Rare-earth doped transparent ceramics for spectral filtering and quantum information processing

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single crystals are very difficult to grow due to their high melting temperature (2400 • C) and phase transition below the melting point, resulting in uncontrolled variations in properties. 19Transparent Y 2 O 3 ceramics could be an alternative to single crystals, and indeed, we measured Γ h = 59 kHz in a 0.1% Eu:Y 2 O 3 sample. 12Although this value is still on the higher side of values measured on single crystals, it suggests that ceramics could be useful for applications in spectral filtering and QIP.
Here, we provide further evidence for the potential of these materials.In transparent 0.5 and 1 at.% Eu 3+ -doped yttria ceramics, we demonstrate an order of magnitude decrease in homogeneous linewidth and a factor of three increase in peak absorption compared to our previous results.Moreover, we measure for the first time the spectral hole lifetime in a ceramic and find that it can exceed 15 min at 6 K, which enables the efficient optical pumping necessary for spectral filtering and QIP applications.
The transparent ceramics were prepared according to the procedure described in Ref. 12 with 99.999% pure Y 2 O 3 and 99.99% pure Eu 2 O 3 powders.0.5 at.% ZrO 2 was added to some samples in order to reach higher transparency, as in ceramics used as laser gain media. 23Grain sizes were determined by optical microscopy.An average grain size of about 2 µm was observed at the center of all ceramics where the optical measurements were carried out.X-ray diffraction data were collected on a Bruker D8 Advance with focusing Bragg-Brentano geometry.Y 2 O 3 crystallizes in the rare-earth sesquioxide C-type structure, space group Ia 3. Eu 3+ can occupy two sites of C 2 and S 6 symmetries and all optical experiments were performed on the former, for which electric dipole transitions are stronger.Crystal structure refinement was carried out via Rietveld analysis using TOPAS 4.2 24 together with the fundamental parameter approach. 25The samples were single phase and showed very sharp reflections, which were narrower than those of the reference standard LaB 6 , and strain was negligible within the resolution of the instrument.Crystallite sizes were found to be larger than 1 µm, in agreement with optical microscopy results.Refined lattice constants are given in Table I.An increase of a with increasing Eu 3+ concentration is observed as expected from the slightly larger effective ionic radius of Eu 3+ compared to Y 3+ (IR (Eu 3+ , VI): 0.950 Å, IR (Y 3+ , VI): 0.892 Å 26 ).This finding, together with the observation of very narrow reflections, suggests that Eu 3+ is well incorporated into the crystallites.Substitution of Y 3+ by Zr 4+ (IR 0.72 Å, VI) leads to a small decrease in a.
Measurements of the inhomogeneous and homogeneous linewidths as well as the hole lifetime were carried out.Inhomogeneous linewidths of the 7 F 0 → 5 D 0 transition were recorded in transmission using a cw dye laser with a 1-MHz linewidth centered at 580.87(5) nm (vacuum).They were recorded at 15 K and at low laser intensity (∼2 mW/cm 2 ) to avoid hole burning and transition saturation effects.Homogeneous linewidths were determined by two pulse photon echo experiments at the center of the 7 F 0 → 5 D 0 transition, while the laser was scanning 1 GHz in ∼3 s to minimize hole burning.The length of the exciting and rephasing pulses was 3.1 and 4 µs, respectively.A single exponential decay of the photon echo intensity as a function of pulse separation was observed.In order to measure the lifetime of spectral holes, first, a spectral hole was burned into the absorption line and afterwards scanned every 60 s with a weak intensity and 1 ms long laser pulse.
Values for the transmission at 580 nm are given in Table I.Reflection losses of about 10% are expected at each surface due to the yttria refractive index at 580 nm n = 1.9318.The transmission of approximately 70% found in the samples with additives is therefore not far from the theoretical limit of 81%, whereas ceramics without additives show a transmission of only 40%-50%.Thus, as expected, the use of additives leads to a significant reduction in scattering losses.In Fig. 1, the inhomogeneous linewidths Γ inh obtained for the ceramics are compared to those found in the single crystal fibers studied in Ref. 19.For comparison, we also measured the laser absorption spectrum of a bulk 0.3% Eu 3+ :Y 2 O 3 single crystal sample where we observed an inhomogeneous linewidth of 7.2 GHz.The observed inhomogeneous linewidths Γ inh for samples without additives are within the range of those observed for single crystals (Table I).Interestingly, for the 1% doped ceramic, Γ inh = 24.2GHz is close to the value of 19.5 GHz found in the 0.5% one.This suggests that the linewidth is only partly due to the mismatch between Eu 3+ and Y 3+ effective ionic radii (Ref.26).Because of the weak dependence of Γ inh on Eu 3+ concentration, peak absorption coefficients of 1.6 cm −1 were observed in the 1% doped ceramic, about three times higher than that found in a 0.1% doped sample. 12The product Γ inh × α scales linearly with Eu 3+ concentration, indicating that the transition oscillator strength does not vary significantly with doping concentration.Table I also shows that the addition of 0.5% ZrO 2 during the synthesis leads to a very large broadening of the absorption line and a corresponding decrease in the peak absorption coefficient.This is explained by both the charge and ionic radii mismatches between Zr 4+ and Y 3+ ions (see discussion above and Ref. 16).Thus, while addition of 0.5% ZrO 2 decreases scattering losses, it also leads to a factor of three increase in linewidth and a strong reduction of the peak absorption coefficient.Such a low absorption would make spectral filtering or quantum storage rather inefficient.A lower level or different additives 23 could lead to a better compromise between transparency and absorption.
