Ultra-narrow optical linewidths in rare-earth molecular crystals

Toward liquid cell quantum sensing: Ytterbium complexes with ultranarrow absorption

The energetic disorder induced by fluctuating liquid environments acts in opposition to the precise control required for coherence-based sensing. Overcoming fluctuations requires a protected quantum subspace that only weakly interacts with the local environment. We report a ytterbium complex that exhibited an ultranarrow absorption linewidth in solution at room temperature with a full width at half maximum of 0.625 milli-electron volts. Using spectral hole burning, we measured an even narrower linewidth of 410 pico-electron volts at 77 kelvin. Narrow linewidths allowed low-field magnetic circular dichroism at room temperature, used to sense Earth-scale magnetic fields. These results demonstrated that ligand protection in lanthanide complexes could substantially diminish electronic state fluctuations. We have termed this system an "atomlike molecular sensor" (ALMS) and proposed approaches to improve its performance.

Elucidating ultranarrow 2F7/2 to 2F5/2 absorption in ytterbium(iii) complexes

Achieving ultranarrow absorption linewidths in the condensed phase enables optical state preparation of specific non-thermal states, a prerequisite for quantum-enabled technologies. The 4f orbitals of lanthanide(iii) complexes are often referred to as "atom-like," reflecting their isolated nature, and are promising substrates for the optical preparation of specific quantum states. To better understand the photophysical properties of 4f states and assess their potential for quantum applications, theoretical building blocks are required for rapid screening. In this study, an atomic-level perturbative calculation (i.e., spin-orbit crystal field, SOCF) is applied to various Yb(iii) complexes to investigate their linear absorption and emission through a fitting mechanism of their experimentally determined transition energies and oscillator strengths. In particular, the optical properties of (thiolfan)YbCl(THF) (thiolfan = 1,1'-bis(2,4-di-tert-butyl-6-thiomethylenephenoxy)ferrocene), a recently reported complex with an ultranarrow optical linewidth, are computed and compared to those of other Yb(iii) compounds. Through a transition energy sampling study, major contributors to the optical linewidth are identified. We observe particularly isolated f-f transitions and narrow linewidths, which we attribute to two distinct factors. Firstly, the ultra-high atomic similarity of the orbitals involved in the optical transition, along with the presence of an anisotropic crystal field, collectively contribute to the observed narrow transitions. Secondly, we note highly correlated excited-ground energy fluctuations that serve to greatly suppress inhomogeneous line-broadening. This article illustrates how SOCF can be used as a low-cost method to probe the influence of crystal field environment on the optical properties of Yb(iii) complexes to assist the development of novel lanthanide series quantum materials.

Nuclear quantum memory for hard x-ray photon wave packets

Optical quantum memories are key elements in modern quantum technologies to reliably store and retrieve quantum information. At present, they are conceptually limited to the optical wavelength regime. Recent advancements in x-ray quantum optics render an extension of optical quantum memory protocols to ultrashort wavelengths possible, thereby establishing quantum photonics at x-ray energies. Here, we introduce an x-ray quantum memory protocol that utilizes mechanically driven nuclear resonant 57Fe absorbers to form a comb structure in the nuclear absorption spectrum by using the Doppler effect. This room-temperature nuclear frequency comb enables us to control the waveform of x-ray photon wave packets to a high level of accuracy and fidelity using solely mechanical motions. This tunable, robust, and highly flexible system offers a versatile platform for a compact solid-state quantum memory at room temperature for hard x-rays.

Electrically driven spin resonance of 4f electrons in a single atom on a surface

A pivotal challenge in quantum technologies lies in reconciling long coherence times with efficient manipulation of the quantum states of a system. Lanthanide atoms, with their well-localized 4f electrons, emerge as a promising solution to this dilemma if provided with a rational design for manipulation and detection. Here we construct tailored spin structures to perform electron spin resonance on a single lanthanide atom using a scanning tunneling microscope. A magnetically coupled structure made of an erbium and a titanium atom enables us to both drive the erbium's 4f electron spins and indirectly probe them through the titanium's 3d electrons. The erbium spin states exhibit an extended spin relaxation time and a higher driving efficiency compared to 3d atoms with spin ½ in similarly coupled structures. Our work provides a new approach to accessing highly protected spin states, enabling their coherent control in an all-electric fashion.

