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We investigate the erbium flip-flop dynamics as a limiting factor of the electron spin lifetime and more generally as an indirect source of decoherence in rare-earth doped insulators. Despite the random isotropic arrangement of dopants in the host crystal, the dipolar interaction strongly depends on the magnetic field orientation following the strong anisotropy of the $g$-factor. In Er$^{3+}$:Y$_2$SiO$_5$, we observe by transient optical spectroscopy a three orders of magnitude variation of the erbium flip-flop rate (10ppm dopant concentration). The measurements in two different samples, with 10ppm and 50ppm concentrations, are well-supported by our analytic modeling of the dipolar coupling between identical spins with an anisotropic $g$-tensor. The model can be applied to other rare-earth doped materials. We extrapolate the calculation to Er$^{3+}$:CaWO$_4$, Er$^{3+}$:LiNbO$_3$ and Nd$^{3+}$:Y$_2$SiO$_5$ at different concentrations.

With their optical wavelength in the near infrared (790-800nm) and their unique spectroscopic properties at cryogenic temperatures, thulium-doped crystals are at the center of many architectures linked to classical signal processing and quantum information. In this work, we focus on Tm-doped YSO, a compound that was left aside in the mid-1990s due to its rather short optical coherence lifetime. By means of time-resolved hole-burning spectroscopy, we investigate the anisotropic enhanced nuclear Zeeman effect and demonstrate deep, sub-MHz, persistent spectral hole burning under specific magnetic field orientation and magnitude. By estimating the experimental parameters corresponding to a real-scale ultrasound optical tomography setup using Tm:YSO as a spectral filter, we validate Tm:YSO as a promising compound for medical imaging in the human body., Comment: 8 pages, 11 figures

Nanostructured rare-earth-ion-doped materials are increasingly being investigated for on-chip implementations of quantum information processing protocols as well as commercial applications such as fluorescent lighting. However, achieving high-quality and optimized materials at the nanoscale is still challenging. Here we present a detailed study into the restriction of phonon processes in the transition from bulk crystals to small ($\ensuremath{\le}40$-nm) nanocrystals by observing the relaxation dynamics between crystal-field levels of ${\mathrm{Tb}}^{3+}:{\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$. We find that the population relaxation dynamics are modified as the particle size is reduced, consistent with our simulations of inhibited relaxation through a modified vibrational density of states and hence modified phonon emission. However, our experiments also indicate that nonradiative processes not driven by phonons are also present in the smaller particles, causing transitions and rapid thermalization between the levels on a time scale of $l100\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$.

Anisotropy of the quadratic Zeeman effect for the $^{3}\mathrm{H}_{6}\ensuremath{\rightarrow}^{3}\mathrm{H}_{4}$ transition at 793 nm wavelength in $^{169}\mathrm{Tm}^{3+}\text{-doped} {\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$ is studied, revealing shifts ranging from near zero up to $+4.69\phantom{\rule{0.28em}{0ex}}{\mathrm{GHz}/\mathrm{T}}^{2}$ for ions in magnetically inequivalent sites. This large range of shifts is used to spectrally resolve different subsets of ions and study nuclear spin relaxation as a function of temperature, magnetic field strength, and orientation in a site-selective manner. A rapid decrease in spin lifetime is found at large magnetic fields, revealing the weak contribution of direct phonon absorption and emission to the nuclear spin-lattice relaxation rate. We furthermore confirm theoretical predictions for the phonon coupling strength, finding much smaller values than those estimated in the limited number of past studies of thulium in similar crystals. Finally, we observe a significant---and unexpected---magnetic field dependence of the two-phonon Orbach spin relaxation process at higher field strengths, which we explain through changes in the electronic energy-level splitting arising from the quadratic Zeeman effect.