We introduce a multilayer superconducting microwave resonator with sub-Ohm impedance optimized for high coupling strength to single electron spins. The design minimizes the magnetic far-field and therefore achieves a Purcell factor F_P > 10^15. We show several ways to fabricate this type of resonator and present resonators with an intrinsic Q-factor exceeding 2 · 10^4 at the single-photon level. We further characterize these resonators in magnetic fields up to 500 mT. Finally, we evaluate the impact of the achievable Purcell factor on single-spin detection through photon counting and dispersive readout.

Strongly anisotropic non-Kramers rare-earth ions combine giant longitudinal g-factors with a vanishing transverse component imposed by time-reversal symmetry, a combination that makes their spin transitions exquisitely sensitive to the orientation of the applied magnetic field. We show that this sensitivity carries a dual identity: it is simultaneously an overlooked decoherence channel and the basis for a spin-coherence-based angular probe. Using pulsed electron paramagnetic resonance at X-band, we report the first measurements of the quantum coherence of Tb^3+ in a native-doped CaWO_4 crystal (15 ppb) and map the Hahn-echo coherence time T_2 as a function of temperature (2 to 10 K) and resonant field (10^3 to 10^4 G). A parameter-free model combining spin-lattice relaxation, instantaneous diffusion and spectral diffusion from all independently quantified impurities overestimates T_2 by an order of magnitude at low temperature and wrongly predicts the field dependence of T_2, inconsistent with the observed monotonic decrease of T_2 with B_r. A two-parameter extension, including dynamical angular fluctuations of the crystal axis, reproduces the full dataset across multiple setups and laboratories. Two controlled experiments nominally identical except for different mechanical configuration of the setup establish the mechanical origin of the dominant contribution. The two-parameter extension corresponds to an angular amplitude noise spectral density of overall order 36 n°/√(Hz) from global external vibrations (ranging from 10 to 66 n°/√(Hz) depending on the exact setup mechanical configuration) estimated at ∼ 2.5 kHz plus a temperature-dependent contribution assumed to come from local phonon-driven angular jitter. It identifies and highlights a decoherence pathway of practical relevance to any anisotropic solid-state spin system.

We report on the characteristics of a microwave photon-counter device based on a superconducting transmon qubit. Its design is similar to that described by Balembois et al. [Phys. Rev. Appl. 21, 014043 (2024)], which achieved a sensitivity of 10-22 W//Hz, but with an additional bandwidth-tuning circuit that permits tuning the detection bandwidth over an order of magnitude to optimize the efficiency and noise level of the device. As a result of this feature and improvements in device fabrication, a power sensitivity of 3 & times; 10-23 W//Hz is reached. We confirm the high performance of the device by measuring single-spin microwave fluorescence.

We investigate for optimal photon absorption a quantum electrodynamical model of an inhomogeneously-broadened spin ensemble coupled to a single-mode cavity. Solutions to this problem under experimental assumptions are developed in the Schr & ouml;dinger picture without using perturbation theory concerning the cavity-spin interactions. Furthermore, we exploit the possibility of modulating the frequency and coupling rate of the resonator. We consider a one-photon input pulse and show some optimal scenarios, where exact formulas and numerical results are obtained for the absorption probabilities and the optimal pulse shapes. In particular, if the external loss dominates the internal loss of the cavity, we find the optimal cooperativity for different parameters and identify cases where absorption with a success probability larger than 99% is achieved.

Quantum state lifetimes T_{2}, or equivalently homogeneous linewidths Γ_{h}=1/πT_{2}, are a key parameter for understanding decoherence processes in quantum systems and assessing their potential for applications in quantum technologies. The most common tool for measuring narrow optical homogeneous linewidths, i.e., long T_{2}, is the measurement of coherent photon echo emissions, which however gives very weak signal when the number of emitters is small. This strongly hampers the development of nanomaterials, such as those based on rare earth ions, for quantum communication and processing. In this work, we propose, and demonstrate in an erbium doped crystal, a measurement of photon echoes based on incoherent fluorescence detection and its variance analysis. It gives access to T_{2} through a much larger signal than direct photon echo detection, and, importantly, with a laser which is incoherent over the measurement timescale, on the order of a few T_{2}. Our results thus open the way to efficiently assess the properties of a broad range of emitters and materials for applications in quantum nanophotonics.

