Spectral stability of cavity-enhanced single-photon emitters in silicon

TL;DR

This work tackles the problem of spectral instability in silicon-based single-photon emitters by embedding Er:Si in high-$Q$ Fabry-Perot cavities with large mode volumes, enabling both reduced dopant concentration and greater emitter-surface separation. The approach yields a fivefold reduction in spectral-diffusion linewidth to 4.0(2) MHz and extends the optical coherence time to 20(1) µs, aided by isotopically purified $^{28} ext{Si}$ that suppresses nuclear-spin noise. Laser-induced instantaneous spectral diffusion remains a limiting factor, scaling with pulse energy and duration, but the Fabry-Perot platform demonstrates clear improvements over nanophotonic devices, achieving near-lifetime-limited coherence under lower noise conditions. Overall, the results establish a path toward spectrally stable, multiplexed spin-photon interfaces in silicon, with implications for quantum networking and distributed quantum information processing, by combining large-mode-volume cavities, isotopic purification, and low dopant concentrations.

Abstract

The unrivaled maturity of its nanofabrication makes silicon a promising hardware platform for quantum information processing. To this end, efficient single-photon sources and spin-photon interfaces have been implemented by integrating color centers or erbium dopants into nanophotonic resonators. However, the optical emission frequencies in this approach are subject to temporal fluctuations on both long and short timescales, which hinders the development of quantum applications. Here, we investigate this limitation and demonstrate that it can be alleviated by integrating the emitters into Fabry-Perot instead of nanophotonic resonators. Their larger optical mode volume enables both increasing the distance to crystal surfaces and operating at a lower dopant concentration, which reduces implantation-induced crystal damage and interactions between emitters. As a result, we observe a fivefold reduction of the spectral diffusion linewidth down to 4.0(2) MHz. Calculations and experimental investigations of isotopically purified 28-Si crystals suggest that the remaining spectral instability is caused by laser-induced electric-field fluctuations. In direct comparison with a nanophotonic device, the instability is significantly reduced at the same intracavity power, enabling a tenfold increase of the optical coherence time up to 20(1) microseconds. These findings represent a key step towards spectrally stable spin-photon interfaces in silicon and their potential applications in quantum networking and distributed quantum information processing.

Figures (7)

