In this Section broadening mechanisms that can be significant to waveguide fab- rication processes are discussed. Fabrication of waveguides has the potential to introduce disorder into the crystal, and introduce excess broadening onto optical and hyperfine transitions. In this Section, I review linewidth broadenings in bulk as a background to broadening in waveguides.
2.5.1
TLS effect on disordered rare-earth crystals
Fiber samples of Eu3+:Y2O3grown by laser-heated pedestal growth and flame fusion were studied using the optical hole burning technique [88]. This study is the most relevant study of TLS for the current work. The optical dephasing of the 7F
0 → 5D
0 transition was analyzed and compared to previous optical photon echo results. Hole burning experiments at low temperature with these samples demonstrated a
§2.5 Observation of broadening associated with disorder in bulk samples 33
diverse range of results that agreed quite well with coherence times observed with the two-pulse photon echo experiments. 10 s after burning a hole, slow and continuous broadening of the spectral hole from 130 kHz to 900 kHz was observed, in which the additional broadening could have been related to disorder modes in the crystalline structure.
The echo decays for Eu3+:Y
2O3 were not exponential showing that the linewidth increased in the measured µs time domain, which was the photon echo time do- main [88]. In the hole burning experiments , the time domain of the experiments were on the scale of 10 ms, and the results were compared with photon echo re- sults. An ultra narrow optical hole with a linewidth of 3.5 kHz was reported in the flame-fusion sample [88].
The hole burning linewidth results in these fiber samples were found to be larger than those obtained from the photon echo experiments. This increase in the linewidth could indicate spectral diffusion, due to the longer time scale of the hole burning experiments. From hole burning experiments performed on one of the fiber samples, a continuous and monotonic increase in the linewidth was observed with increasing the delay between the burn and read pulses. The frequency scale of the spectral diffusion was 2 orders of magnitude higher than what would have been possible if the magnetic interactions with the 89Y nuclear moments were taken into account. The obtained results from these experiments indicated the presence of an additional dynamic process in the fiber samples, which was related to some form of low energy excitation occurring over a long time scale. Comparing the narrow homogeneous linewidths in the fiber samples with glass, could be an indication that the density of two-level systems (TLS) was much less in these crystalline materials or that the average Eu3+ ion was a long way away from any localized dynamic center.
When one moves away from bulk crystal structures to two dimensional systems like nano-crystals or thin films, the properties of the rare-earth may change. One path that was taken in this thesis was to try to grow rare-earth ion single crystalline thin films [23]. The resultant thin films were polycrystalline thin films, and so they may be comparable to nano-crystalline structures.
A study of electron and phonon interaction was carried out by Meltzer et. al, which resulted in the conclusion that the situation changes in nano-crystals where the size of the crystal is extremely small [89]. The particle size and temperature dependency of spectral hole linewidths were examined. The experiments were per- formed on the 7F
nano-particles, the well known T7 low temperature dependency of the homogeneous linewidth was reduced to T3. The experimental results showed that the phonon modes broaden with respect to frequency as ω2. Assuming the nano-particles were spherical, and with ω = 25 cm−1, coherence times of T2 = 40 ns were obtained. The linewidth of the phonon interactions in these nano-particles were determined by comparing the results obtained from experiments and theory calculations. It was predicted, and later shown by experiments, that the hole linewidth is dependent on the size by ≈D−2.5.
2.5.2
Intrinsic disorder of LiNbO
3When doping rare-earth ions into LiNbO3, additional defects are introduced in the lattice that can cause additional strain, change the symmetry of the lattice and alter the coherence properties of the doped rare-earth ion. Furthermore, additional intrin- sic disorder arises from the growth process of bulk LiNbO3 single crystals [90, 91]. These intrinsic defects and disorder of the LiNbO3 crystal lattice lead to a large inhomogeneous broadening of the optical and hyperfine transitions. For exam- ple in a Tm3+:LiNbO
3 crystal, the inhomogeneous broadening was reported to be 300 GHz [92,93]. And for a Pr3+:LiNbO
3 bulk crystal, the combined inhomogeneous linewidth of the two sites of Pr3+ was reported to be about 1500 GHz, which is 1000 times larger than the observed linewidth of Pr3+:Y
2SiO5 [94].
Furthermore, the lattice disorder and strain in rare-earth ion doped LiNbO3, can result in glass like behavior causing a dynamic disorder in these crystals [95, 96, 97]. Also, the nuclear spins in the LiNbO3 crystal lattice results in dynamic magnetic disorder causing additional decoherence in the lattice [65, 98, 99]. It was approximated that the magnetic fluctuations caused by the host ion spins in the crystalline lattice was 30 times higher than Y2SiO5 [94]. This magnetic disorder, can lead to additional spectral diffusion and cause large homogeneous linewidths. For example, the observed homogeneous linewidth in Tm3+:LiNbO3 was increased from 28 KHz to about 50 KHz [94]. Also, the homogeneous linewidth reported in a Pr3+:LiNbO
3 bulk crystal, was observed to be about 80 kHz, which is about 10 times larger than in Pr3+:Y
2SiO5 [94].
From the large inhomogeneous and homogeneous linewidth reported in rare- earth ions of Tm3+ and Pr3+ doped in LiNbO
3 crystals, it can be observed that although high quality waveguides can be fabricated using LiNbO3, it may not be the best host crystal for quantum information devices. The large inhomogeneous linewidths observed in these crystals results in low optical depths compared to rare-