1. Introduction

Rare earth ion doped solids have attracted much attention as optical quantum memory materials [1–6]. The 4f-4f transitions of rare-earth ions have long optical coherence lifetime on the order of tens of microseconds, which enables the transfer of photonic quantum states to atomic states back and forth, constituting a photonic quantum memory. Although research in this field has been focusing on single crystalline materials, rare-earth ion doped polycrystalline ceramics could be alternatives to single crystals [7–13]. In previous work we reported Er³⁺ doped Y₂O₃ transparent ceramics with coherence lifetime (Er^{3+ 4}I_13/2-⁴I_15/2 transition) comparable to that of Er³⁺ doped Y₂O₃ single crystals [12–13]. These Er³⁺ doped Y₂O₃ transparent ceramics were made by sintering Er³⁺ doped Y₂O₃ nanoparticles which were synthesized via a wet-chemistry approach. Such a bottoms-up process offers convenient and low-cost methods to tune ceramic compositions and refractive index for photonic device fabrications.

Ceramic optical waveguides are highly desirable platform for optical quantum memories. Waveguide structures can offer several advantages such as significantly higher optical density, longer interaction length, more robust and compact device packaging, etc. However, fabricating ceramic waveguide quantum memories is challenging. One barrier is to find the proper core and cladding material combination that provides strong optical confinement, and at the same time does not detrimentally affect the optical coherence properties.

We report here a method to tune optical refractive index of Er³⁺ doped Y₂O₃ transparent ceramics without reducing optical coherence lifetime of Er^{3+ 4}I_13/2−⁴I_15/2 transitions. La³⁺ dopants are used as index modifiers to change the refractive index of transparent Y₂O₃ ceramics. We choose La³⁺ because i) La³⁺ can be dissolved into Y₂O₃ at a maximum concentration of about 10% without phase separation based on the phase diagram of Y-La-O system [14], and ii) the 4f orbital of La³⁺ is empty and thus, it has no electronic states or spin states that can strongly interact with Er³⁺. On the other hand, the dominant La isotope is ¹³⁹La, which has a natural abundance of 99.9% and a magnetic moment of 2.7832 ${\mu _N}$. Therefore, there would be some super-hyperfine interaction due to the nuclear spin of La. La³⁺ and Er³⁺ are doped into Y₂O₃ nanoparticles via a solution synthesis method and La³⁺, Er³⁺ co-doped Y₂O₃ transparent ceramics are made by sintering nanoparticles using hot isostatic press (HIP). La³⁺ doping increases optical refractive index of Y₂O₃ ceramics by about Δn = +0.001 per percent of La³⁺ (in molar; based on La/(La + Y)). The incorporation of La³⁺ increases the inhomogeneous linewidth by 2 orders of magnitude, from about 0.5 GHz (0% La³⁺) to 42 GHz (10% La³⁺). On the other hand, La³⁺ doping up to 10% doesn’t increase the homogeneous linewidth. At a temperature of 2 K and in a 0.65 T magnetic field, the homogeneous linewidth of Er³⁺ in La³⁺ doped Y₂O₃ ceramics is about 10 kHz, constituting an inhomogeneous linewidth to homogeneous linewidth ratio of $4\,{\times}\,{10^6}$.

2. Results and discussion

La, Er co-doped Y₂O₃ nanoparticles. La³⁺, Er³⁺ co-doped Y₂O₃ nanoparticles are synthesized by the reaction of urea, LaCl₃, ErCl₃, and YCl₃ in boiled water, followed by thermal annealing. In a typical synthesis, a urea solution (6.7 mol urea in 0.35 L water at 100 ^oC) is poured into a metal salts solution (a mixture of LaCl₃, ErCl₃, and YCl₃, 0.22 mol in 4L water at 100 °C). The reaction is kept at 100 °C for 1 hour. The thermal decomposition of urea provides OH^- and CO₃^2- which bond to metal ions and produce Y_1-x-yLa_xEr_y(OH)CO₃·H₂O amorphous nanoparticles. The amorphous nanoparticles are collected by filtration and are converted into crystalline (Y_1-x-yLa_xEr_y)₂O₃ nanoparticles by thermal annealing in air at 750 °C. The chemical yield is about 95%. The Er³⁺ and La³⁺ doping concentration can be tuned by varying Er/Y and La/Y ratios in the starting materials. All samples discussed in this work have the same Er³⁺ doping concentration of 20 ppm.

