate. The horizontal error bars are due to the uncertainty in $T_{\mathrm{sub}}$ and are $\pm 0.5°\mathrm{C}$.

Figure 4

Density of states of bulk $\alpha$-quartz. The Fermi level $E_F$ is at $E=0$. The valence band maximum $E_{v,\text{bulk}}$ and conduction band minimum $E_{c,\text{bulk}}$ of bulk $\alpha$-quartz, and the vacuum levels of the ${\mathrm{SiO}}_2(0001)$ surface without and with Rb adsorbates, respectively, ${\overline{V}}_{\text{clean}}(\infty )$ and ${\overline{V}}_{\mathrm{Rb}}(\infty )$, are labeled. ${\overline{V}}_{\mathrm{Rb}}(\infty )$ is shown as a function of coverage in fractions of a monolayer (ML). Increasing the amount of Rb coverage shifts the vacuum level down in energy. With one ML of Rb on the surface (red line), the vacuum energy dips below the bottom of the conduction band (green line), indicating the formation of a NEA surface.