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Er$^{3+}$:Y$_2$SiO$_5$ crystal is a promising candidate with a great variety of its potential applications in quantum information processing and quantum communications ranging from optical/microwave quantum memories to circuit QED and microwave-to-optics frequency converters. Some of the above listed applications require ultra-low temperature environment, i.e., temperatures $T\lesssim0.1~$K. Most of the experiments with erbium doped crystals have been so far carried out at temperatures above 1.5~K. Therefore, only little information is known about Er$^{3+}$:Y$_2$SiO$_5$ coherence properties at millikelvins. Here, we investigate optical decoherence of $^{167}$Er:Y$_2$SiO$_5$ crystal by performing 2- and 3-pulse echo experiments at millikelvin temperature range and at weak and moderate magnetic fields. We show that the deep freezing of the crystal results in an increase of optical coherence time by one order of magnitude compared to temperature of 1.5 Kelvin and magnetic field of $\sim$0.2~T, taken as a reference point. We further describe the detailed investigation of the decoherence mechanisms in this regime., Comment: 9 pages, 7 figures, 1 table, 47 references

Recent progress in observing and manipulating mechanical oscillators at quantum regime provides new opportunities of studying fundamental physics, for example, to search for low energy signatures of quantum gravity. For example, it was recently proposed that such devices can be used to test quantum gravity effects, by detecting the change in the [x,p] commutation relation that could result from quantum gravity corrections. We show that such a correction results in a dependence of a resonant frequency of a mechanical oscillator on its amplitude, which is known as amplitude-frequency effect. By implementing this new method we measure amplitude-frequency effect for 0.3 kg ultra high-Q sapphire split-bar mechanical resonator and for 10 mg quartz bulk acoustic wave resonator. Our experiments with sapphire resonator have established the upper limit on quantum gravity correction constant for $\beta_0<5 \times10^6$ which is a factor of 6 better than previously detected. The reasonable estimates of $\beta_0$ from experiments with quartz resonators yield an even more stringent limit of $4\times10^4$. The data sets of 1936 measurement of physical pendulum period by Atkinson results in significantly stronger limitations on $\beta_0 \ll 1$. Yet, due to the lack of proper pendulum frequency stability measurement in these experiments, the exact upper bound on $\beta_0$ can not be reliably established. Moreover, pendulum based systems only allow testing a specific form of the modified commutator that depends on the mean value of momentum. The electro-mechanical oscillators to the contrary enable testing of any form of generalized uncertainty principle directly due to much higher stability and a higher degree of control., Comment: 3 figures

We present optical vector network analysis (OVNA) of an isotopically purified $^{166}$Er$^{3+}$:$^7$LiYF$_4$ crystal. The OVNA method is based on generation and detection of modulated optical sideband by using a radio-frequency vector network analyzer. This technique is widely used in the field of microwave photonics for the characterization of optical responses of optical devices such as filters and high-Q resonators. However, dense solid-state atomic ensembles induce a large phase shift on one of the optical sidebands which results in the appearance of extra features on the measured transmission response. We present a simple theoretical model which accurately describes the observed spectra and helps to reconstruct the absorption profile of a solid-state atomic ensemble as well as corresponding change of the refractive index in the vicinity of atomic resonances., Comment: 4 pages, 5 figures

We report on hybrid circuit QED experiments with focused ion beam implanted Er$^{3+}$ ions in Y$_2$SiO$_5$ coupled to an array of superconducting lumped element microwave resonators. The Y$_2$SiO$_5$ crystal is divided into several areas with distinct erbium doping concentrations, each coupled to a separate resonator. The coupling strength is varied from 5 MHz to 18.7 MHz, while the linewidth ranges between 50 MHz and 130 MHz. We confirm the paramagnetic properties of the implanted spin ensemble by evaluating the temperature dependence of the coupling. The efficiency of the implantation process is analyzed and the results are compared to a bulk doped Er:Y$_2$SiO$_5$ sample. We demonstrate the successful integration of these engineered erbium spin ensembles with superconducting circuits., Comment: 5 pages, 4 figures

Rare-earth-doped crystals are excellent hardware for quantum storage of optical information. Additional functionality of these materials is added by their waveguiding properties allowing for on-chip photonic networks. However, detection and coherent properties of rare-earth single-spin qubits have not been demonstrated so far. Here, we present experimental results on high-fidelity optical initialization, effcient coherent manipulation, and optical readout of a single electron spin of Ce$^{3+}$ ion in a YAG crystal. Under dynamic decoupling, spin coherence lifetime reaches $T_2$=2 ms and is almost limited by the measured spin-lattice relaxation time $T_1$=3.8 ms. Strong hyperfine coupling to aluminium nuclear spins suggests that cerium electron spins can be exploited as an interface between photons and long-lived nuclear spin memory. Combined with high brightness of Ce$^{3+}$ emission and a possibility of creating photonic circuits out of the host material, this makes cerium spins an interesting option for integrated quantum photonics., Comment: 10 pages, 4 figures

Quantum memories are integral parts of both quantum computers and quantum communication networks. Naturally, such a memory is embedded into a hybrid quantum architecture, which has to meet the requirements of fast gates, long coherence times and long distance communication. Erbium doped crystals are well suited as a microwave quantum memory for superconducting circuits with additional access to the optical telecom C-band around 1.55 {\mu}m. Here, we report on circuit QED experiments with an Er3+:YAlO3 crystal and demonstrate strong coupling to a superconducting lumped element resonator. The low magnetic anisotropy of the host crystal allows for attaining the strong coupling regime at relatively low magnetic fields, which are compatible with superconducting circuits. In addition, Ce3+ impurities were detected in the crystal, which showed strong coupling as well.