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We report a series of measurements of the effect of an electric field on the frequency of the ultranarrow linewidth $^7F_0 \rightarrow$ $^5D_0$ optical transition of $\rm Eu^{3+}$ ions in an $\rm Y_2SiO_5$ matrix at cryogenic temperatures. We provide linear Stark coefficients along two dielectric axes and for the two different substitution sites of the $\rm Eu^{3+}$ ions, with an unprecedented accuracy, and an upper limit for the quadratic Stark shift. The measurements, which indicate that the electric field sensitivity is a factor of seven larger for site 1 relative to site 2 for a particular direction of the electric field are of direct interest both in the context of quantum information processing and laser frequency stabilization with rare-earth doped crystals, in which electric fields can be used to engineer experimental protocols by tuning transition frequencies., Comment: https://aip.scitation.org/doi/full/10.1063/5.0025356

Material strain has recently received growing attention as a complementary resource to control the energy levels of quantum emitters embedded inside a solid-state environment. Some rare-earth ion dopants provide an optical transition which simultaneously has a narrow linewidth and is highly sensitive to strain. In such systems, the technique of spectral hole burning, in which a transparent window is burnt within the large inhomogeneous profile, allows to benefit from the narrow features, which are also sensitive to strain, while working with large ensembles of ions. However, working with ensembles may give rise to inhomogeneous responses among different ions. We investigate experimentally how the shape of a narrow spectral hole is modified due to external mechanical strain, in particular, the hole broadening as a function of the geometry of the crystal sites and the crystalline axis along which the stress is applied. Studying these effects are essential in order to optimize the existing applications of rare-earth doped crystals in fields which already profit from the more well-established coherence properties of these dopants such as frequency metrology and quantum information processing, or even suggest novel applications of these materials, for example as robust devices for force-sensing or highly sensitive accelerometers.

Rare-earth ion doped crystals for hybrid quantum technologies is an area of growing interest in the solid-state physics community. We have earlier theoretically proposed a hybrid scheme of a mechanical resonator which is fabricated out of a rare-earth doped mono-crystalline structure. The rare-earth ion dopants have absorption energies which are sensitive to crystal strain, and it is thus possible to couple the ions to the bending motion of the crystal cantilever. Here, we present the design and fabrication method based on focused-ion-beam etching techniques which we have successfully employed in order to create such microscale resonators, as well as the design of the environment which will allow to study the quantum behavior of the resonators.

We present an experimental technique for realizing a specific absorption spectral pattern in a rare-earth-doped crystal at cryogenic temperatures. This pattern is subsequently probed on two spectral channels simultaneously, thereby producing an error signal allowing frequency locking of a laser on the said spectral pattern. Appropriate combination of the two channels leads to a substantial reduction of the detection noise, paving the way to realizing an ultra-stable laser for which the detection noise can be made arbitrarily low when using multiple channels. We use such technique to realize a laser with a frequency instability of $1.7\times 10^{-15}$ at 1 second, not limited by the detection noise but by environmental perturbation of the crystal. This is comparable with the lowest instability demonstrated at 1 second to date for rare-earth doped crystal stabilized lasers.

Rare-earth doped crystals have numerous applications ranging from frequency metrology to quantum information processing. To fully benefit from their exceptional coherence properties, the effect of mechanical strain on the energy levels of the dopants - whether it is a resource or perturbation - needs to be considered. We demonstrate that by applying uniaxial stress to a rare-earth doped crystal containing a spectral hole, we can shift the hole by a controlled amount that is larger than the width of the hole. We deduce the sensitivity of $\rm Eu^{3+}$ ions in an $\rm Y_2SiO_5$ matrix as a function of crystal site and the crystalline axis along which the stress is applied.