Upconversion-Enabled Single-Photon Er Emissions

• Upconversion-enabled single-photon Er³⁺ emissions are processes that convert telecom-band photons into visible and near-infrared wavelengths via sequential excited-state absorption and nonlinear mixing.
• Advanced nanofabrication of SiC hollow nanopillars and precise Er³⁺ implantation enable background-free, high-contrast detection with microsecond coherence times.
• Key performance metrics include telecom emission rates of ~1 kcps per ion, signal-to-background ratios ≥50:1, and scalable integration into chip-scale quantum photonic circuits.

Upconversion-enabled single-photon erbium (Er³⁺) emissions refer to the detection and utilization of individual Er³⁺ ion emission events in the telecommunications C-band (1530–1565 nm) that are converted into visible or near-infrared wavelengths via upconversion processes. These mechanisms leverage excited-state absorption (ESA) or nonlinear frequency-mixing to enable highly efficient, background-free detection and state readout of single Er³⁺ ions using photodetectors optimized for shorter wavelengths. This paradigm yields significant advances for quantum memory, photonic information interfaces, and cryogen-free quantum technology platforms.

1. Energy-Level Structure and Transitions in Single Er³⁺ Qudits

Single Er³⁺ ions in crystalline hosts, particularly within SiC hollow nanopillars (HNPs), form five-level electronic qudits using internal 4f¹¹ manifolds. The relevant term levels and transitions are summarized below:

Level Index	Manifold	Transition/Wavelength
1	$^4I_{15/2}$	Ground state
2	$^4I_{13/2}$	$4I_{15/2} \leftrightarrow 4I_{13/2}$ (1533.9 nm, telecom C-band)
3	$^4I_{11/2}$	$4I_{15/2} \leftrightarrow 4I_{11/2}$ (980 nm, NIR upconversion)
4	$^4F_{9/2}$	$4I_{15/2} \leftrightarrow 4F_{9/2}$ (660 nm, visible)
5	$^2H_{11/2}$	$4I_{15/2} \leftrightarrow 2H_{11/2}$ (518 nm, visible)

The single-photon upconversion process is mediated by a sequence of pump excitations (typically at 1533.9 nm), resonant $\pi$-pulses addressing $^4I_{15/2} \rightarrow ^4I_{13/2}$, followed by one or more ESA steps populating higher-lying manifolds. Upconverted emission is then observed at 980 nm, 660 nm, or 518 nm corresponding to radiative transitions back to the ground state (Kaloyeros et al., 17 Jan 2026).

2. Upconversion Mechanisms and Rate Modeling

Upconversion-enabled emissions rely on the efficient excitation of Er³⁺ ions and subsequent sequential absorption of photons (ESA) to reach higher energy manifolds, enabling radiative emission at visible or NIR wavelengths. The relevant population dynamics are described by coupled rate equations: $$\begin{aligned} \frac{dN_1}{dt} &= -W_{12}N_1 + \frac{N_2}{\tau_2} \ \frac{dN_2}{dt} &= W_{12}N_1 - (W_{23} + \tau_2^{-1})N_2 + \frac{N_3}{\tau_3} \ \frac{dN_3}{dt} &= W_{23}N_2 - (W_{34} + \tau_3^{-1})N_3 + \frac{N_4}{\tau_4} \ \frac{dN_4}{dt} &= W_{34}N_3 - (W_{45} + \tau_4^{-1})N_4 + \frac{N_5}{\tau_5} \ \frac{dN_5}{dt} &= W_{45}N_4 - \tau_5^{-1}N_5 \end{aligned}$$ with $W_{ij} = \sigma_{ij} I_p/h\nu_p$ the ESA rates for transitions $i \rightarrow j$, and $\tau_i$ radiative lifetimes ($\tau_2 \approx 1.2\,\mathrm{ms}$, $\tau_3 \approx 0.7\,\mathrm{ms}$, $\tau_4 \approx 0.31\,\mathrm{ms}$, $\tau_5 \approx 0.16\,\mathrm{ms}$). The upconversion quantum efficiency is

$$\eta_{\rm up} = \frac{P_{\rm up}/h\nu_{\rm up}}{P_{\rm pump}/h\nu_{\rm pump}}$$

where $P_{\rm up}$ and $P_{\rm pump}$ are the upconverted and pump photon powers, respectively (Kaloyeros et al., 17 Jan 2026).

In frequency conversion contexts, such as four-wave mixing Bragg scattering (FWM-BS) in silicon nitride waveguides, the upconversion between 1550 nm and 980 nm leverages strong classical pumps. Here the signal and idler exchange is governed by the coupled-mode equation: $$\eta(z) = \frac{4\gamma_1\gamma_2 P_1 P_2}{g^2} \sin^2(gz)$$ where $g^2 = (\Delta\beta/2)^2 + \gamma_1\gamma_2 P_1 P_2$, and $\gamma(\omega) = n_2\omega/(cA_{\rm eff}(\omega))$ characterizes the Kerr nonlinearity ($\gamma \approx 6$ W$^{-1}$ m$^{-1}$) (Agha et al., 2013).

