Inhomogeneous linewidths and Raman spectroscopy 

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The host studied in this work: yttrium oxide (Y2O3 )

Metal oxides have a large field of applications in several fields, such as catalysis, coating, electrochemistry, optical fibers, sensors, batteries etc. [76–78].
In particular, yttrium oxide materials are interesting for several applications such as infrared windows, high-power lasers, radiation detection and in particular phosphors [79, 80]. Recently, it was shown in our group that Eu3+:Y2O3 could also have applications in quantum information applications [46]. In addition, particles of this host can easily be synthesized by several bottom-up routes. This last point is very important because some systems, such as Eu3+:YSO, do not easily form dispersed crystalline particles from chemical routes.
As the majority of RE sesquioxides, Y2O3 can crystallize as cubic phase, with Ia-3 space group. Cubic Y2O3 has a high dielectric constant from 14 to 18, a large bandgap of 5.8 eV and also optical isotropy, with a refractive index of 1.91 in the visible range. In addition, this system shows high chemistry and thermal stabilities because of the high melting point, about 2400 oC. The dominant phonon energy is 380 cm−1 with a cuto↵ value of 600 cm−1, which is one of the lowest phonon energies among oxides materials [80]. The cubic Y2O3 phase has two cationic sites in which the lanthanides preferentially enter. This Y2O3 unit cell consists of 32 octahedrally coordinated cation sites, that is 24 sites with C2-symmetry and 8 sites with C3i-symmetry (or S6) (Figure 2.6).

Eu3+:Y2O3 materials

Lanthanide-activated rare earth oxides remain promising materials for nextgeneration display technology because of several important properties, such as luminescent characteristics, stability in vacuum, and corrosion-free gas emission under electron bombardment compared with traditional cathode ray tube red phosphors used in current field emission displays [85–88]. In particular, Eu3+:Y2O3 is a commercial available phosphor with extremely high quantum efficiency. The combination of an efficient red emission and long-term stability have wide commercial application in high resolution and projection TV, projection devices, plasma display panels and field emission displays [89, 90].
In general, Ln3+ ions have been found to be randomly distributed in both C2 and C3i sites in Y2O3 single crystals [91], although a preferential occupation of the C2 site was suggested in the case of Gd3+ and Eu3+ [92, 93]. According to the Judd-Ofelt theory, the electric dipole transitions are not allowed for the Eu3+ ions occupying the C3i sites since it is the odd parity crystal field components that mix the 4fn configuration to opposite parity ones. In centrosymmetric Ln3+ complexes, only the vibronic coupling mechanism can induce f-f electric-dipole intensity. Therefore, it can be assumed that the major contribution to the intensity of the observed transitions originates from the Eu3+ ion is the C2 sites in which electric dipole transitions are allowed.
Eu3+:Y2O3 bulk crystals show low nuclear moment density, low inhomogeneous broadening and long coherent optical T2, which are fundamental features for QIP applications [22, 24]. The main characteristics of Eu3+ are summarized in Table 2.1.

State of the art of Eu3+:Y2O3 bulk and nanocrystals

As introduced previously, RE atoms doped into various hosts are known to exhibit very sharp optical lines, especially at low temperatures. Among several materials, Eu3+:Y2O3 bulk crystals stand out because of its kilohertzscale homogeneous linewidth for liquid helium temperatures [22]. Macfarlane and Shelby probed T2 lifetimes by photon echo technique at low temperature for Eu3+:Y2O3 single crystal prepared by Verneuil method. These authors found 510 μs for the optical coherence lifetime of the 7F0-5D0 transition, which is the longest coherence lifetime seen for Eu3+:Y2O3 , corresponding to 600 Hz of homogeneous linewidth [22]. Babbit and coauthors have reported at liquid-helium temperatures 10 GHz inhomogeneous absorption widths for 7F0 !5 D0 transition in 2.0 at.% Eu3+:Y2O3 and an homogeneous linewidth around 2.5 kHz [23]. Flinn and coauthors have done two-pulse photon echo measurements on Eu3+:Y2O3 samples prepared under di↵erent crystal-growth techniques, founding additional sample-dependent contribution to the homogeneous broadening in comparison with a crystal growth by the flame fusion technique. The broadening found is not correlated with Eu3+ concentration in the matrix, suggesting the presence of disorder in samples with large homogeneous linewidths [94]. The homogeneous linewidth values found in Flinn’s work are showed in Table 2.2.

Synthesis of Eu3+:Y2O3 particles

Y(NO3)3.6 H2O (99.9% pure, Alfa Aesar) and Eu(NO3)3.6 H2O (99.99% pure, Reacton) were used as yttrium and europium sources, respectively. The Eu3+ concentrations used were varied between 0.3 and 5.0 at. %. In a typical synthesis, an appropriate amount of urea (CO(NH2)2, 99% pure, Sigma) was dissolved in a mixed Eu/Y aqueous nitrate solutions to make a total solution volume of 800 mL. The concentrations varied as 0.3, 0.5, 2.0 and 3.0 mol.L−1 for urea and 7.5 mmol.L−1 for metals (Eu3+ and Y3+).
The mixed solutions were heated at 85 oC for 24 h in a Teflon reactor. After this reaction time, the final suspensions were cooled to ambient conditions and the colloidal particles collected via centrifugation. The wet precipitates were washed with distilled water once to remove the byproducts, then rinsed twice with absolute ethanol, and dried at 80oC for 24 h to yield a Eu3+: Y(OH)CO3 powder. The Eu3+:Y2O3 samples were obtained by calcination of these original powders [Eu3+:Y(OH)CO3 . n H2 O] under air during di↵erent times at temperatures ranging from 900 to 1200 oC, which were reached using a heating rate of 3 oC min−1. A simple summary of this experimental procedure is presented in the Figure 3.1.

