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The rise of quantum information science has provided new perspectives on quantum mechanics, as well as a common language for quantum engineering. The focus on platforms for the manipulation and processing of quantum information bridges between different research areas in physics as well as other disciplines. Such a crossover between borders is well embodied by the development of hybrid quantum systems, where heterogeneous physical systems are combined to leverage their individual strengths for the implementation of novel functionalities. In the microwave domain, the hybridization of various quantum degrees of freedom has been tremendously helped by superconducting quantum circuits, owing to their large zero-point field fluctuations, small dissipation, strong nonlinearity and design flexibility. These efforts take place by expanding the framework of circuit quantum electrodynamics. Here, we review recent research on the creation of hybrid quantum systems based on circuit quantum electrodynamics, encompassing mechanical oscillators, quantum acoustodynamics with surface acoustic waves, quantum magnonics and coupling between superconducting circuits and ensembles or single spins. Hybrid quantum systems combine heterogeneous physical systems for the implementation of new functionalities at the quantum level. This article reviews recent research on the creation of hybrid quantum systems within the circuit quantum electrodynamics framework.

Coherent control of quantum states has been demonstrated in a variety of superconducting devices. In all of these devices, the variables that are manipulated are collective electromagnetic degrees of freedom: charge, superconducting phase, or flux. Here we demonstrate the coherent manipulation of a quantum system based on Andreev bound states, which are microscopic quasi-particle states inherent to superconducting weak links. Using a circuit quantum electrodynamics setup, we performed single-shot readout of this Andreev qubit. We determined its excited-state lifetime and coherence time to be in the microsecond range. Quantum jumps and parity switchings were observed in continuous measurements. In addition to having possible quantum information applications, such Andreev qubits are a test-bed for the physics of single elementary excitations in superconductors.

Electron spin resonance spectroscopy is the method of choice for characterizing paramagnetic impurities, with applications ranging from chemistry to quantum computing 1 , 2 , but it gives access only to ensemble-averaged quantities owing to its limited signal-to-noise ratio. Single-electron spin sensitivity has, however, been reached using spin-dependent photoluminescence 3 – 5 , transport measurements 6 – 9 and scanning-probe techniques 10 – 12 . These methods are system-specific or sensitive only in a small detection volume 13 , 14 , so that practical single-spin detection remains an open challenge. Here, we demonstrate single-electron magnetic resonance by spin fluorescence detection 15 , using a microwave photon counter at millikelvin temperatures 16 . We detect individual paramagnetic erbium ions in a scheelite crystal coupled to a high-quality-factor planar superconducting resonator to enhance their radiative decay rate 17 , with a signal-to-noise ratio of 1.9 in one second integration time. The fluorescence signal shows anti-bunching, proving that it comes from individual emitters. Coherence times up to 3 ms are measured, limited by the spin radiative lifetime. The method has the potential to be applied to arbitrary paramagnetic species with long enough non-radiative relaxation times, and allows single-spin detection in a volume as large as the resonator magnetic mode volume (approximately 10 μm 3 in the present experiment), orders of magnitude larger than other single-spin detection techniques. As such, it may find applications in magnetic resonance and quantum computing. Spectroscopic measurements of individual rare-earth ion electron spins are performed by detecting their microwave fluorescence, with the method coming close to practical single-electron spin resonance at millikelvin temperatures.