3. Nanofabrication and Quantum Platform Architectures

High-performance upconversion-enabled Er³⁺ single-photon emitters are realized via CMOS-compatible fabrication of SiC hollow nanopillars (HNPs). Key process innovations include:

• Patterning a sacrificial HSQ mandrel by electron-beam lithography.
• Conformal deposition of amorphous SiC (thickness $\leq 5$ nm) by CVD, setting the critical dimension (C.D.) below lithography limits.
• Selective etching and post-processing to achieve vertical hollow nanopillars with C.D. $\leq 5$ nm and $<2$ Å sidewall roughness.
• Er³⁺ ion implantation through sidewall apertures with $<5$ nm spatial precision.

This spatial confinement provides robust isolation of single Er³⁺ ions and minimizes surface-induced dephasing. The optical setup enables telecom-band excitation (1533.9 nm) with high-NA confocal collection, dichroic filtering, superconducting nanowire single-photon detection (SNSPD) in the telecom, and EMCCD detection for upconversion readout (518/660/980 nm). Background is minimized by sub-nanometer spectral filtering, temporal gating, and use of a wide-bandgap SiC host (Kaloyeros et al., 17 Jan 2026).

4. Performance Metrics and Coherence Properties

Key experimental metrics for upconversion-enabled single-photon Er³⁺ emission platforms are:

• Single-photon count rates:
  • Telecom (1533.9 nm): up to $\sim$1 kcps per ion (SNSPD).
  • Visible upconversion (518/660 nm): 0.3–0.8 kcps per ion (EMCCD).
• Signal-to-background ratio (SBR): $\geq50:1$ in telecom; $\geq100:1$ in 518 nm upconversion.
• Optical coherence (C-band $^4I_{15/2} \leftrightarrow {}^4I_{13/2}$): homogeneous dephasing $T_2^* = 32\pm4$ μs (Ramsey), Hahn-echo $T_2 = 568\pm61$ μs (photon-echo) at 300 K.
• Photoluminescence excitation (PLE) linewidths: $\sim$67 MHz for telecom, $\sim$37 MHz for 660 nm upconversion.
• Internal upconversion efficiencies: $\eta_{\rm up} \sim 10^{-4} - 10^{-3}$ (estimated from PL rates and pump flux).

In chip-scale FWM-BS upconversion of Er³⁺-like 1550 nm photons to 980 nm, measured internal conversion efficiencies reach $-62$ dB (upconversion) at 50 mW continuous pump, with split-step Fourier simulations projecting $\eta\gtrsim 25\%$ at $\sim$10 W (nanosecond pulse peaks). Wide-band FWM-BS yields SBR $>10$ and can reach $>50$ with optimized pump detuning (Agha et al., 2013).

5. Frequency Upconversion for Quantum Photonic Integration

Upconversion from the telecom C-band to visible or near-infrared enables silicon-based single-photon avalanche diode (SPAD) detection, with lower dark counts and higher efficiency than InGaAs detectors at 1550 nm. Four-wave mixing Bragg scattering in Si₃N₄ waveguides is central to this integration pathway, providing:

• Noiseless, photon-statistics-preserving frequency translation ($\omega_i^+ = \omega_2 + (\omega_s-\omega_1)$).
• Broadband transparency and low two-photon absorption down to visible in Si₃N₄.
• Waveguide dispersion and phase-matching control through geometric tuning ($h=550$ nm, $w=700$–1200 nm).
• Extension to quantum emitters at 637–852 nm (NV, Rb, Cs) for interfacing with 1550 nm networks (Agha et al., 2013).

This approach enables deterministic, chip-scale single-photon upconversion suitable for quantum key distribution, quantum repeaters, and photonic quantum networks.

6. Theoretical Modeling and Simulation

Physical modeling encompasses SRIM simulations to control vacancy and implantation profiles relative to pillar geometry for single-ion placement, 2D finite-element computations for waveguide dispersion ($D(\lambda)$), and split-step Fourier propagation for nonlinear field evolution. Population dynamics are fit via photoluminescence saturation: $$I_{\rm PL}(P) = I_\infty \frac{P}{P+P_{\rm sat}},\qquad P_{\rm sat} = \frac{h\nu_p}{\sigma_{12}\tau_2}\sim1\,\mathrm{W/cm^2}$$ Quantum coherence dynamics (Ramsey, Rabi oscillations) are measured and fit as: $$I(tp) = A\,\sin^2(\Omega_R\,tp) + B,\qquad I(T_{\mathrm{free}}) = I_0 \exp(-2T_{\mathrm{free}}/T_2^*)$$ FWM-BS frequency conversion performance is projected from measured and simulated efficiencies, establishing viability for high-efficiency single-photon upconversion in photonic circuits (Kaloyeros et al., 17 Jan 2026, Agha et al., 2013).

7. Implications for Telecom Quantum Technologies

Upconversion-enabled single-photon Er³⁺ emission with background-free, high-contrast readout and microsecond-scale room-temperature coherence enables:

• Cryogen-free, on-chip quantum memories and spin–photon interfaces in the telecom C-band.
• Scalable quantum photonic integrated circuits (qPICs) with deterministic, sub-5 nm single emitter placement.
• Integration of robust, low-SWaP quantum sensors and quantum Internet repeaters.
• Utilization of Si₃N₄ and SiC nanophotonic platforms for frequency conversion and coherent photonic connectivity.

These advances facilitate the development of a practical quantum internet, offering the potential for widespread deployment of room-temperature quantum nodes and interfaces (Kaloyeros et al., 17 Jan 2026, Agha et al., 2013).