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Structural characterization: Eu3+:Y(OH)CO3

Monodispersed spherical particles with a chemical composition of Eu3+ doped yttrium basic carbonate [Eu3+:Y(OH)CO3 . n H2 O] were synthesized by the homogeneous precipitation method. In this synthesis urea is added to RE salts (nitrate and chloride) and the solution is aged at temperatures between 70 and 90 oC. The molar ratio between urea and RE salts strongly influences morphology and size of products. Other parame3.3. ters like reaction time, type of precursor anions and initial pH solution, can also a↵ect the size, morphology and kinetics of Eu3+:Y(OH)CO3 particle formation. Here, metal nitrates were used instead of chlorides in order to avoid any Cl− contamination in the final product, since NO−3 species are eliminated with thermal treatments at high temperatures. RE cations precipitate with anions such as CO2− 3 and OH− produced by the dissolution of urea and forming an amorphous [Eu3+:Y(OH)CO3 . n H2 O] compound.
The precipitation is done homogeneously due to slow decomposition of urea. Reactions involved in this synthesis route, initially proposed by Aiken and Matijevi´c, are shown below [123]: Urea decomposition (NH2)2CO ⌦ NH+ 4 + OCN−.

Table of contents :

1 Introduction 
1.1 Quantum information processing (QIP)
1.2 Main requirements for QIP
Dynamical interactions
1.3 Motivation to work at the nanoscale
1.4 Thesis goals
2 High resolution and coherent spectroscopy of Eu3+:Y2O3 materials 
2.1 Rare earth doped materials
2.1.1 Rare earth ions
2.1.2 The free-ion Hamiltonian
2.1.3 The crystal field
2.1.4 Intensities of rare-earth optical transitions
2.2 The host studied in this work: yttrium oxide (Y2O3 )
2.3 Eu3+:Y2O3 materials
2.4 State of the art of Eu3+:Y2O3 bulk and nanocrystals
2.5 Conclusions
3 Synthesis and Structural Characterization 
3.1 Synthesis of Eu3+:Y2O3 particles
3.2 Characterization techniques
3.3 Structural characterization: Eu3+:Y(OH)CO3
3.3.1 Mechanism of particle formation
3.3.1.1 E↵ect of aging time
3.3.1.2 E↵ect of reactional temperature
3.3.1.3 E↵ect of metal concentration
3.3.1.4 E↵ect of urea concentration
3.3.1.5 E↵ect of Eu3+ concentration
3.4 Structural characterization: Eu3+:Y2O3
3.4.1 E↵ect of annealing time
3.4.2 E↵ect of annealing temperature
3.4.3 E↵ect of Eu3+ concentration
3.4.4 Crystallite size estimation of Eu3+:Y2O3 particles
3.4.4.1 Crystallite size estimation as a function of [Eu3+]
3.5 Conclusion
4 Inhomogeneous linewidths and Raman spectroscopy 
4.1 Characterization Techniques
4.1.1 Optical inhomogeneous linewidth measurements
4.1.2 Raman spectroscopy measurements
4.1.3 Electron paramagnetic resonance (EPR)
4.2 Optical inhomogeneous linewidths
4.2.1 E↵ect of particle and grain sizes
4.2.2 E↵ect of annealing time for thermal treatments at 1200 !C
4.2.3 E↵ect of Eu3+ concentration
4.3 Raman spectroscopy
4.3.1 E↵ect of particle and grain sizes
4.3.2 E↵ect of Eu3+ concentration
4.4 Electron Paramagnetic Resonance (EPR)
4.5 Conclusion
5 Emission spectroscopy 
5.1 Characterization Techniques
5.2 Fluorescence spectroscopy
5.2.1 Emission spectra under excitation of the 7F0!5D2 transition
5.2.2 Emission spectra under excitation of the 7F0!5D0 transition
5.2.3 Emission spectra of Eu3+:Y2O3 single particle under excitation at 7F0 ! 5D1
5.2.4 Emission spectra under excitation in the ultraviolet .
5.3 Excited state lifetimes
5.3.1 Decay lifetimes of the 5D0 excited level
5.3.2 Decay lifetimes of the 5D2 excited level
5.3.3 Nd3+:Y2O3 particles
5.4 Conclusions
6 Homogeneous linewidths and spectral hole lifetimes 
6.1 Experimental setup
6.1.1 Photon echo sequences
6.1.2 Two-pulse photon echoes (2PPE)
6.1.3 Three-pulse photon echo (3PPE)
6.1.4 Hole burning experiments
6.1.4.1 Measurements on Eu3+:Y2O3 particle ensemble
6.1.4.2 Measurements on small aggregates of Eu3+:Y2O3 particles
6.2 Spectroscopy of 0.5 % Eu3+:Y2O3 sample
6.2.1 0.5 % Eu3+:Y2O3 sample
6.2.2 Two-pulse photon echo
6.2.3 Temperature dependence
6.2.4 Three-pulse photon echo
6.2.5 Holeburning
6.2.6 Hole burning on small Eu3+:Y2O3 aggregates
6.3 E↵ect of material parameters
6.3.1 Particle size
6.3.2 Calcination temperature
6.3.3 Time of annealing
6.4 Conclusion
7 General conclusion 

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