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arXiv:2305.16231

Distinguishing erbium dopants in Y$_2$O$_3$ by site symmetry: \textit{ ab initio} theory of two spin-photon interfaces

Churna Bhandari, Cüneyt Şahin, Durga Paudyal, Michael E. FlattÃcopyright

Published May 25, 2023• 0 citations
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Abstract

We present a first-principles study of defect formation and electronic structure of erbium (Er)-doped yttria (Y$_2$O$_3$). This is an emerging material for spin-photon interfaces in quantum information science due to the narrow linewidth optical emission from Er dopants at standard telecommunication wavelengths and their potential for quantum memories and transducers. We calculate formation energies of neutral, negatively, and positively charged Er dopants and find the charge neutral configuration to be the most stable, consistent with experiment. Of the two substitutional sites of Er for Y, the $C_2$ (more relevant for quantum memories) and $C_{3i}$ (more relevant for quantum transduction), we identify the former as possessing the lowest formation energy. The electronic properties are calculated using the Perdew-Burke-Ernzerhof (PBE) functional along with the Hubbard $U$ parameter and spin-orbit coupling (SOC), which yields a $\sim$ 6 $μ_B$ orbital and a $\sim$ 3 $μ_B$ spin magnetic moment, and 11 electrons in the Er $4f$ shell, confirming the formation of charge-neutral Er$^{3+}$. This standard density functional theory (DFT) approach underestimates the band gap of the host and lacks a first-principles justification for $U$. To overcome these issues, we performed screened hybrid functional (HSE) calculations, including a negative $U$ for the $4f$ orbitals, with mixing ($α$) and screening ($w$) parameters. These produced robust electronic features with slight modifications in the band gap and the $4f$ splittings depending on the choice of tuning parameters. We also computed the many-particle electronic excitation energies and compared them with experimental values from photoluminescence.