Rare-earth-ions (REI) doped crystals have remarkable optical and spin properties characterized by narrow homogeneous linewidths, which can be studied despite the large inhomogeneous broadening of the ensemble line through spectral hole burning (SHB). Here, we report SHB spectroscopic measurements in a scheelite crystal of CaWO4 by pumping the spin transition of a paramagnetic REI (Er3+) at microwave frequency and millikelvin temperatures, with nuclear spin states of neighboring 183W atoms serving as the auxiliary levels. The repeated application of pairs of microwave pulses generates a periodic modulation of the Er3+ density profile, which we observe spectrally and in the time-domain as an accumulated echo. The lifetime of the holes and accumulated echoes rises steeply as the sample temperature is decreased, exceeding a week at 10mK. Our results demonstrate that millikelvin temperatures can be beneficial for signal processing applications requiring long spectral hole lifetimes.

Pushing the sensitivity of nuclear magnetic resonance spectroscopy to the single spin level would have a major impact in chemistry and biology and is the goal of intense research efforts. We report magnetic resonance spectroscopy measurements of individual nuclear spins in a crystal coupled to a neighboring paramagnetic center, detected using microwave fluorescence at millikelvin temperatures. We observe real-time quantum jumps of the nuclear spin state, a proof of their individual nature. By driving the forbidden transitions of the coupled electron-nuclear spin system, we also achieve single-spin solid-effect dynamical nuclear polarization. Relying exclusively on microwave driving and microwave photon counting, the methods reported here are, in principle, applicable to a large number of electron-nuclear spin systems, in a wide variety of samples.

Counting the microwave photons emitted by an ensemble of electron spins when they relax radiatively has recently been introduced as a sensitive new method for electron paramagnetic resonance spectroscopy at millikelvin temperatures. Here, we apply this spin fluorescence method to a scheelite crystal of CaWO4, finding some known (Er3+, Yb3+, Nd3+, and Fe3+) and other unknown paramagnetic impurities. Investigating the zero nuclear spin isotope (I = 0) transition of Er3+ : CaWO4 as a model system, we provide a quantitative analysis of the time-dependent photon counting rate following an excitation pulse, as a function of its power. The achieved signal-to-noise ratio is found to be an order of magnitude higher than the one obtained by inductively detected Hahn echo under identical conditions. Finally, we use spin fluorescence spectroscopy at low excitation power to probe the properties of rare-earth ions close to a metallic wire deposited on the surface; our data reveal line distortion caused by the mechanical strain imparted by the thermal contractions of the metal relative to the underlying crystal. Coherent oscillations are also observed for the most highly strained ions.

The ability to coherently control and read out qubits is a crucial requirement for any quantum processor. Individual nuclear spins in solid-state systems have been used as long-lived qubits with control and readout performed using individual electron spin ancilla qubits that can be addressed either electrically or optically. Here we present a platform for quantum information processing, consisting of 183W nuclear spin qubits adjacent to an Er3+ impurity in a CaWO4 crystal coupled to a superconducting resonator. We study two nuclear spin qubits with T2*\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{2}<^>{* }$$\end{document} of 0.8(2) s and 1.2(3) s, and T2 of 3.4(4) s and 4.4(6) s, respectively. The nuclear spin state influences the number of photons emitted after repeated excitation of the Er3+ electron ancilla spin qubit, enabling quantum non-demolition readout using a single microwave photon detector. Using stimulated Raman driving on the coupled electron-nuclear-spin system, we implement all-microwave one- and two-qubit gates on a timescale of a few milliseconds, and prepare a decoherence-protected Bell state. Our results position this platform as a potential route towards quantum processing using nuclear spins.

