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arXiv:2303.02054 · Physical review. B./Physical review. B

Optical coherence properties of Kramers' rare-earth ions at the nanoscale for quantum applications

Mohammed K. Alqedra, Chetan Deshmukh, Shuping Liu, Diana Serrano, Sebastian P. Horvath, Safi Rafie-Zinedine, Abdullah Abdelatief, Lars Rippe, Stefan Kröll, Bernardo Casabone, Alban Ferrier, Alexandre Tallaire, Philippe Goldner, Hugues de Riedmatten, Andreas Walther

Published Aug 3, 2023• 20 citations
arXivHTMLPDF

Abstract

Rare Earth (RE) ion doped nanomaterials are promising candidates for a range of quantum technology applications. Among RE ions, the so-called Kramers' ions possess spin transitions in the GHz range at low magnetic fields, which allows for high-bandwidth multimode quantum storage, fast qubit operations as well as interfacing with superconducting circuits. They also present relevant optical transitions in the infrared. In particular, ${\mathrm{Er}}^{3+}$ has an optical transition in the telecom band, while ${\mathrm{Nd}}^{3+}$ presents a high-emission-rate transition close to 890 nm. In this paper, we measure spectroscopic properties that are of relevance to using these materials in quantum technology applications. We find the inhomogeneous linewidth to be 10.7 GHz for ${\mathrm{Er}}^{3+}$ and 8.2 GHz for ${\mathrm{Nd}}^{3+}$, and the excited state lifetime ${T}_{1}$ to be 13.68 ms for ${\mathrm{Er}}^{3+}$ and $540\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{s}$ for ${\mathrm{Nd}}^{3+}$. We study the dependence of homogeneous linewidth on temperature for both samples, with the narrowest linewidth being 379 kHz (${T}_{2}=839$ ns) for ${\mathrm{Er}}^{3+}$ measured at 3 K, and 62 kHz (${T}_{2}=5.14\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{s}$) for ${\mathrm{Nd}}^{3+}$ measured at 1.6 K. Further, we investigate time-dependent homogeneous linewidth broadening due to spectral diffusion and the dependence of the homogeneous linewidth on magnetic field to get additional clarity of mechanisms that can influence the coherence time. In light of our results, we discuss two applications: single qubit-state readout and a Fourier-limited single photon source.

DOI
10.1103/physrevb.108.075107

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Narrow inhomogeneous and homogeneous optical linewidths in a rare earth doped transparent ceramic

Alban Ferrier, Charles W. Thiel, Biagio Tumino +5 more

Inhomogeneous and homogeneous linewidth are reported in a Eu${}^{3+}$ doped transparent Y${}_{2}$O${}_{3}$ ceramic for the ${}^{7}$F${}_{0}$-${}^{5}$D${}_{0}$ transition, using high-resolution coherent spectroscopy. The 8.7-GHz inhomogeneous linewidth is close to that of single crystals, as is the 59-kHz homogeneous linewidth at 3 K (${T}_{2}$ $=$ 5.4 $\ensuremath{\mu}$s). The homogeneous linewidth exhibits a temperature dependence that is typical of a crystalline environment, and additional dephasing observed in the ceramic is attributed to magnetic impurities or defects introduced during the synthesis process. The absence of Eu${}^{3+}$segregation at the grain boundaries, evidenced through confocal microfluorescence, further indicates that the majority of Eu${}^{3+}$ions in the ceramic experience an environment comparable to a single crystal. The obtained results suggest that ceramic materials can be competitive with single crystals for applications in quantum information and spectral hole burning devices, beyond their current applications in lasers and scintillators.

