Twenty-three-millisecond electron spin coherence of erbium ions in a natural-abundance crystal

Roadmap on nanoscale magnetic resonance imaging

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.

Analytical Impact-Excitation Theory of Er/O/B Codoped Si Light-Emitting Diodes

Er doped Si light-emitting diodes may find important applications in silicon photonics and optical quantum computing. These diodes exhibit an emission efficiency 2 orders of magnitude higher at reverse bias than forward bias due to impact excitation. However, physics of impact excitation in these devices remains largely unexplored. In this work, we fabricated an Er/O/B codoped Si light-emitting diode which exhibits a strong electroluminescence by the impact excitation of electrons inelastically colliding the Er ions. An analytical impact-excitation theory was established to predict the electroluminescence intensity and internal quantum efficiency which fit well with the experimental data. From the fittings, we find that the excitable Er ions reach a record concentration of 1.8×10^{19}  cm^{-3} and up to 45% of them is in an excitation state by impact excitation. This work has important implications for developing efficient classical and quantum light sources based on rare earth elements in semiconductors.

Nanocavity-Mediated Purcell Enhancement of Er in TiO2 Thin Films Grown via Atomic Layer Deposition

The use of trivalent erbium (Er3+), typically embedded as an atomic defect in the solid-state, has widespread adoption as a dopant in telecommunication devices and shows promise as a spin-based quantum memory for quantum communication. In particular, its natural telecom C-band optical transition and spin-photon interface make it an ideal candidate for integration into existing optical fiber networks without the need for quantum frequency conversion. However, successful scaling requires a host material with few intrinsic nuclear spins, compatibility with semiconductor foundry processes, and straightforward integration with silicon photonics. Here, we present Er-doped titanium dioxide (TiO2) thin film growth on silicon substrates using a foundry-scalable atomic layer deposition process with a wide range of doping controls over the Er concentration. Even though the as-grown films are amorphous after oxygen annealing, they exhibit relatively large crystalline grains, and the embedded Er ions exhibit the characteristic optical emission spectrum from anatase TiO2. Critically, this growth and annealing process maintains the low surface roughness required for nanophotonic integration. Finally, we interface Er ensembles with high quality factor Si nanophotonic cavities via evanescent coupling and demonstrate a large Purcell enhancement (≈300) of their optical lifetime. Our findings demonstrate a low-temperature, nondestructive, and substrate-independent process for integrating Er-doped materials with silicon photonics. At high doping densities this platform can enable integrated photonic components such as on-chip amplifiers and lasers, while dilute concentrations can realize single ion quantum memories.

Microwave Fluorescence Detection of Spin Echoes

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.

Indistinguishable telecom band photons from a single Er ion in the solid state

Atomic defects in the solid state are a key component of quantum repeater networks for long-distance quantum communication1. Recently, there has been significant interest in rare earth ions2-4, in particular Er3+ for its telecom band optical transition5-7 that allows long-distance transmission in optical fibres. However, the development of repeater nodes based on rare earth ions has been hampered by optical spectral diffusion, precluding indistinguishable single-photon generation. Here, we implant Er3+ into CaWO4, a material that combines a non-polar site symmetry, low decoherence from nuclear spins8 and is free of background rare earth ions, to realize significantly reduced optical spectral diffusion. For shallow implanted ions coupled to nanophotonic cavities with large Purcell factor, we observe single-scan optical linewidths of 150 kHz and long-term spectral diffusion of 63 kHz, both close to the Purcell-enhanced radiative linewidth of 21 kHz. This enables the observation of Hong-Ou-Mandel interference9 between successively emitted photons with a visibility of V = 80(4)%, measured after a 36 km delay line. We also observe spin relaxation times T1,s = 3.7 s and T2,s > 200 μs, with the latter limited by paramagnetic impurities in the crystal instead of nuclear spins. This represents a notable step towards the construction of telecom band quantum repeater networks with single Er3+ ions.

Single-electron spin resonance detection by microwave photon counting

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 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.

