Heating of a Trapped Ion Induced by Dielectric Materials

Electric-field noise due to surfaces disturbs the motion of nearby trapped ions, compromising the fidelity of gate operations that are the basis for quantum computing algorithms. We present a method that predicts the effect of dielectric materials on the ion’s motion. Such dielectrics are integral components of ion traps. Quantitative agreement is found between a model with no free parameters and measurements of a trapped ion in proximity to dielectric mirrors. We expect that this approach can be used to optimize the design of ion-trap-based quantum computers and network nodes.

Figure 1

A charged particle is placed a distance $d$ from a dielectric material with permittivity ${\epsilon }_1$. The particle oscillates in vacuum (permittivity ${\epsilon }_0$) with amplitude $\delta \zeta \ll d$, with $\delta \zeta \in \{\delta x,\delta z\}$. The charge generates an electric field ${\mathbf{E}}_{\zeta }$ outside the dielectric and a displacement field ${\mathbf{D}}_{\zeta }$ inside.

Figure 2

A trapped ion with axial and radial frequencies ${\omega }_z$ and ${\omega }_{x,y}$ is placed in the vicinity of two optical fibers. The facets of the optical fibers are laser ablated and coated with dielectric stacks, composed of alternating layers of ${\mathrm{SiO}}_2$ and ${\mathrm{Ta}}_2{\mathrm{O}}_5$, with respective permittivities ${ϵ}_{r,S}$ and ${ϵ}_{r,T}$. For our simulations, we neglect the mirror radii of curvature, which are $312(5)\mu \mathrm{m}$ for the photonic-crystal fiber and $318(5)\mu \mathrm{m}$ for the multimode fiber.

Figure 3

The heating rate as a function of axial frequency for ion-dielectric separations of 450 (squares) and $600\mu \mathrm{m}$ (circles). The dashed lines represent the predictions based on the literature values, and light-orange and light-blue areas show systematic uncertainties of the ion-fiber distance. The systematic uncertainties are determined from predictions that consider one fiber $55\mu \mathrm{m}$ closer to the ion and the other fiber $55\mu \mathrm{m}$ more distant. For both versions of such an asymmetric placement, the heating rates are larger than for the symmetric case, and thus, the systematic uncertainty is single sided.

Figure 4

The heating rate as a function of ion-fiber distance. The green points represent the prediction with error bars corresponding to the systematic uncertainty of the ion-fiber distance. The dashed line depicts a fit for a trap frequency of ${\omega }_z=2\pi \times 1.6\mathrm{MHz}$, and the respective systematic uncertainty is illustrated in light green. The asymmetry of the systematic uncertainty is discussed in the caption of Fig. 3.