Interfacing photonic and solid-state qubits within a hybrid quantum architecture offers a promising route towards large scale distributed quantum computing. Ideal candidates for coherent qubit interconversion are optically active spins, magnetically coupled to a superconducting resonator. We report on an on-chip cavity QED experiment with magnetically anisotropic Er(3+)∶Y2SiO5 crystals and demonstrate collective strong coupling of rare-earth spins to a lumped element resonator. Moreover, the electron spin resonance and relaxation dynamics of the erbium spins are detected via direct microwave absorption, without the aid of a cavity.

The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes–Cummings model by applying a rotating wave approximation. The rotating wave approximation breaks down in the ultra-strong coupling regime, where the effective coupling strength g is comparable to the energy ω of the bosonic mode, and remarkable features in the system dynamics are revealed. Here we demonstrate an analog quantum simulation of an effective quantum Rabi model in the ultra-strong coupling regime, achieving a relative coupling ratio of g/ω ~ 0.6. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model.

Interfacing superconducting quantum processors, working in the GHz frequency range, with optical quantum networks and atomic qubits is a challenging task for the implementation of distributed quantum information processing as well as for quantum communication. Using spin ensembles of rare-earth ions provides an excellent opportunity to bridge microwave and optical domains at the quantum level. In this Rapid Communication, we demonstrate the ultralow-power, on-chip, electron-spin-resonance spectroscopy of Er 3+ spins doped in a Y 2 SiO 5 crystal using a high-Q, coplanar, superconducting resonator.Quantum communication is a rapidly developing field of science and technology, which allows the transmission of information in an intrinsically secure way. 1 As well as its classical counterpart, a quantum communication network can combine various types of systems which transmit, receive, and process information using quantum algorithms. 2 For example, the nodes of such a network can be implemented by superconducting (SC) quantum circuits operated in the GHz frequency range, 3 whereas fiber optics operated at near infrared can be used to link them over long distances. For the reversible transfer of quantum states between systems operating at GHz and optical frequency ranges, one must use a hybrid system. 4 Spin ensembles coupled to a microwave resonator or to a SC qubit represent one of the possible implementations of such a system. 5-8 The collective coupling strength of a spin ensemble is increased with respect to a single spin by the square root of the number of spins. Transparent crystals doped with paramagnetic ions often possess long coherence times, 9,10 and the collective coupling has been recently demonstrated with nitrogen-vacancy centers in diamond, 11-13 organic molecules, 14 and (Cr 3+ ) ions in ruby. 12 In this Rapid Communication, we report on the ultralowpower electron-spin-resonance (ESR) spectroscopy of an erbium-ion spin ensemble at sub-Kelvin temperatures using a high-Q, coplanar, SC resonator. The Er 3+ ions are distinct from other spin ensembles due to their optical transition at the telecom C band, i.e., inside the so-called erbium window at 1.54 μm wavelength, and their long measured optical coherence time. 15 The energy-level diagram of erbium ions embedded inside a crystal is shown in Fig. 1(a). The electronic configuration of a free Er 3+ ion is 4f 11 , with a 4 I term. The spin-orbit coupling splits it into several fine structure levels. An optical transition at the telecom wavelength occurs between the ground state 2S+1 L J = 4 I 15/2 and the first excited state 4 I 13/2 , where S, L, and J are the respective spin, orbital, and total magnetic momenta of the ion. The weak crystal field splits the ground state into eight (J + 1/2) Kramers doublets. 16 At cryogenic temperature, only the lowest doublet Z 1 is populated, therefore the system can be described as an effective electronic spin with S = 1/2. However, erbium has five even isotopes, 162 Er, 164 Er, 166 Er, 168 Er, and 170 Er, and one odd ...

Superconducting high kinetic inductance elements constitute a valuable resource for quantum circuit design and millimeter-wave detection. Granular aluminum (grAl) in the superconducting regime is a particularly interesting material since it has already shown a kinetic inductance in the range of nH/□ and its deposition is compatible with conventional Al/AlOx/Al Josephson junction fabrication. We characterize microwave resonators fabricated from grAl with a room temperature resistivity of 4×10^{3}  μΩ cm, which is a factor of 3 below the superconductor to insulator transition, showing a kinetic inductance fraction close to unity. The measured internal quality factors are on the order of Q_{i}=10^{5} in the single photon regime, and we demonstrate that nonequilibrium quasiparticles (QPs) constitute the dominant loss mechanism. We extract QP relaxation times in the range of 1 s and we observe QP bursts every ∼20  s. The current level of coherence of grAl resonators makes them attractive for integration in quantum devices, while it also evidences the need to reduce the density of nonequilibrium QPs.

Superconducting quantum information processing machines are predominantly based on microwave circuits with relatively low characteristic impedance, of about 100 Ohm, and small anharmonicity, which can limit their coherence and logic gate fidelity. A promising alternative are circuits based on so-called superinductors, with characteristic impedances exceeding the resistance quantum RQ = 6.4 kΩ. However, previous implementations of superinductors, consisting of mesoscopic Josephson junction arrays, can introduce unintended nonlinearity or parasitic resonant modes in the qubit vicinity, degrading its coherence. Here we present a fluxonium qubit design using a granular aluminum (grAl) superinductor strip. Granular aluminum is a particularly attractive material, as it self-assembles into an effective junction array with a remarkably high kinetic inductance, and its fabrication can be in-situ integrated with standard aluminum circuit processing. The measured qubit coherence time T R 2 up to 30 µs illustrates the potential of grAl for applications ranging from protected qubit designs to quantum limited amplifiers and detectors. arXiv:1809.10646v1 [cond-mat.supr-con]