The sensitivity of electron spin resonance has been improved up to the quantum limit through the use of a Josephson parametric microwave amplifier combined with high-quality-factor superconducting microresonators cooled at millikelvin temperatures. The detection and characterization of paramagnetic species by electron spin resonance (ESR) spectroscopy is widely used throughout chemistry, biology and materials science 1 , from in vivo imaging 2 to distance measurements in spin-labelled proteins 3 . ESR relies on the inductive detection of microwave signals emitted by the spins into a coupled microwave resonator during their Larmor precession. However, such signals can be very small, prohibiting the application of ESR at the nanoscale (for example, at the single-cell level or on individual nanoparticles). Here, using a Josephson parametric microwave amplifier combined with high-quality-factor superconducting microresonators cooled at millikelvin temperatures, we improve the state-of-the-art sensitivity of inductive ESR detection by nearly four orders of magnitude 4 , 5 . We demonstrate the detection of 1,700 bismuth donor spins in silicon within a single Hahn 6 echo with unit signal-to-noise ratio, reduced to 150 spins by averaging a single Carr–Purcell–Meiboom–Gill sequence 7 . This unprecedented sensitivity reaches the limit set by quantum fluctuations of the electromagnetic field instead of thermal or technical noise, which constitutes a novel regime for magnetic resonance. The detection volume of our resonator is ∼0.02 nl, and our approach can be readily scaled down further to improve sensitivity, providing a new versatile toolbox for ESR at the nanoscale.

By coupling donor spins in silicon to a superconducting microwave cavity and tuning the spins to the cavity resonance, the rate of spin relaxation is increased by three orders of magnitude compared to that of detuned spins; in such a regime, spontaneous emission of radiation is the dominant mechanism of spin relaxation. New spin on the Purcell effect The Purcell effect, in which the slow rate of spontaneous emission from a quantum system is accelerated in a resonant cavity, is central to quantum optics. Here, Patrice Bertet and colleagues demonstrate an analogue of the Purcell effect in a system of spins in solids. The spontaneous emission in this system affects spin relaxation, and the authors show how to modulate spin relaxation through three orders of magnitude. This could give researchers a means of controlling and tuning spin relaxation. Spins in solids, in this case donor spins in silicon, are promising platforms for quantum information processing, and this technique could have ramifications for new spin qubit architectures. Spontaneous emission of radiation is one of the fundamental mechanisms by which an excited quantum system returns to equilibrium. For spins, however, spontaneous emission is generally negligible compared to other non-radiative relaxation processes because of the weak coupling between the magnetic dipole and the electromagnetic field. In 1946, Purcell realized 1 that the rate of spontaneous emission can be greatly enhanced by placing the quantum system in a resonant cavity. This effect has since been used extensively to control the lifetime of atoms and semiconducting heterostructures coupled to microwave 2 or optical 3 , 4 cavities, and is essential for the realization of high-efficiency single-photon sources 5 . Here we report the application of this idea to spins in solids. By coupling donor spins in silicon to a superconducting microwave cavity with a high quality factor and a small mode volume, we reach the regime in which spontaneous emission constitutes the dominant mechanism of spin relaxation. The relaxation rate is increased by three orders of magnitude as the spins are tuned to the cavity resonance, demonstrating that energy relaxation can be controlled on demand. Our results provide a general way to initialize spin systems into their ground state and therefore have applications in magnetic resonance and quantum information processing 6 . They also demonstrate that the coupling between the magnetic dipole of a spin and the electromagnetic field can be enhanced up to the point at which quantum fluctuations have a marked effect on the spin dynamics; as such, they represent an important step towards the coherent magnetic coupling of individual spins to microwave photons.

Vacuum fluctuations of the electromagnetic field set a fundamental limit to the sensitivity of a variety of measurements, including magnetic resonance spectroscopy. We report the use of squeezed microwave fields, which are engineered quantum states of light for which fluctuations in one field quadrature are reduced below the vacuum level, to enhance the detection sensitivity of an ensemble of electronic spins at millikelvin temperatures. By shining a squeezed vacuum state on the input port of a microwave resonator containing the spins, we obtain a 1.2-dB noise reduction at the spectrometer output compared to the case of a vacuum input. This result constitutes a proof of principle of the application of quantum metrology to magnetic resonance spectroscopy.