Back to the future of organolanthanide chemistry

At the dawn of the development of structural organometallic chemistry, soon after the discovery of ferrocene, the description of the LnCp₃ complexes, featuring large and mostly trivalent lanthanide ions, was rather original and sparked curiosity. Yet, the interest in these new architectures rapidly dwindled due to the electrostatic nature of the bonding between π-aromatic ligands and 4f-elements. Almost 70 years later, it is interesting to focus on how the discipline has evolved in various directions with the reports of multiple catalytic reactivities, remarkable potential in small molecule activation, and the development of rich redox chemistry. Aside from chemical reactivity, a better understanding of their singular electronic nature - not precisely as simplistic as anticipated - has been crucial for developing tailored compounds with adapted magnetic anisotropy or high fluorescence properties that have witnessed significant popularity in recent years. Future developments shall greatly benefit from the detailed reactivity, structural and physical chemistry studies, particularly in photochemistry, electro- or photoelectrocatalysis of inert small molecules, and manipulating the spins' coherence in quantum technology.

Spectral multiplexing of telecom emitters with stable transition frequency

In a quantum network, coherent emitters can be entangled over large distances using photonic channels. In solid-state devices, the required efficient light-emitter interface can be implemented by confining the light in nanophotonic structures. However, fluctuating charges and magnetic moments at the nearby interface then lead to spectral instability of the emitters. Here, we avoid this limitation when enhancing the photon emission up to 70(12)-fold using a Fabry-Perot resonator with an embedded 19-micrometer-thin crystalline membrane, in which we observe around 100 individual erbium emitters. In long-term measurements, they exhibit an exceptional spectral stability of <0.2 megahertz that is limited by the coupling to surrounding nuclear spins. We further implement spectrally multiplexed coherent control and find an optical coherence time of 0.11(1) milliseconds, approaching the lifetime limit of 0.3 milliseconds for the strongest-coupled emitters. Our results constitute an important step toward frequency-multiplexed quantum-network nodes operating directly at a telecommunication wavelength.

Spin-Echo Silencing Using a Current-Biased Frequency-Tunable Resonator

The ability to control microwave emission from a spin ensemble is a requirement of several quantum memory protocols. Here, we demonstrate such ability by using a resonator whose frequency can be rapidly tuned with a bias current. We store excitations in an ensemble of rare-earth ions and suppress on demand the echo emission ("echo silencing") by two methods: (1) detuning the resonator during the spin rephasing, and (2) subjecting spins to magnetic field gradients generated by the bias current itself. We also show that spin coherence is preserved during silencing.

Purcell Enhancement of Erbium Ions in TiO2 on Silicon Nanocavities

Isolated solid-state atomic defects with telecom optical transitions are ideal quantum photon emitters and spin qubits for applications in long-distance quantum communication networks. Prototypical telecom defects, such as erbium, suffer from poor photon emission rates, requiring photonic enhancement using resonant optical cavities. Moreover, many of the traditional hosts for erbium ions are not amenable to direct incorporation with existing integrated photonics platforms, limiting scalable fabrication of qubit-based devices. Here, we present a scalable approach toward CMOS-compatible telecom qubits by using erbium-doped titanium dioxide thin films grown atop silicon-on-insulator substrates. From this heterostructure, we have fabricated one-dimensional photonic crystal cavities demonstrating quality factors in excess of 5 × 10⁴ and corresponding Purcell-enhanced optical emission rates of the erbium ensembles in excess of 200. This easily fabricated materials platform represents an important step toward realizing telecom quantum memories in a scalable qubit architecture compatible with mature silicon technologies.

First-principles study of the electronic and optical properties of Ho[Formula: see text] impurities in single-layer tungsten disulfide

The electronic and optical properties of single-layer (SL) tungsten disulfide (WS[Formula: see text]) in the presence of substitutional Holmium impurities (Ho[Formula: see text]) are studied. Although Ho is much larger than W, density functional theory (DFT) including spin-orbit coupling is used to show that Ho:SL WS[Formula: see text] is stable. The magnetic moment of the Ho impurity is found to be 4.75[Formula: see text] using spin-dependent DFT. The optical selection rules identified in the optical spectrum match exactly the optical selection rules derived by means of group theory. The presence of neutral Ho[Formula: see text] impurities gives rise to localized impurity states (LIS) with f-orbital character in the band structure. Using the Kubo-Greenwood formula and Kohn-Sham orbitals we obtain atom-like sharp transitions in the in-plane and out-of-plane components of the susceptibility tensor, Im[Formula: see text] and Im[Formula: see text]. The optical resonances are in good agreement with experimental data.