Quantum Coherence of Rare-Earth Ions in Heterogeneous Photonic Interfaces

Abstract

Harnessing rare-earth ions in oxides for quantum networks requires integration with bright emitters in III-V semiconductors, but local disorder and interfacial noise limit their optical coherence. Here, we investigate the microscopic origins of the ensemble spectrum in Er$^{3+}$:TiO$_2$ epitaxial thin films on GaAs and GaSb substrates. Ab initio calculations combined with noise-Hamiltonian modeling and Monte Carlo simulations quantify the effects of interfacial and bulk spin noise and local strain on erbium crystal-field energies and inhomogeneous linewidths. Photoluminescence excitation spectroscopy reveals that Er$^{3+}$ ions positioned at increasing distances from the III-V/oxide interface produce a systematic blue shift of the $Y_1\rightarrow Z_1$ transition, consistent with strain relaxation predicted by theory. Thermal annealing produces a compensating redshift and linewidth narrowing, isolating the roles of oxygen-vacancy and gallium-diffusion noise. These results provide microscopic insight into disorder-driven decoherence, offering pathways for precise control of hybrid quantum systems for scalable quantum technologies.

Figures (5)

• Figure 1: (a) Schematic of the synthesized heteroepitaxial Er$^{3+}$:TiO$_2$ thin film on III-V substrates featuring an undoped buffer layer grown under high vacuum. Photoluminescence excitation (PLE) spectra of the $Y_1\rightarrow Z_1$ transition in Er$^{3+}$ doped into the rutile (b) and anatase (c) phase thin films grown on GaAs and GaSb substrates.
• Figure 2: (a) Schematic of the GaX-TiO$_{2}$ heterostructure indicating Er ions (cyan) at interfacial distance $d$ that interact with Ga spins (brown) that diffuse into TiO$_2$ with characteristic length $\lambda$ and oxygen vacancies (red) $V_\textrm{O}$. (b) Illustration of linewidth broadening arising from the fluctuating magnetic fields $\delta B_z(t)$ on the $Y_{1}\rightarrow Z_{1}$ transition of the crystal-field-split energy levels of Er$^{3+}$. (c) Spectral noise density $S_z(d)$ due to Ga nuclear spins as a function of distance $d$, compared to the expected $d^{-3}$ (gray dashed) and $d_c^{-3}e^{-(d-d_c)/\lambda}$ (red dotted) dependencies with $\lambda=4$ nm and $d_c=0.35$ nm. Insets show a schematic of Ga spin density distributions near and far from the interface. (d) Distance-dependent $Y_{1}\rightarrow Z_{1}$ transition frequency $\omega(d)$, illustrating the influence of interfacial strain. (e) Illustration of the asymmetric inhomogeneous lineshape resulting from the interplay between strain and distance-dependent individual Er$^{3+}$ homogeneous linewidths.
• Figure 3: (a) Schematic of the selectively-doped Er$^{3+}$:TiO$_2$ thin film on GaAs featuring a $2~nm$-thin doped layer introduced at an interfacial distance $d$. (b) PLE spectra around the $Y_1\rightarrow Z_1$ transition of Er$^{3+}$ ions in such annealed thin films exhibit significant frequency shifts due to distance-dependent strain in the thin film. (c) Frequency shift of the $Y_1\rightarrow Z_1$ transition ($\nu_\delta$) before and after annealing, relative to the measured frequency in uniformly-doped samples ($\nu_\textrm{bulk}$), highlights the interplay between strain and oxygen-vacancy contributions.
• Figure 4: (a) Effect of in-plane compressive and tensile strain (with 1% fixed $c$-axis compression) on crystal field energy levels. (b) Defect formation energy of Er-doped TiO$_2$ with (blue) and without (red) $V_O$ at the next nearest neighbor. (c) Spin density of neutral Er-doped A-TiO$_2$ ($q=0$). The large spin density on Er arises from its $\sim$3 $\mu_B$ spin moment (Er$^{3+}$), while nearby O atoms show small induced spin densities due to Er-4f and O-$2p$ hybridization (see Supplemental Material).
• Figure 5: (a) Inhomogeneous linewidth $\Gamma_{inh}$ as a function of distance from GaX-TiO$_2$ interface before and after annealing of the $\delta$-doped $\mathrm{A\text{-}TiO_2}$ samples. (b) Experimental and simulated lineshape for the $Y_{1}\rightarrow Z_{1}$ transition in $\mathrm{A-TiO_{2}}$. (c) Experimental and Monte Carlo–simulated lineshape for the $Y_{1}\rightarrow Z_{1}$ transition in $\mathrm{R-TiO_{2}}$.