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Interfacing rare-earth doped crystals with superconducting circuit architectures provides an attractive platform for quantum memory and transducer devices. Here we present the detailed characterization of such a hybrid system: a locally implanted rare-earth Gd$^{3+}$ in Al$_2$O$_3$ spin system coupled to a superconducting micro-resonator. We investigate the properties of the implanted spin system through angular dependent micro-resonator electron spin resonance (micro-ESR) spectroscopy. We find, despite the high energy near-surface implantation, the resulting micro-ESR spectra to be in excellent agreement with the modelled Hamiltonian, supporting the integration of dopant ions into their relevant lattice sites whilst maintaining crystalline symmetries. Furthermore, we observe clear contributions from individual microwave field components of our micro-resonator, emphasising the need for controllable local implantation., Comment: 6 pages, 3 figures

We demonstrate the coupling of rare-earth ions locally implanted in a substrate (Gd$^{3+}$ in Al$_{2}$O$_{3}$) to a superconducting NbN lumped-element micro-resonator. The hybrid device is fabricated by a controlled ion implantation of rare-earth ions in well-defined micron-sized areas, aligned to lithographically defined micro-resonators. The technique does not degrade the internal quality factor of the resonators which remain above $10^{5}$. Using microwave absorption spectroscopy we observe electron-spin resonances in good agreement with numerical modelling and extract corresponding coupling rates of the order of $1$ MHz and spin linewidths of $50 - 65$ MHz., Comment: 4 pages, 2 Figures

Here we find the increase in 1/f noise of superconducting resonators at low temperatures to be completely incompatible with the standard tunneling model (STM) of Two Level Systems (TLS), which has been used to describe low-frequency noise for over three decades. We revise the STM to include a significant TLS - TLS interaction. The new model is able to explain the temperature and power dependence of noise in our measurements, as well as recent studies of individual TLS lifetimes using superconducting qubits. The measurements were made possible by implementing an ultra-stable frequency-tracking technique used in atomic clocks and by producing a superconducting resonator insensitive to temperature fluctuations. The latter required an epitaxially grown Nb film with a Pt capping layer to minimize detrimental oxides at all interfaces., Comment: 7 pages, 3 figures