We report an axion dark matter search with a haloscope equipped with a microwave photon counter. The haloscope is a tunable high quality factor three-dimensional microwave cavity placed in a magnetic field. The photon counter, operated cyclically, maps an incoming microwave photon onto the state of a superconducting transmon qubit. The measurement protocol continuously monitors the power emitted by the haloscope cavity as well as the dark count background and enables tuning of the cavity frequency to probe different axion masses. With this apparatus, we enhance by a factor of 20 the search speed that can be reached with quantum-limited linear amplifiers and set a new standard for probing the existence of axions with resonant detectors above 5 GHz.

While single-photon counting is routinely achieved in the optical domain, operational single microwave photon detectors (SMPDs) have only recently been demonstrated. SMPDs are critical for sensing weak signals from incoherent emitters, with applications ranging from the detection of individual electron spins and dark-matter candidates to advancements in hybrid quantum devices and superconducting quantum computing. These detectors offer a substantial advantage over quantum-limited amplification schemes by bypassing the standard quantum limit for power detection, therefore further reductions in their intrinsic noise are essential for advancing quantum sensing at microwave frequencies. Several SMPD designs utilize the state of a superconducting qubit to encode the detection of an itinerant photon, and rely on a non-destructive photon-qubit interaction. Here, we leverage this Quantum-Non-Demolition feature by repeatedly measuring the impinging photon with cascaded Four-Wave-Mixing processes and encoding the detection on several qubits. This cascaded detector mitigates the intrinsic local noise of individual qubits, achieving a two-order-of-magnitude reduction in intrinsic detector noise at the cost of halving the efficiency. We report an intrinsic sensitivity of 8(1)×10^-24W/√(Hz), with an operational sensitivity of 5.9(6)× 10^-23W/√(Hz) limited by thermal photons in the input line.

We use an erbium doped CaWO 4 crystal as a resonant transducer between the RF and optical domains at 12 GHz and 1532 nm respectively. We employ a RF resonator to enhance the spin coupling but keep a single -pass (non -resonant) optical setup. The overall efficiency is low but we carefully characterize the transduction process and show that the performance can be described by two different metrics that we define and distinguish: the electro-optics and the quantum efficiencies. We reach an electro-optics efficiency of -84 dB for 15.7 dBm RF power. The corresponding quantum efficiency is -142 dB for 0.4 dBm optical power. We develop the Schr & ouml;dinger-Maxwell formalism, well-known to describe light -matter interactions in atomic systems, in order to model the conversion process. We explicitly make the connection with the cavity quantum electrodynamics (cavity QED) approach that are generally used to describe quantum transduction.

Single photon detection played an important role in the development of quantum optics. Its implementation in the microwave domain is challenging because the photon energy is 5 orders of magnitude smaller. In recent years, significant progress has been made in developing single microwave photon detectors (SMPDs) based on superconducting quantum bits or bolometers. In this paper we present a practical SMPD based on the irreversible transfer of an incoming photon to the excited state of a transmon qubit by a four-wave mixing process. This device achieves a detection efficiency $\eta = 0.43$ and an operational dark count rate $\alpha = 85$ $\mathrm{s^{-1}}$, mainly due to the out-of-equilibrium microwave photons in the input line. The corresponding power sensitivity is $\mathcal{S} = 10^{-22}$ $\mathrm{W/\sqrt{Hz}}$, one order of magnitude lower than the state of the art. The detector operates continuously over hour timescales with a duty cycle $\eta_\mathrm{D}=0.84$, and offers frequency tunability of at least 50 MHz around 7 GHz.

