Influence of monolayer contamination on electric-field-noise heating in ion traps

Electric field noise is a hinderance to the assembly of large-scale quantum computers based on entangled trapped ions. Apart from ubiquitous technical noise, experimental studies of trapped ion heating have revealed additional limiting contributions to this noise, originating from atomic processes on the electrode surfaces. In a recent work [Safavi-Naini, Rabl, Weck, and Sadeghpour, Phys. Rev. A 84, 023412 (2011)] we described a microscopic model for this excess electric field noise, which points a way towards a more systematic understanding of surface adsorbates as progenitors of electric field jitter noise. Here, we address the impact of surface monolayer contamination on adsorbate-induced noise processes. Using exact numerical calculations for H and N atomic monolayers on a Au(111) surface, representing opposite extremes of physisorption and chemisorption, we show that an additional monolayer can significantly affect the noise power spectrum and, respectively, enhance and suppress the heating rates.

Figure 1

(a) A schematic binding potential $U\left(z\right)$ of an adsorbate on a bare Au surface as a function of the adatom-surface distance $z$. The dotted lines are the bound states of the potential and the corresponding wave functions are shown using solid lines. (b) The typical dependence of the phonon-induced dipole fluctuation spectrum of the adatom as a function of $\omega /{\Gamma }_0$, where ${\Gamma }_0$ is the characteristic transition rate from the first excited state to the ground state. The dipole fluctuation spectrum is in arbitrary units. The temperature is given in units of ${\nu }_{10}$, the separation between the ground state and the first excited vibrational state. The inset shows the temperature dependence of the noise in the low- and high-frequency regions of the spectrum. See text and spectrum for more details.

Figure 2

The binding potentials for H adsorbate atoms on bare Au surface (solid) and Au surface covered with one ML of He (dotted) or one ML of N (dashed). The peak of the local potential at the position of the first Au layer, in direct contact with the N(He) ML, does (not) vary appreciably, indicating the formation of a sizable (negligible) dipole moment. One hartree $=$ 27.21 eV.

Figure 3

Au(111) slab models covered by a one-sided ML (one ML) of (a) He atoms and (b) N atoms. The variation of the corresponding plane averaged electrostatic potential $\overline{V}\left(z\right)$ along the $z$ axis normal to the surface is represented for (c) He-covered and (d) N-covered Au(111) slabs, together with a clean Au(111) slab reference. The Fermi energy $E_{\mathrm{F}}$ (horizontal dashed line) and the work functions (vertical arrows) of the clean and adsorbate-covered slabs, $W_{\mathrm{clean}}$ and $W_{\mathrm{ads}}$, respectively, are also represented.

Figure 4

PDOS: (a) bulk Au, (b) bare Au$\left(111\right)$ surface, (c) one ML He-covered Au(111) surface, and (d) one ML N-covered Au(111) surface. The curves in black are the calculated total PDOS and the shaded areas in red, blue, and green represent the partial PDOS projected to the surface atoms, He atoms, and N atoms, respectively. The peaks labeled by “T” and “L” refer to the transverse and longitudinal PDOS, respectively.

Figure 5

The dipole fluctuation spectrum $S_{\mu }\left(\omega \right)$ as a function of $\omega /{\Gamma }_{0,\mathrm{Au}}$ for adsorbate of mass $m\sim 100$ amu on a He ML (black), a N ML (red), and a bare system (blue). For each system the solid curve corresponds to $T=50$ K while the dashed curve corresponds to $T=150$ K. The frequency $\omega$ is scaled by ${\Gamma }_{0,\mathrm{Au}}$, the characteristic rate corresponding to the bare surface. The spectrum is given in units of ${\mu }_0^2/{\Gamma }_{0,\mathrm{Au}}$, where ${\mu }_0$ is the dipole moment of the adatom in the vibrational ground state.