DOI
10.48550/arxiv.2305.16231

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We present a first-principles study of the defect formation and electronic structure of erbium (Er)--doped yttria (Y2O3)({\mathrm{Y}}_{2}{\mathrm{O}}_{3})(Y2​O3​). This is an emerging material for spin-photon interfaces in quantum information science due to the narrow-linewidth optical emission from Er dopants at standard telecommunication wavelengths and their potential for quantum memories and transducers. We calculate formation energies of neutral and negatively and positively charged Er dopants and find the charge-neutral configuration to be the most stable, consistent with experiment. Of the two substitutional sites of Er for Y, the C2{C}_{2}C2​ (more relevant for quantum memories) and C3i{C}_{3i}C3i​ (more relevant for quantum transduction), we identify the former as possessing the lowest formation energy. The electronic properties are calculated using the Perdew-Burke-Ernzerhof functional along with the Hubbard UUU parameter and spin-orbit coupling, which yields a $\ensuremath{\sim}6\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ orbital and a $\ensuremath{\sim}3\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ spin magnetic moment, and 11 electrons in the Er 4f4f4f shell, confirming the formation of charge-neutral Er3+{\mathrm{Er}}^{3+}Er3+. This standard density functional theory approach underestimates the band gap of the host and lacks a first-principles justification for UUU. To overcome these issues we performed screened hybrid functional calculations, including a negative UUU for the 4f4f4f orbitals, with mixing $(\ensuremath{\alpha})$ and screening (w)(w)(w) parameters. These produced robust electronic features with slight modifications in the band gap and the 4f4f4f splittings depending on the choice of tuning parameters. We also computed the many-particle electronic excitation energies and compared them with experimental values from photoluminescence.
Rare-earth ion dopants in solid-state hosts are ideal candidates for quantum communication technologies, such as quantum memories, due to the intrinsic spin–photon interface of the rare-earth ion combined with the integration methods available in the solid state. Erbium-doped cerium oxide (Er:CeO2) is a particularly promising host material platform for such a quantum memory, as it combines the telecom-wavelength (∼1.5μm) 4f–4f transition of erbium, a predicted long electron spin coherence time when embedded in CeO2, and a small lattice mismatch with silicon. In this work, we report on the epitaxial growth of Er:CeO2 thin films on silicon using molecular beam epitaxy, with controlled erbium concentration between 2 and 130 parts per million (ppm). We carry out a detailed microstructural study to verify the CeO2 host structure and characterize the spin and optical properties of the embedded Er3+ ions as a function of doping density. In as-grown Er:CeO2 in the 2–3 ppm regime, we identify an EPR linewidth of 245(1) MHz, an optical inhomogeneous linewidth of 9.5(2) GHz, an optical excited state lifetime of 3.5(1) ms, and a spectral diffusion-limited homogeneous linewidth as narrow as 4.8(3) MHz. We test the annealing of Er:CeO2 films up to 900 °C, which yields narrowing of the inhomogeneous linewidth by 20% and extension of the excited state lifetime by 40%.
Rare-earth ions in solid-state hosts exhibit low homogeneous broadening and long spin coherence at cryogenic temperatures thus making them a promising candidate for optical quantum memories [1], optical-microwave transducers [2] and single dopant-based devices such as single photon emitters operating at the telecommunication wavelengths [3]. Here, we present an overview of the spin and optical properties of Er ensembles in Si accessed via resonant photoluminescence excitation (PLE) spectroscopy [4]. Samples were positioned directly on top of tailor-fabricated superconducting single photon detectors, placed in a dilution refrigerator unit and resonantly excited using fiber optics. Our method provided high collection efficiency and allowed spectral measurements of low Er density samples. The observed Er PLE spectra were strongly affected by the presence of co-dopants such as O, B or P reflecting their influence on the formation of optically active Er sites and corresponding Er optical transition energies. Higher O densities resulted in especially rich PLE spectra suggesting that a variety of Er-O complexes formed due to O doping. Lowering the O concentration, we achieved PLE spectra dominated by a single Er site in P doped samples. Interestingly, the Er spin relaxation and optical coherence properties were barely affected by the employed co-dopants and mainly depended on the Er concentration. By lowering the Er concentration from relatively high (1018cm-3) to low densities (1016cm-3), we were able to increase Er spin lifetimes from ~0.1 s to ~30 s. Long spin relaxation times allowed us to identify PLE spectra of new Er sites in Si. In both concentration regimes, we observed sub-MHz transient spectral holes suggesting long optical coherence times. Furthermore, we observed sub-MHz spin transitions in both natural and isotopically purified Si and achieved spin coherence times above 1 ms in isotopically purified Si. Narrow optical linewidths and long transverse and longitudinal spin relaxation times show that Er in Si is an excellent candidate for future quantum information and communication applications.
We present an effective ab initio method to calculate the crystal field coefficients of an erbium (Er3+) ion experiencing different local site symmetries in several wide-band-gap oxides, and then evaluate crystal field splittings of these Er3+ ions for their ground and excited states. The optical transitions between the ground state (Z) and excited state (Y) manifolds of the environmentally shielded 4f states of these Er3+ ions have wavelengths ~1.5 microns and thus have potential applications to quantum communications and quantum memories. These results are in excellent agreement with recent low-temperature measurements, provided the inadequate calculation of the 4f shell screening is adjusted by reducing the radial extent of the 4f wavefunctions by approximately a factor of 2.
Optically active solid-state spin qubits thrive as an appealing technology for quantum interconnects and quantum networks, thanks to their atomic size, scalable synthesis, long-lived coherence, and ability to coherently interface with flying qubits. Trivalent erbium dopants, in particular, emerge as an attractive candidate due to their emission in the telecom C band and shielded 4f intra-shell spin and optical transitions. Nevertheless, prevailing top-down architectures for rare-earth qubits and devices have not yet achieved simultaneous long optical and spin coherence, which is necessary for efficient long-distance quantum networks. Here, we demonstrate dual Er3+ telecom spin-photon interfaces in two distinct lattice symmetry sites within an epitaxial thin-film platform. By leveraging high matrix crystallinity, controlled proximity of dopants to surfaces, and exploiting host lattice symmetry, we simultaneously achieve kilohertz-level optical linewidth in a strongly symmetry-protected site, and erbium qubit spin coherence times exceeding 10 milliseconds. Additionally, we realize single-shot readout and microwave coherent control of erbium qubits in a fiber-integrated package, enabling rapid deployment and scalability. These advancements highlight the significant potential of high-quality rare-earth qubits and quantum memories assembled using a bottom-up method, paving the way for scalable development of quantum light-matter interfaces tailored for telecommunication quantum networks. Erbium quantum emitters operating in the telecom C band are promising for spin-photon interfaces but achieving both optical and spin coherence has been challenging. Gupta et al. report two types of erbium dopants in epitaxial Y2O3 thin films occupying distinct lattice sites and exhibiting long spin and optical coherence times
Atomic layer deposited (ALD) Y 2 O 3 thin films have been thoroughly investigated for optical or electronic applications. The coherent spectroscopy of lanthanide ions doped into this material has also recently attracted increasing interest in the field of quantum technologies for which they are considered promising candidates in quantum memories or as spin–photon interfaces. However, these most demanding applications require a deep control over the local positioning of the ions and their close environment in the crystalline matrix. This study focuses on the structural as well as optical properties of Eu 3+ and Er 3+ dopants in Y 2 O 3 using photoluminescence (PL), luminescence decay times, and inhomogeneous line width (Γ inh ) measurements within this particular context. While as-grown ALD films do not provide an ideal host for the emitters, we demonstrate that by optimizing the deposition conditions and using appropriate annealing post treatments narrow inhomogeneous lines can be obtained for the 7 F 0 ↔ 5 D 0 transition of Eu 3+ even for nanoscale films. Furthermore, about 1.5 ms lifetime has been measured for the infrared telecom transition of Er in ultrathin films (<10 nm), which is an order of magnitude higher than in nanoparticles of the same size. These results validate optimized rare-earth-doped ALD Y 2 O 3 films as a suitable platform for photonics applications where few-nanometer-thick films with well-localized emitters are mandatory. This approach provides the first building blocks toward the development of more complex devices for quantum sensing or hybrid structures coupled with other systems such as two-dimensional materials.