Figure 1(a) shows an SEM image of Y₂O₃ nanoparticles doped by 20 ppm Er³⁺ and 2% La³⁺. The nanoparticles are individually about 40 nm and are agglomerated. The particle size doesn’t show a clear change when the La³⁺ doping concentration is varied in a range of 0-10%. Powder X-ray diffraction of 10% La³⁺ doped Y₂O₃ nanoparticles reveals a pure cubic phase. This pattern matches well with a cubic Y₂O₃ phase, but all peaks are slightly shifted (Fig. 1(b)). This indicates that La³⁺ dopants are incorporated into Y₂O₃ lattice and expand the unit cell (La³⁺ is larger than Y³⁺). The unit cell parameter (a-axis) was calculated by Rietveld refinement of XRD patterns. The incorporation of La³⁺ into Y₂O₃ lattice expands cell parameters from 10.6143 ± 0.001 Å (Y₂O₃ nanoparticles), to 10.6275 ± 0.001 Å (2% La³⁺ doping) and 10.6728 ± 0.001 Å (10% La³⁺ doping) (Fig. 1(c)). This is due to the 14% larger ionic radius of La³⁺ (1.160 Å) compared with Y³⁺ (1.019 Å) [15]

 

Fig. 1. a) Scanning electron microscopy images of La³⁺(2%), Er³⁺(20 ppm) co-doped Y₂O₃ NPs. b) Powder X-ray diffraction pattern of La³⁺(10%), Er³⁺(20 ppm) co-doped Y₂O₃ nanoparticles. The red stick pattern corresponds to PDF 00-041-1105 (cubic Y₂O₃). c) Unit cell parameters of Y₂O₃ nanoparticles doped with different concentrations of La³⁺. The unit cell parameters are calculated by Rietveld refinement of XRD patterns.

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La³⁺, Er³⁺ co-doped Y₂O₃ transparent ceramics. Hot isostatic pressing (HIP) is used to sinter La³⁺, Er³⁺ co-doped Y₂O₃ nanoparticles into transparent ceramics. In a typical process, La³⁺, Er³⁺ co-doped Y₂O₃ nanoparticles (2 grams) are pressed into a ¾ inch diameter pellet in a steel die at approximately 8 klb force. This pellet is isostatically pressed at 25 kpsi in a latex isopressing sheath at room temperature, followed by sintering at 1600 °C in air for 2 h. The pellet is then hot isostatically pressed at 1590 °C for 16 h at 29 kpsi under an argon atmosphere. Figure 2(a) shows the optical transmission of a sample with 2% La³⁺ and 20 ppm Er³⁺ after HIP process. The axial transmission through 1.6 mm thickness (50 nm surface roughness) is about 80% in the wavelength range of 1250-2000 nm. This is close to the theoretical limit of Y₂O₃ at 1535 nm (82.7%) when only considering the surface reflections.

 

Fig. 2. a) Axial optical transmission through the thickness (1.6 mm) of a La³⁺(2%), Er³⁺(20 ppm) co-doped Y₂O₃ ceramic sample. A dip at about 850 nm is due to detector switch. b) Optical refractive index of Y₂O₃ transparent ceramics doped with different concentrations of La³⁺.

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La³⁺ doping increases the optical refractive index of transparent Y₂O₃ ceramics by about Δn = +0.001 per molar percent of La³⁺, as shown in Fig. 2(b). The highest La³⁺ doping we have achieved is 10%, which increases the index by 0.009 (Δn/n = 0.48%). Such an index difference can be used to fabricate optical waveguides where the core is La³⁺, Er³⁺ co-doped Y₂O₃ and the cladding is Y₂O₃.

La³⁺ doping significantly reduces the grain size of Y₂O₃ ceramics. Figure 3 shows the grain images of ceramic samples prepared by the same thermal process with different La³⁺ doping concentrations. The average grain area was reduced from 1072 µm² (Y₂O₃) to 398 µm² (1% La³⁺) and 1 µm² (4% La³⁺).

 

Fig. 3. Electron back scattering diffraction (EBSD) images of grains in Er³⁺(20 ppm)-Y₂O₃ transparent ceramics doped with different concentrations of La³⁺. The ceramics are prepared by the same thermal process. The black dots at grain boundaries are where EBSD couldn’t identify crystal orientations. a) Y₂O₃; the average grain area is 1072 µm². b) 1% La³⁺ doping; the average grain area is 398 µm². c) 4% La³⁺ doping; the average grain area is 1 µm². The average grain area is calculated by > 1500 grains. The scale bar is 100 µm in Fig. 3(a) and Fig. 3(b), 10 µm in Fig. 3(c).

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Optical dephasing properties of Er³⁺ in La³⁺ co-doped Y₂O₃ transparent ceramics. Incorporation of La³⁺ significantly increases the static structural disorder of the crystalline structure, due to the different sizes of La³⁺ and Y³⁺ ions and the random substitution. This can be directly observed from the inhomogeneous linewidth increase due to the La³⁺ co-doping (Fig. 4(a)). Here one can see that the inhomogeneous linewidth increases from 0.5 GHz without La³⁺ to about $42\, \pm \,3$ GHz at 10% doping, a 80 times increase. The initial increase is about 8 GHz broadening per percent La³⁺ doping, similar to those observed in Eu³⁺ doped Er³⁺:Y₂SiO₅ [16].

