Deterministic Single-Ion Implantation of Rare-Earth Ions for Nanometer-Resolution Color-Center Generation

Single dopant atoms or dopant-related defect centers in a solid state matrix are of particular importance among the physical systems proposed for quantum computing and communication, due to their potential to realize a scalable architecture compatible with electronic and photonic integrated circuits. Here, using a deterministic source of single laser-cooled ${\mathrm{Pr}}^{+}$ ions, we present the fabrication of arrays of praseodymium color centers in yttrium-aluminum-garnet substrates. The beam of single ${\mathrm{Pr}}^{+}$ ions is extracted from a Paul trap and focused down to 30(9) nm. Using a confocal microscope, we determine a conversion yield into active color centers of up to 50% and realize a placement precision of 34 nm.

Figure 1

(a) Sketch of the single-ion implantation setup. (b) Fluorescence of ions imaged. ($A$) Pure ${\mathrm{Ca}}^{+}$ crystals; the distance between two ${\mathrm{Ca}}^{+}$ ions is $9.5\mu \mathrm{m}$. ($B$) Crystals containing an additional ${\mathrm{Pr}}^{+}$ ion. (c) Histograms of the profiling edge measurement for ${}^{40}{\mathrm{Ca}}^{+}$ and ${}^{141}{\mathrm{Pr}}^{+}$ ions. For calcium, the extraction took about 15 min for 308 ions, whereas for praseodymium it took about 2 h for 150 ions. The events of the single-ion extraction are split into two cases; blue presents the detected ions and green the blocked ions. The black line shows the Bayesian fit function which corresponds to the last measured parameter values for beam position $x_0$, radius $\sigma$, and detector efficiency $a$. The mean value of the beam position of the $x$ axis is set to $x_0=0$ (dotted line), and the gray lines show the $1\sigma$ radius of the beam waist, which is ${\sigma }_{\mathrm{Ca}}=11.3\pm 2.0\mathrm{nm}$ for calcium and ${\sigma }_{\mathrm{Pr}}=30.7\pm 8.5\mathrm{nm}$ for praseodymium.

Figure 2

(a) Electronic level structure of ${\mathrm{Pr}}^{3+}$ in a YAG crystal. For optical characterization, the blue transition (487 nm) originating from ${\mathrm{\Gamma }}_3$ and exciting the $z$ dipole directions was used. Levels have symmetry representations ${\mathrm{\Gamma }}_3$ ($0{\mathrm{cm}}^{-1}$), ${\mathrm{\Gamma }}_1$ ($19{\mathrm{cm}}^{-1}$), and ${\mathrm{\Gamma }}_4$ ($50{\mathrm{cm}}^{-1}$). Transitions from a ${}^3{H}_4$ to a ${}^3{P}_0$ state (${\mathrm{\Gamma }}_1$ symmetry) are polarized either along the $z$ axis or along the $x$ axis. (b) Orientation of the six dodecahedral rare-earth sites, indicated by matchboxes [26]. The excitation laser propagates along the [111], and its polarization is adjusted so that two out of six sites are rendered dark. As an example, sites 1 and 2 are not excited, which leads to sites 3–6 being excited with equal, nonzero probability.

Figure 3

Up-converting microscopy scans of (a) area $A$, after subtraction of the preimplantation scanned background. (b) Area $B$, after subtraction of the preimplantation scanned background. (c) Area $B$, after the implantation and annealing procedure. (d) Difference in REI fluorescence signals $\mathrm{\Delta }C=C_{\text{before}}-C_{\text{after}}$, before and after a second annealing process.

Figure 4

(a) Net fluorescence signal (per 6 ms and after subtraction of the background) of implanted spots for areas $A$ and $B$. The observed count rate is consistent with the discrete nature of the integer number of REI emitters per spot. For the error bars, we assume a Poissonian photon-counting statistics. (b) Fitted ${\mathrm{Pr}}^{3+}$ ion locations with respect to the centroid of each respective spot. For this analysis, we excluded the implantation spots 1, 7, and 9 in area $B$ and spot 12 in area $A$, since these suffer from drifts far larger than the standard deviation of the rest of the implanted spots. The mode of the precision ${\sigma }_{\text{precision}}=34\mathrm{nm}$ was revealed using the Rayleigh distribution and is an indication of the precision of ion placement. The inset shows the histogram of the radial distances of implanted ions to their center of mass together with the Rayleigh distribution of the data using the maximum likelihood method (black curve) and the mode of the precision ${\sigma }_{\text{precision}}$ (dotted line). The precision error of the multi-Gaussian fitting method was estimated from Monte Carlo simulations to $\pm 18\mathrm{nm}$. (c) Calculated difference in position between the implanted spots and the ideal grid positions. The mode of the accuracy ${\sigma }_{\text{accuracy}}=72\mathrm{nm}$ was revealed using the Rayleigh distribution and is an indication of the accuracy of ion placement. The inset shows the histogram of the radial distance from the implantation to the ideal grid position together with the Rayleigh distribution (blue curve) of the data and the mode of the accuracy ${\sigma }_{\text{accuracy}}$ (dotted line).