Observing ${\mathrm{Er}}^{3+}$ Sites in Si With an In Situ Single-Photon Detector

We present a flexible method to study the optical properties of an ${\mathrm{Er}}^{3+}$ ensemble in $\mathrm{Si}$ accessed via resonant excitation and in situ single-photon detection. The technique allows an efficient resonant photoluminescence detection of optically active centers with weak oscillator strength in transparent crystals without the need for nanofabrication on the sample. We observe 70 ${\mathrm{Er}}^{3+}$ resonances in $\mathrm{Si}$, of which 62 resonances have not been observed in the literature, with optical lifetimes ranging from 0.5 to 1.5 ms. We observe inhomogeneous broadening of less than 400 MHz and an upper bound on the homogeneous linewidth of 0.75 and 1.4 MHz for two separate resonances. These narrow, stable resonances confirm ${\mathrm{Er}}^{3+}$ in $\mathrm{Si}$ as a promising quantum information candidate. We discuss the use of this technique for rapid characterization of future samples, with the aim of enhancing the prevalence of sites which are favorable for quantum information applications.

Figure 1

(a) Schematic layout of the experiment (not to scale). The $\mathrm{Si}$ sample consisting of a 400-nm ${\mathrm{Er}}^{3+}$-doped region is placed on top of a SSPD situated in a cryostat at 0.3 K. The PLE spectrum is obtained by producing 100-$\text{μ}\mathrm{s}$ pulses using two acousto-optical modulators with an on:off ratio of more than 100 dB and collecting the luminescence. A magnetic field is applied orthogonal to the sample during the Zeeman measurements. (b) Top: PLE spectrum of ${\mathrm{Er}}^{3+}$-implanted $\mathrm{Si}$. Bottom: resonance positions for the PLE spectrum (red lines). Inset: a single optically detected inhomogeneous resonance centered at $1535.199\mathrm{nm}$, which is fit with a Lorentzian function resulting in a 0.34-GHz full width at half maximum (FWHM) linewidth.

Figure 2

(a) Inhomogeneously broadened resonance at $1534.194\mathrm{nm}$ at zero field and the splitting into multiple resonances when 50 mT is applied. (b) Inhomogeneously broadened resonance at $1523.126\mathrm{nm}$ under $-50$, 0, and 50 mT. P1 indicates the polarization which results in a maximum intensity of the left peak at $-50$ mT, while P2 indicates the polarization which results in a maximum intensity of the right peak at $-50$ mT.

Figure 3

(a) Top: expected decay signal when the probe offset is larger than the homogeneous linewidth. Middle: expected decay signal when the pump and probe frequency are equal. Bottom: pulse sequence for spectral hole measurements. The curves are normalized to ${\rho }_{\mathrm{res}}(t_{\mathrm{pump}}+t_{\mathrm{probe}})$, which is the occupation number when the subset is resonantly excited. (b) Upper bound on the homogeneous linewidth at $1538.685\mathrm{nm}$. The vertical axis gives the integrated number of counts up to 1 ms after the probe pulse as a function of $f_{\mathrm{probe}}-f_{\mathrm{pump}}$. The data is fitted with a Lorentzian distribution, resulting in a FWHM of 1.5 MHz.

Figure 4

(a) Photoluminescence decay curve for the resonance at $1527.565$ nm ($I_{\mathrm{res}}$) and the background at $1527.461$ nm ($I_{\mathrm{offres}}$). The on-resonant time trace shows a biexponential decay, which is due to the biexponential off-resonant decay. Since the off-resonant decay is due to noncompetitive processes, the ${\mathrm{Er}}^{3+}$ decay can be extracted by subtracting the off-resonant time trace, resulting in a single exponential decay except for a few, as can be found in Table 1. (b) Fit result of the lifetime for the 70 resonances. Errorbars show the standard error of the fit.

Figure 5

Experimental setup. A continuous-wave laser provided narrow-band light. A portion of the laser light is monitored by the wavemeter. The EOM is added when performing the spectral hole burning measurements. Two AOMs are used to pulse the intensity of the light with a contrast of over 100 dB. Ten percent of the laser light continued to an optical power meter to calculate the power on the sample. The other portion of the laser light continued through polarization paddles to control the polarization on the sample. The sample, SSPD, bias tee, and HEMT amplifier are inside the HelioxVL at 300 mK. The high-frequency SSPD signal coupled out through the HEMT amplifier and two room-temperature amplifiers into the counter.

Figure 6

Direction of the laser light, the sample, and optical stack-embedded SSPD (not to scale). The sample is coated with 190 nm of ${\mathrm{Si}\mathrm{N}}_x$ on both sides to enhance the transmission through the sample. The chip is placed upside down on the SSPD stack so the $400\mathrm{nm}{\mathrm{Er}}^{3+}$-doped region is in close proximity with the SSPD. The SSPD is embedded in an optical stack to increase the collection efficiency. A fiber is placed on top of the sample, which provides the laser light and clamps the sample on top of the SSPD. The remaining air gap between the sample and the SSPD is limited by the flatness of both surfaces.

Figure 7

Pulsing schematic for the pulsed bias current measurements. During the 100-$\text{μ}\mathrm{s}$ long optical pulse, the superconducting single-photon detector (SSPD) current is reduced from the switching current ($I_{\mathrm{sw}}$) to 0 A. Afterwards, the bias current is increased to $I_{\mathrm{sw}}$ for $900\text{μ}\mathrm{s}$ so the SSPD is able to detect the single photons for $900\text{μ}\mathrm{s}$ after the end of the optical pulse. This pulse sequence is repeated 1000 times at a fixed optical frequency before the laser frequency is changed to the next frequency. The minimum time required for the SSPD to detect the single photons after the end of the optical pulse is $1.5\text{μ}\mathrm{s}$. This reset time corresponded to the $RC$ time of the SSPD biasing circuit.

Figure 8

Overlapping plots of spectral hole burning with two different delays at $0\text{μ}\mathrm{s}$ and $90\text{μ}\mathrm{s}$. The linewidth of the two holes are approximately equal regardless of the delay between the pulses.