 

Fig. 4. a) Inhomogeneous linewidth ${\Gamma _{inh}}$ of Er³⁺(20 ppm)-Y₂O₃ transparent ceramics co-doped with different concentrations of La³⁺, measured at 1.7 K and zero magnetic field. b) Temperature dependence of the homogeneous linewidth ${\Gamma _h}$ (B = 0.65 T) of Er³⁺(20 ppm)-Y₂O₃ transparent ceramics co-doped with different concentrations of La³⁺.

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To see if La³⁺ co-doping affects the optical dephasing properties of Er³⁺, we measured the homogeneous linewidth $({\Gamma _h})$ of Er^{3+ 4}I_13/2−⁴I_15/2 transition around 1535 nm in Er³⁺, La³⁺ co-doped Y₂O₃ transparent ceramics by two-pulse photon echo spectroscopy (details see Method section) [17], and compared it to the homogeneous linewidth of the Er³⁺ doped Y₂O₃ ceramics without La³⁺ co-dopants. The concentration of Er³⁺ is 20 ppm in all these samples, and all the thermal treatment procedures are the same. As shown in Fig. 4(b), doping La³⁺ into Y₂O₃ does not increase the homogeneous linewidth of Er³⁺, which is about 10 kHz at a temperature of 2 K and in a 0.65 T magnetic field. There is a small variation of linewidth for different La³⁺ doping concentration. However, it does not show a definite trend, and we suspect it is mainly caused by sample to sample variation. Nevertheless, previous reports have observed decreased linewidths in Eu³⁺ co-doped Er³⁺:Y₂SiO₅ and Sr³⁺ co-doped Eu³⁺/Y₂O₃ [16,18–19]. They were attributed to increased broadening of spin transition, which resulted in less resonant spin-spin interaction between Er³⁺ or Eu³⁺ ions.

3. Conclusions

La³⁺ is used as an index modifier to tune refractive index of Er³⁺ doped Y₂O₃ transparent ceramics. La³⁺ and Er³⁺ are incorporated into Y₂O₃ through a solution-phase nanoparticle synthesis and transparent ceramics are made by sintering La³⁺, Er³⁺ co-doped Y₂O₃ nanoparticles. A maximum of 10% La³⁺ can be dissolved in Y₂O₃ ceramics without phase separation. La³⁺ doping increases optical refractive index of Y₂O₃ by about 0.001 per molar percent of La³⁺, but doesn’t influence the homogeneous linewidth of Er^{3+ 4}I_13/2-⁴I_15/2 transition. The homogeneous linewidth of La³⁺, Er³⁺ co-doped Y₂O₃ transparent ceramics is about 10 kHz at 2 K and in a 0.65 T magnetic field, which is close to the reported homogeneous linewidth of Er³⁺ doped Y₂O₃ ceramics and single crystals. This work opens broad opportunities for making ceramic optical waveguides for quantum memory applications.

4. Methods

Materials. YCl₃·6H₂O (99.9%), ErCl₃·6H₂O (99.995%), LaCl₃·7H₂O (99.999%) and urea (99.0-100.5%) are purchased from Aldrich and used as received.

Optical Inhomogeneous Broadening Measurement. The inhomogeneous linewidth $({\Gamma _{inh}})$ is measured directly using an optical spectrum analyzer (OSA), except the one without La³⁺ co-doping, which was measured using a scanning laser. For all inhomogeneous linewidth measurement, the sample is measured at zero field and 1.7 K to minimize the broadening due to inhomogeneous Zeeman splitting or phonon broadening.

Optical Homogeneous Broadening Measurement. The homogeneous linewidth (Γ_h) of Er^{3+ 4}I_13/2-⁴I_15/2 transition at 1534.94 nm in Er³⁺, La³⁺ co-doped Y₂O₃ transparent ceramics is measured by the two-pulse photon echo technique. The sample is placed in the Oxford Instruments Spectromag SM4000, with a pair of superconducting magnets. The light source is a tunable diode laser (Toptica DLpro) with <50 kHz linewidth. The light is temporally shaped by an acoustic-optic modulator (AOM, pulse width 50 ns), before being amplified by a fiber amplifier. The energy of the input pulse is carefully controlled so that there is no gain depletion seen from pulse to pulse. The output is filtered through a 1 nm bandpass filter and an electro-optic modulator (pulse width 50 ns) to cutoff amplified spontaneous emission from the amplifier. The beam is focused down to a spot of ∼50 µm. The input peak intensity on the sample is about a few kW/cm². The resulting echo is filtered through a second electro-optic modulator, and detected by an InGaAs avalanche photo-diode and averaged on the oscilloscope.