Physical Review B•Jan 11, 2013•29 citations
Rare Earth (RE) ion doped nanomaterials are promising candidates for a range of quantum technology applications. Among RE ions, the so-called Kramers' ions possess spin transitions in the GHz range at low magnetic fields, which allows for high-bandwidth multimode quantum storage, fast qubit operations as well as interfacing with superconducting circuits. They also present relevant optical transitions in the infrared. In particular, Er3+{\mathrm{Er}}^{3+}Er3+ has an optical transition in the telecom band, while Nd3+{\mathrm{Nd}}^{3+}Nd3+ presents a high-emission-rate transition close to 890 nm. In this paper, we measure spectroscopic properties that are of relevance to using these materials in quantum technology applications. We find the inhomogeneous linewidth to be 10.7 GHz for Er3+{\mathrm{Er}}^{3+}Er3+ and 8.2 GHz for Nd3+{\mathrm{Nd}}^{3+}Nd3+, and the excited state lifetime T1{T}_{1}T1​ to be 13.68 ms for Er3+{\mathrm{Er}}^{3+}Er3+ and 540\textmus540\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{s}540\textmus for Nd3+{\mathrm{Nd}}^{3+}Nd3+. We study the dependence of homogeneous linewidth on temperature for both samples, with the narrowest linewidth being 379 kHz (T2=839{T}_{2}=839T2​=839 ns) for Er3+{\mathrm{Er}}^{3+}Er3+ measured at 3 K, and 62 kHz (T2=5.14\textmus{T}_{2}=5.14\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{s}T2​=5.14\textmus) for Nd3+{\mathrm{Nd}}^{3+}Nd3+ measured at 1.6 K. Further, we investigate time-dependent homogeneous linewidth broadening due to spectral diffusion and the dependence of the homogeneous linewidth on magnetic field to get additional clarity of mechanisms that can influence the coherence time. In light of our results, we discuss two applications: single qubit-state readout and a Fourier-limited single photon source.
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%.
Erbium-doped solids are a promising platform for quantum technology due to the Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ 1.5-\textmu{}m optical transition in the telecom C band that can offer long coherence times. To characterize the intrinsic C2{\mathrm{C}}_{2}C2​ site of Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ in Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ for quantum information and photonic signal-processing applications, absorption and site-selective fluorescence spectroscopy were used to assign the Er3+4I15/2\mathrm{E}{\mathrm{r}}^{3+}\phantom{\rule{4pt}{0ex}}^{4}I_{15/2}Er3+4I15/2​$\ensuremath{\leftrightarrow}$4I13/2^{4}I_{13/2}4I13/2​ transitions. The lowest-to-lowest transition occurs at 1535.608 nm and laser absorption determined an inhomogeneous linewidth of 780 MHz in a 0.005%-doped crystal at 3.4 K. Time-resolved fluorescence established an upper limit for the excited-state lifetime of 8.5 ms. Angular-dependent Zeeman absorption was used to determine ground- and excited-state ggg tensors. The C2{\mathrm{C}}_{2}C2​-site ggg tensor components for the ground state are gx=1.60{g}_{x}=1.60gx​=1.60, gy=4.71{g}_{y}=4.71gy​=4.71, and gz=11.93{g}_{z}=11.93gz​=11.93 with a tipping angle of \ensuremath{\alpha} = $2.{06}^{\ensuremath{\circ}}$, whereas for the excited state the components are gx=1.08{g}_{x}=1.08gx​=1.08, gy=4.36{g}_{y}=4.36gy​=4.36, and gz=10.07{g}_{z}=10.07gz​=10.07 with a tipping angle of \ensuremath{\alpha} = $\ensuremath{-}11.{7}^{\ensuremath{\circ}}$. Optical decoherence can be suppressed by the application of a magnetic field parallel to $\ensuremath{\langle}111\ensuremath{\rangle}$ crystal axes where all C2{\mathrm{C}}_{2}C2​ sites become nearly magnetically equivalent with large ggg values so that spin flips of neighboring Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ ions can be simultaneously suppressed. Using this magnetic field direction, two-pulse photon echoes gave a homogeneous linewidth of 5 kHz for an applied magnetic field of 0.5 T, narrowing and saturating at 2.5 kHz at 3.5 T. Decoherence over intermediate magnetic fields was described by spectral diffusion due to $\mathrm{E}{\mathrm{r}}^{3+}\text{\ensuremath{-}}\mathrm{E}{\mathrm{r}}^{3+}$ magnetic dipole interactions driven by the direct phonon process. With Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+:Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ absorption at a convenient telecom laser wavelength and the ability to fabricate waveguides, our study suggests that this is a promising material system for quantum information and spectral hole-burning signal-processing applications.