][29] The extrapolated zero power homogeneous linewidths are Γ h = 7.5 ± 0.2 kHz (corresponding to a coherence lifetime T 2 = 1/(πΓ h ) of 42 µs) at 3.5 K.The same value was found for the 1.0% sample without additives, while the 0.5% sample with additives showed a slightly larger homogeneous linewidth of 9.2 ± 0.6 kHz (T 2 = 35 µs).Even though those homogeneous linewidths are still about one order of magnitude larger than that observed in the very best crystal known (Γ h = 760 Hz), 20 they are in the lower range of values observed for Eu 3+ :Y 2 O 3 crystals (Γ h = 2.4 − 42 kHz 19 ) and considerably narrower than that previously reported in transparent ceramics Γ h = 59 kHz. 12he contribution to the homogeneous linewidth Γ h from the excited state population is given by Γ pop = 1/(2πT 1 ).The excited-state lifetimes measured in the ceramic samples (Table I) are similar to those reported for single crystals. 19Thus, Γ pop is less than 200 Hz and therefore much smaller than the observed Γ h .Other possible contributions to Γ h are dynamic structural fluctuations due to tunneling between configurations with nearly equal energy referred to as two-level systems (TLSs).However, a considerable influence of this process, usually found in disordered environments like amorphous solids, can be excluded on the basis of the temperature dependence of the homogeneous linewidth (Fig. 3).Indeed, in case of pronounced TLS influence, a "quasi-linear" temperature dependence of Γ h in the low temperature regime is expected. 19Here, a behavior similar to that of single crystals is observed (Fig. 3) with a nearly flat region up to 9 K followed by a steep increase due to phonon scattering typical of single crystals. 19The same result was also previously obtained in the 0.1% Eu 3+ doped transparent ceramics. 12he remaining contribution to Γ h at low temperature should come from electronic and nuclear spin fluctuations. 1As the magnetic moments of Y 3+ and O 2− are both small, the influence of spin fluctuations Γ ion−s pin in pure Y 2 O 3 is predicted to be small, as evidenced by the observation of very long T 2 in one single crystal. 20Given the low Eu 3+ magnetic moment, Eu-Eu spin interactions are also unlikely to be a limitation even at a concentration of 1%, as observed in Eu 3+ :Y 2 SiO 5 . 16he additional dephasing in the ceramics is therefore attributed to magnetic impurities, e.g., very small amounts of transition metal ions or defects. 12,19,30,31This is in very good agreement with the presence of electron spin impurities (probably transition metal ions) detected by electron paramagnetic resonance for previous samples 12,32 with larger Γ h .For the samples studied here, these impurities could not be detected, presumably because of the higher purity of the Y 2 O 3 starting material (99.999% vs. 99.99%).This is likely to be the reason for their narrower Γ h , although other defects (produced, e.g., during thermal treatments) could also play a role.The fact that T 2 does not significantly vary for samples with additive also suggests that T 2 is still limited by paramagnetic impurities or defects in the samples studied here.Indeed, additional dephasing due to 91 Zr 4+ nuclear spins (I = 5/2, abundance 11.2%) is not observed.
Finally, we studied the persistent spectral hole lifetime in a 0.5% Eu 3+ :Y 2 O 3 sample without additives.The decay of the spectral hole depth at 6 K is shown in Fig. 4.An exponential fit the data gives T hole = 15 ± 5 min.As the holes were several MHz wide due to laser jitter, T hole is unlikely to include a contribution from spectral diffusion.The ratio T hole /T 1 = 9 × 10 5 is high enough to lead to negligible residual ground state population after optical pumping. 17,21This conclusion would hold even better at lower temperatures, as at 3.5 K the hole depth showed no decay within 30 min.We note that the hole lifetime at 6 K is shorter than that of the single crystal studied in Ref. 21 (≈54 h at 6 K), which could be due to interactions with small amounts of flipping magnetic impurities or defects.
In conclusion, we have observed homogeneous linewidths below 10 kHz in Y 2 O 3 transparent ceramics doped with 0.5 and 1% Eu 3+ .This is about one order of magnitude lower than values previously reported in ceramics.The higher Eu 3+ concentration also increases the peak absorption coefficient to a value of 1.6 cm −1 at 580.87 nm with an inhomogeneous broadening of 24.2 GHz for the 1% Eu-doped samples.Hole lifetimes of 15 ± 5 mn have been obtained, allowing for efficient optical pumping and spectral tailoring.Together, these results suggest that high quality transparent ceramics can meet the requirements of spectral filtering and quantum information processing applications, while providing advantageous structural properties (e.g., complex shaping) compared to single crystals.

TABLE I .
5efined lattice constants of Eu 3+ :Y 2 O 3 transparent polycrystalline ceramics (space group Ia 3), room temperature transmission extrapolated at 580 nm without taking Eu 3+ absorption into account (sample thickness: 6.1 mm), absorption coefficients for the center of the 7 F 0 → 5 D 0 line at 15 K, inhomogeneous linewidths at 15 K,5D 0 excited state lifetimes T 1 , and coherence lifetimes T 2 .FIG. 1. Γ inh of Eu 3+ : Y 2 O 3 transparent ceramics and crystals.Values of the 0.1% Eu 3+ :Y 2 O 3 ceramic and the single crystal fibers are taken from Refs. 12 and 19.