We use an erbium doped CaWO4 crystal as a resonant transducer between the RF and optical domains at 12 GHz and 1532 nm respectively. We employ a RF resonator to enhance the spin coupling but keep a single-pass (non-resonant) optical setup. The overall efficiency is low but we carefully characterize the transduction process and show that the performance can be described by two different metrics that we define and distinguish: the electro-optics and the quantum efficiencies. We reach an electro-optics efficiency of -84 dB for 15.7 dBm RF power. The corresponding quantum efficiency is -142 dB for 0.4 dBm optical power. We develop the Schrödinger-Maxwell formalism, well-known to describe light-matter interactions in atomic systems, in order to model the conversion process. We explicitly make the connection with the cavity quantum electrodynamics (cavity QED) approach that are generally used to describe quantum transduction.

Understanding the dephasing dynamics of quantum materials with a low number of emitters is crucial for optimizing them for quantum nanophotonics. Here, we investigate the recovery of photon echoes from fluorescence emissions in rare-earth doped systems.

The field of nanoscale magnetic resonance imaging (NanoMRI) was started 30 years ago. It was motivated by the desire to image single molecules and molecular assemblies, such as proteins and virus particles, with near-atomic spatial resolution and on a length scale of 100 nm. Over the years, the NanoMRI field has also expanded to include the goal of useful high-resolution nuclear magnetic resonance (NMR) spectroscopy of molecules under ambient conditions, including samples up to the micron-scale. The realization of these goals requires the development of spin detection techniques that are many orders of magnitude more sensitive than conventional NMR and MRI, capable of detecting and controlling nanoscale ensembles of spins. Over the years, a number of different technical approaches to NanoMRI have emerged, each possessing a distinct set of capabilities for basic and applied areas of science. The goal of this roadmap article is to report the current state of the art in NanoMRI technologies, outline the areas where they are poised to have impact, identify the challenges that lie ahead, and propose methods to meet these challenges. This roadmap also shows how developments in NanoMRI techniques can lead to breakthroughs in emerging quantum science and technology applications.

We report magnetic resonance spectroscopy measurements of individual nuclear spins in a crystal coupled to a neighbouring paramagnetic center, detected using microwave fluorescence at millikelvin temperatures. We observe real-time quantum jumps of the nuclear spin state, a proof of their individual nature. By driving the forbidden transitions of the coupled electron-nuclear spin system, we also achieve single-spin solid-effect dynamical nuclear polarization. Relying exclusively on microwave driving and microwave photon counting, the methods reported here are in principle applicable to a large number of electron-nuclear spin systems, in a wide variety of samples.

Electron spin resonance spectroscopy is the method of choice for characterizing paramagnetic impurities, with applications ranging from chemistry to quantum computing1,2, 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 photoluminescence3–5, transport measurements6–9 and scanning-probe techniques10–12. These methods are system-specific or sensitive only in a small detection volume13,14, so that practical single-spin detection remains an open challenge. Here, we demonstrate single-electron magnetic resonance by spin fluorescence detection15, using a microwave photon counter at millikelvin temperatures16. We detect individual paramagnetic erbium ions in a scheelite crystal coupled to a high-quality-factor planar superconducting resonator to enhance their radiative decay rate17, 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 μm3 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.

Counting the microwave photons emitted by an ensemble of electron spins when they relax radiatively has recently been proposed as a sensitive method for electron paramagnetic resonance spectroscopy, enabled by the development of operational single microwave photon detectors at millikelvin temperature. Here, we report the detection of spin echoes in the spin fluorescence signal. The echo manifests itself as a coherent modulation of the number of photons spontaneously emitted after a π/2_{X}-τ-π_{Y}-τ-π/2_{Φ} sequence, dependent on the relative phase Φ. We demonstrate experimentally this detection method using an ensemble of Er^{3+} ion spins in a scheelite crystal of CaWO_{4}. We use fluorescence-detected echoes to measure the erbium spin coherence time, as well as the echo envelope modulation due to the coupling to the ^{183}W nuclear spins surrounding each ion. We finally compare the signal-to-noise ratio of inductively detected and fluorescence-detected echoes, and show that it is larger with the fluorescence method.