We identify and analyze dephasing mechanisms that broaden the optical transitions of rare-earth ions in randomly oriented transparent ceramics. The study examines the narrow $^{7}F_{0}\phantom{\rule{4pt}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{4pt}{0ex}}^{5}D_{0}$ transition of Eu3+{\mathrm{Eu}}^{3+}Eu3+ dopants in a series of Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ ceramic samples prepared under varying conditions. We characterize the temperature and magnetic field dependence of the homogeneous linewidth, as well as long-term spectral diffusion on time scales up to 1 s. The results highlight significant differences between samples with differing thermal treatments and Zr4+{\mathrm{Zr}}^{4+}Zr4+ additive concentrations. In particular, several distinct magnetic interactions from defect centers are observed, which are clearly distinguished from the broadening due to interactions with two-level systems and phonons. By minimizing the broadening due to the different defect centers, linewidths of the order of 4 kHz are achieved for all samples. The linewidths are limited by temperature-dependent interactions and by an interaction that is yet to be identified. Although the homogeneous linewidth can be narrowed further in these ceramic samples, the broadening is now comparable to the linewidths achieved in rare-earth-ion--doped single crystals. Thus, this work emphasizes the usefulness of studying ceramics to gain insights into dephasing mechanisms relevant to single crystals and suggests that ceramics may be an interesting alternative for applications in classical and quantum information processing.
Microwave and optical transitions of rare-earth ions enable microwave-to-optical frequency transduction. This transduction is a coherent process; therefore, the narrow linewidths and long coherence times of rare-earth ions are crucial for achieving efficient frequency conversion. Particularly long coherence times can be achieved with small-spin materials, as unpaired electronic and nuclear spins introduce magnetic noise, serving as a decoherent source of the transitions. However, complete spin-free rare-earth materials cannot exist without charge compensation. Consequently, residual spins in existing rare-earth materials act as a bottleneck, limiting both their spin and optical coherence times. Rather than focusing on nearly spin-free materials, this thesis investigates the microwave and optical transitions of rare-earth ions in materials that are fully concentrated with electronic spins. Recent studies on rare-earth magnetic materials have demonstrated narrow optical linewidths resulting from magnetic ordering and a particularly strong coupling between microwave cavity modes and the collective excitations of rare-earth ions. Although these recent studies are noteworthy, the energy-level transitions, especially optical transitions, of rare-earth ions in magnetic materials remain largely unexamined. In this thesis, various spectroscopic studies are employed to characterise their transition properties and to develop a model of energy levels. The model presented is expected to be applicable to other rare-earth magnetic materials, thereby opening avenues for further investigation in this class of systems. Two types of rare-earth magnetic materials are investigated: neodymium gallate with a stoichiometric concentration of neodymium ions, and gadolinium vanadate doped with a low (ppm) concentration of erbium ions. Microwave and optical transmission spectroscopy are employed under externally applied magnetic fields to characterise the energy-state transitions of the rare-earth ions in both materials. The magnetic phases and corresponding spin configurations influence the observed spectra, making conventional approaches to spectral simulation inadequate. To address this challenge, mean field and magnon-coupled crystal-field models are developed in this thesis to predict magnon and optical transition spectra. These simulations exhibit good agreement with experimental results, allowing for the characterisation of transition properties. Following the characterisation of the material, a new transduction approach is introduced, developed, and implemented using doped rare-earth ions in a magnetic material. In this scheme, coherent conversion between microwave and optical modes is achieved by exciting an optical transition of the doped ions.