A quantum memory at microwave frequencies, able to store the state of multiple superconducting qubits for long times, is a key element for quantum information processing. Electronic and nuclear spins are natural candidates for the storage medium as their coherence time can be well above 1 s. Benefiting from these long coherence times requires one to apply the refocusing techniques used in magnetic resonance, a major challenge in the context of hybrid quantum circuits. Here, we report the first implementation of such a scheme, using ensembles of nitrogen-vacancy centers in diamond coupled to a superconducting resonator, in a setup compatible with superconducting qubit technology. We implement the active reset of the nitrogen-vacancy spins into their ground state by optical pumping and their refocusing by Hahn-echo sequences. This enables the storage of multiple microwave pulses at the picowatt level and their retrieval after up to 35μs , a 3 orders of magnitude improvement compared to previous experiments.

We study a generic cavity QED setup under conditions where the coupling between the two-level systems and a single bosonic mode is significantly degraded by low-frequency noise. To overcome this problem, we identify pulsed dynamical decoupling strategies that suppress the effects of noise while still allowing for a coherent exchange of excitations between the individual subsystems. The corresponding pulse sequences can be further designed to realize either Jaynes-Cummings, anti-Jaynes-Cummings, or Rabi couplings, as well as different types of cavity-mediated interactions between the two-level systems. A detailed analysis of the residual imperfections demonstrates that this decoupling strategy can boost the effective cooperativity of the cavity QED system by several orders of magnitude and improve the fidelity of quantum-technologically relevant operations accordingly.

Physical systems reach thermal equilibrium through energy exchange with their environment, and for spins in solids the relevant environment is almost always their host lattice. However, recent studies 1 motivated by observations by Purcell 2 have shown how radiative emission into a microwave cavity can become the dominant relaxation path for spins if the spin–cavity coupling is sufficiently large (such as for small-mode-volume cavities). In this regime, the cavity electromagnetic field overrides the lattice as the dominant environment, inviting the prospect of controlling the spin temperature independently from that of the lattice, by engineering a suitable cavity field. Here, we report on precisely such control over spin temperature, illustrating a novel and universal method to increase the electron spin polarization above its thermal equilibrium value (termed hyperpolarization). By switching the cavity input between resistive loads at different temperatures we can control the electron spin polarization, cooling it below the lattice temperature. Our demonstration uses donor spins in silicon coupled to a superconducting microresonator and we observe more than a twofold increase in spin polarization. This approach provides a general route to signal enhancement in electron spin resonance, or nuclear magnetic resonance through dynamical nuclear spin polarization 3 , 4 . Electron spins in solid usually relax their energy through the coupling with phonons in the host lattice. By using the coupling to microwave photons in a cavity as an alternative relaxation path, it is demonstrated that spins can be cooled below the lattice temperature.

Electron spins are amongst the most coherent solid-state systems known. However, to be used in devices for quantum sensing and information processing applications, they must typically be placed near interfaces. Understanding and mitigating the impacts of such interfaces on the coherence and spectral properties of electron spins is critical to realizing such applications, but it is also challenging: Inferring such data from single-spin studies requires many measurements to obtain meaningful results, while ensemble measurements typically give averaged results that hide critical information. Here, we report a comprehensive study of the coherence of near-surface bismuth donor spins in 28-silicon at millikelvin temperatures. In particular, we use strain-induced frequency shifts caused by a metallic electrode to infer spatial maps of spin coherence as a function of position relative to the electrode. By measuring magnetic-field-insensitive clock transitions, we separate magnetic noise caused by surface spins from charge noise. Our results include quantitative models of the strain-split spin resonance spectra and extraction of paramagnetic impurity concentrations at the silicon surface. The interplay of these decoherence mechanisms for such near-surface electron spins is critical for their application in quantum technologies, while the combination of the strain splitting and clock transition extends the coherence lifetimes by up to 2 orders of magnitude, reaching up to 300 ms at a mean depth of only 100 nm. The technique we introduce here to spatially map coherence in near-surface ensembles is directly applicable to other spin systems of active interest, such as defects in diamond, silicon carbide, and rare earth ions in optical crystals.