• Figure 1: Limitation to the spectral stability of erbium caused by nuclear spin noise. (a) Monte-Carlo simulations are used to calculate the average frequency fluctuations that emitters in site A exhibit owing to the coupling to fluctuating magnetic moments of the nuclear spin bath at the natural isotopic abundance of $^{29}\text{Si}$. The resulting full-width-at-half-maximum (FWHM) of the spectral diffusion linewidth shows a strong dependence on the direction of an applied external magnetic bias field $B$ of $100mT$. (b) The simulation is repeated as a function of the magnetic field in the directions parallel (red, left axis) and perpendicular (dark blue, right axis) to the $\mathrm{C}_2$ symmetry axis of the emitters. (c) At $100mT$, applied perpendicular (top) or parallel (bottom) to the emitter symmetry axis, close-by $^{29}\text{Si}$ nuclear spins in randomly-chosen configurations (colors) can cause a splitting of the lines (orange, green) that depends on their superhyperfine coupling. The individual positions of these strongly-coupled nuclear spins are indicated by the same colors in (d) relative to the erbium (red) position, which is assumed to be displaced by 0.25 unit cells from the unit cell center along the $\mathrm{C}_{2}$ symmetry axis (red dashed line). For the blue curve in (c), no $^{29}\text{Si}$ nuclear spin is found within the unit cell.
• Figure 2: Experimental setup. (a) Sample preparation. The $2µm$ thick device layer (grey, top) of a silicon-on-insulator wafer is implanted with erbium dopants (red sketch of the concentration profile), such that a peak concentration of $10^{15}\,cm^{-3}$ is obtained. After dicing into chips of $1cm^2$, the handle wafer (grey, bottom) and buried oxide (blue) are removed in four quadratic windows of $2\cdot 2mm^2$ using masked chemical etching. (b) Photograph of the silicon chip before transferring one of the four membranes into the resonator. (c) Experimental device (not to scale). The erbium-doped (red spin symbols) silicon membrane (gray) is integrated into the optical mode (red) of a Fabry-Perot resonator. The latter is formed by two distributed Bragg reflectors (dark blue) deposited on a flat mirror substrate (top, light blue) and a concave optical fiber end (bottom), respectively. The mirrors are integrated into a piezo tube (ocher) to allow tuning and stabilization of the resonance frequency. A titanium spring (dark gray) ensures mechanical rigidity. (d) Optical setup. A frequency-stable continuous-wave laser is switched and frequency-shifted by acousto-optical modulators (AOMs). After adjusting the polarization with a polarization controller (PC), it is coupled to the fiber end of the resonator via a 97:3 beam splitter (BS). The reflected light and the dopant emission are guided to a superconducting nanowire single-photon detector (SNSPD) after a fiber-based frequency filter and a switch that prevents detector blinding during excitation pulses.
• Figure 3: Pulsed resonant fluorescence spectroscopy. (a) When scanning the excitation laser frequency, the fluorescence spectrum contains many sharp peaks, most of which originate from single erbium dopants. We randomly select a set of dopants with strong Purcell enhancement, marked with numbers, for detailed investigation of their spectral stability. At lower power, individual emitters are resolved even in the center of the inhomogeneous distribution. (b) The spectral emission of a randomly chosen emitter, "8", remains stable over many hours. A Lorentzian fit of the time-averaged data exhibits a spectral diffusion linewidth of $5.2(3)MHz$ FWHM. (c) In total, we measured 13 emitters with less averaging --- nine on the FZ and four on the $^{28}\text{Si}$ sample. Their SD lines are well-fit by Lorentzian curves (solid lines) and range between $12.4(12)MHz$ (orange, "3") and $4.0(2)MHz$ (green, "6"). The difference between the emitters shows that the spectral instability is dominated by local fluctuations at each dopant. No linewidth reduction is observed in the isotopically purified sample ("$^{28}\text{Si}$", dark blue, $5.2(5)MHz$). High-resolution measurements of the emitters (7), (8), and (9) were performed during a second cooldown.
• Figure 4: Laser-induced decoherence. (a) (Inset) A photon-echo measurement, consisting of an optical $\pi$ pulse centered in between two $\pi/2$ pulses, allows determining the optical coherence time $T_2$ of individual emitters. The used pulses exhibit Gaussian envelopes with varying pulse lengths $\tau_{\pi}$, while the pulse area is kept constant. (Main panel) Two representative photon-echo measurements on the same emitter, highlighted by blue circles in panel b. (b) The coherence time $T_2$ decreases for $\pi$ pulses of higher intensity and corresponding shorter duration $\tau_{\pi}$, which indicates that laser-induced instantaneous spectral diffusion limits the optical coherence. The data obtained from different emitters in the same device (blue symbols) shows slight fluctuations. A common fit to $T_2=\xi \cdot \tau_{\pi}$ matches the data well (solid lines). A single emitter in an isotopically purified $^{28}\text{Si}$ sample (green) shows the same scaling. A measurement on a nanophotonic device with a tenfold higher dopant concentration (gray) exhibits a much stronger laser-induced spectral instability. Still, it follows the same scaling at short $\tau_{\pi}$, but saturates at long $\tau_{\pi}$, where the curve approaches the lifetime limit (gray dashed line).
• Figure 5: Monte-Carlo simulation of the spectral diffusion linewidth caused by Er-Er interactions. The coupling to surrounding fluctuating erbium dopants at a concentration of $10^{15}\,cm^{-3}$ leads to fluctuations of the optical transition frequency, which are much smaller than those caused by the nuclear spin bath; the angular dependence, however, is very similar.