This thesis presents a spectroscopic study of Pr3+ ions in a novel passive waveguide architecture. To make this structure, the high refractive glass TeO2 was selected as the thin film and it was deposited on a Pr3+:Y2SiO5 crystal. In this waveguide, the 3H4 to 1D2 transition of Pr3+ ions were probed by the optical evanescent field extending into the substrate. The main concern in assessing the suitability of this material for quantum information applications was ensuring that the coherence properties of rare-earth ions, making them suitable for quantum information purposes, are preserved in this architecture. After which, to make low loss devices with these waveguides, efficient coupling techniques had to be developed. To prove that the coherence properties of the rare-earth ion doped crystal were preserved, the critical parameters of inhomogeneous linewidth, the absorption of the ions, the coherence time and spin lifetimes of the Pr3+ ions were studied. The inhomogeneous linewidth of evanescent coupled ions was about 10.0 GHz, which was consistent with the linewidth of bulk samples with the same Pr3+ doping concentration (Hedges, 2011). The absorption due to the evanescent coupling was 9.38 dB, approximately 90% of what was expected with respect to the bulk crystal with the same doping concentration. Therefore, despite using the evanescent field, the absorption is high enough for quantum memory applications. An optical coherence time of about 121 microseconds was measured, which corresponded to a homogeneous linewidth of about 2.6 kHz. This is very close to bulk sample measurements of 111 microseconds, with the same temperature and doping concentration (R. W. Equall, 1995). The spin state lifetime observed was about 9.8 s, which is also very close to the bulk sample measurement of 8.67 s (Mieth, 2016). Initial Stark shifting experiments were performed to determine whether the active ions in the substrate of the passive waveguides could be electrically controlled by applying a small voltage to electrodes on the thin film. In these experiments with a voltage change of 100 mV, the measured holewidth broadening was increasing about 0.55 MHz, which was similar to the calculated values of 0.45 MHz. The Stark coefficient for site 1 was 51.6 kHzcm/V along the D2 axis of the crystal (site 1 will be explained in Section 4.3). (F.R. Graf, 1997). Prism coupling and grating coupling were used to couple light to the ions in the substrate. Prism coupling is an easy and quick method to couple light into a waveguide and observe the properties of the system. However, grating coupling is much more practical when moving towards building a device using this method. The measurements described above indicated that the properties of ions interacting with the evanescent tail of the waveguide mode were consistent with those of bulk ions. This investigation also showed that depositing a glass thin film on a rare-earth ion doped crystal was not affecting the good coherence properties of the substrate. These results establish the foundation for large, integrated, controllable and high performance rare earth ion quantum waveguide systems.
Inhomogeneous and homogeneous linewidth are reported in a Eu3+{}^{3+}3+ doped transparent Y2{}_{2}2​O3{}_{3}3​ ceramic for the 7{}^{7}7F0{}_{0}0​-5{}^{5}5D0{}_{0}0​ transition, using high-resolution coherent spectroscopy. The 8.7-GHz inhomogeneous linewidth is close to that of single crystals, as is the 59-kHz homogeneous linewidth at 3 K (T2{T}_{2}T2​ === 5.4 $\ensuremath{\mu}$s). The homogeneous linewidth exhibits a temperature dependence that is typical of a crystalline environment, and additional dephasing observed in the ceramic is attributed to magnetic impurities or defects introduced during the synthesis process. The absence of Eu3+{}^{3+}3+segregation at the grain boundaries, evidenced through confocal microfluorescence, further indicates that the majority of Eu3+{}^{3+}3+ions in the ceramic experience an environment comparable to a single crystal. The obtained results suggest that ceramic materials can be competitive with single crystals for applications in quantum information and spectral hole burning devices, beyond their current applications in lasers and scintillators.