We present cavity QED experiments with an Er 3+ :Y2SiO5 (Er:YSO) crystal magnetically coupled to a 3D cylindrical sapphire loaded copper resonator. Such waveguide cavities are promising for the realization of a superconducting quantum processor. Here, we demonstrate the coherent integration of a rare-earth spin ensemble with the 3D architecture. The collective coupling strength of the Er 3+ spins to the 3D cavity is 21 MHz. The cylindrical sapphire loaded resonator allowed us to explore the anisotropic collective coupling between the rare-earth doped crystal and the cavity. This work shows the potential of spin doped solids in 3D quantum circuits for application as microwave quantum memories as well as for prospective microwave to optical interfaces.Today, the field of quantum information science is looking for the possible physical and technological realization of future quantum processors. A considerable attention is focused on the study of isolated quantum systems such as trapped ions, electronic and nuclear spins, optical photons and superconducting (SC) quantum circuits. A promising route towards the realization of a feasible technology lies in the coherent integration of different systems resulting in hybrid quantum system [1]. Such a hybrid system will benefit from the best physical features of its isolated parts, as for instance, scalability and rapid manipulation of SC qubits, and long coherence time of atoms [2, 3].One way of implementing a hybrid quantum system, is to couple atomic ensembles magnetically to a planar superconducting quantum circuit [3]. Here, the strong confinement of a resonator mode along a coplanar microwave line mediates a strong collective coupling between the spins of the trapped atoms and the SC resonator. In spite of the persisting development of experiments on coupling trapped rubidium atoms to planar SC circuits, the SC hybrid circuits based on trapped atoms are still challenging to realize in practice [4,5]. In that respect, crystals doped with magnetic ions (nitrogen vacancy centers in diamond or rare-earth ion doped solids) are an appealing alternative atomic system [6][7][8][9][10][11][12]. Such solid states spin systems can easily be integrated with various planar SC quantum circuits.In contrast to the long coherence times of spin systems [13,14], the coherence of modern SC planar circuits is still limited by few microseconds, due to uncontrollable coupling to the environment [15]. The drastic improvement in coherence is possible by introducing a new architecture for SC quantum circuits based on threedimensional resonators, which has been recently proposed and successfully implemented [16,17]. Two-qubit gate operations have been demonstrated [18], and multiqubit entanglement schemes in 3D circuit QED have been proposed [19].From the perspective of electron spin resonance (ESR) spectroscopy, 3D cavities are used since the beginning of the field. It is also known, that a paramagnetic material with a very narrow inhomogeneous spin linewidth Γ 2 /2π (∼ 100 kHz at the microwav...

Cylindrical re-entrant cavities are unique three-dimensional structures that resonate with their electric and magnetic fields in separate parts of the cavity. To further understand these devices, we undertake rigorous analysis of the properties of the resonance using "in-house" developed Finite Element Method (FEM) software capable of dealing with small gap structures of extreme aspect ratio. Comparisons between the FEM method and experiments are consistent and we illustrate where predictions using established lumped element models work well and where they are limited. With the aid of the modeling we design a highly tunable cavity that can be tuned from 2 GHz to 22 GHz just by inserting a post into a fixed dimensioned cylindrical cavity. We show this is possible, as the mode structure transforms from a re-entrant mode during the tuning process to a standard cylindrical transverse magnetic mode.

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