Spectral Hole-Burning Studies of a Mononuclear Eu(III) Complex Reveal Narrow Optical Linewidths of the 5D0→7F0 Transition and Seconds Long Nuclear Spin Lifetimes

Coordination complexes of rare-earth ions (REI) show optical transitions with narrow linewidths enabling the creation of coherent light-matter interfaces for quantum information processing (QIP) applications. Among the REI-based complexes, Eu(III) complexes showing the 5D0→7F0 transition are of interest for QIP applications due to the narrow linewidths associated with the transition. Herein, we report on the synthesis, structure, and optical properties of a novel Eu(III) complex and its Gd(III) analogue composed of 2,9-bis(pyrazol-1-yl)-1,10-phenanthroline (dpphen) and three nitrate (NO3) ligands. The Eu(III) complex-[Eu(dpphen)(NO3)3]-showed sensitized metal-centred emission (5D0→7FJ; J=0,1,2,3, 4, 5, or 6) in the visible region, upon irradiation of the ligand-centred band at 369 nm, with the 5D0→7F0 transition centred at 580.9 nm. Spectral hole-burning (SHB) studies of the complex with stoichiometric Eu(III) concentration revealed a narrow homogeneous linewidth (Γh) of 1.55 MHz corresponding to a 0.205 μs long optical coherence lifetime (T2opt). Remarkably, long nuclear spin lifetimes (T1spin) of up to 41 s have been observed for the complex. The narrow optical linewidths and long T1spin lifetimes obtained for the Eu(III) complex showcase the utility of Eu(III) complexes as tuneable, following molecular engineering principles, coherent light-matter interfaces for QIP applications.

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.

Covalency versus magnetic axiality in Nd molecular magnets: Nd-photoluminescence, strong ligand-field, and unprecedented nephelauxetic effect in fullerenes NdM2N@C80 (M = Sc, Lu, Y)

Nd-based nitride clusterfullerenes NdM2N@C80 with rare-earth metals of different sizes (M = Sc, Y, Lu) were synthesized to elucidate the influence of the cluster composition, shape and internal strain on the structural and magnetic properties. Single crystal X-ray diffraction revealed a very short Nd-N bond length in NdSc2N@C80. For Lu and Y analogs, the further shortening of the Nd-N bond and pyramidalization of the NdM2N cluster are predicted by DFT calculations as a result of the increased cluster size and a strain caused by the limited size of the fullerene cage. The short distance between Nd and nitride ions leads to a very large ligand-field splitting of Nd3+ of 1100-1200 cm-1, while the variation of the NdM2N cluster composition and concomitant internal strain results in the noticeable modulation of the splitting, which could be directly assessed from the well-resolved fine structure in the Nd-based photoluminescence spectra of NdM2N@C80 clusterfullerenes. Photoluminescence measurements also revealed an unprecedentedly strong nephelauxetic effect, pointing to a high degree of covalency. The latter appears detrimental to the magnetic axiality despite the strong ligand field. As a result, the ground magnetic state has considerable transversal components of the pseudospin g-tensor, and the slow magnetic relaxation of NdSc2N@C80 could be observed by AC magnetometry only in the presence of a magnetic field. A combination of the well-resolved magneto-optical states and slow relaxation of magnetization suggests that Nd clusterfullerenes can be useful building blocks for magneto-photonic quantum technologies.

Molecular nanomagnets: a viable path toward quantum information processing?

Molecular nanomagnets (MNMs), molecules containing interacting spins, have been a playground for quantum mechanics. They are characterized by many accessible low-energy levels that can be exploited to store and process quantum information. This naturally opens the possibility of using them as qudits, thus enlarging the tools of quantum logic with respect to qubit-based architectures. These additional degrees of freedom recently prompted the proposal for encoding qubits with embedded quantum error correction (QEC) in single molecules. QEC is the holy grail of quantum computing and this qudit approach could circumvent the large overhead of physical qubits typical of standard multi-qubit codes. Another important strength of the molecular approach is the extremely high degree of control achieved in preparing complex supramolecular structures where individual qudits are linked preserving their individual properties and coherence. This is particularly relevant for building quantum simulators, controllable systems able to mimic the dynamics of other quantum objects. The use of MNMs for quantum information processing is a rapidly evolving field which still requires to be fully experimentally explored. The key issues to be settled are related to scaling up the number of qudits/qubits and their individual addressing. Several promising possibilities are being intensively explored, ranging from the use of single-molecule transistors or superconducting devices to optical readout techniques. Moreover, new tools from chemistry could be also at hand, like the chiral-induced spin selectivity. In this paper, we will review the present status of this interdisciplinary research field, discuss the open challenges and envisioned solution paths which could finally unleash the very large potential of molecular spins for quantum technologies.

Rare Earths-The Answer to Everything

Rare earths, scandium, yttrium, and the fifteen lanthanoids from lanthanum to lutetium, are classified as critical metals because of their ubiquity in daily life. They are present in magnets in cars, especially electric cars; green electricity generating systems and computers; in steel manufacturing; in glass and light emission materials especially for safety lighting and lasers; in exhaust emission catalysts and supports; catalysts in artificial rubber production; in agriculture and animal husbandry; in health and especially cancer diagnosis and treatment; and in a variety of materials and electronic products essential to modern living. They have the potential to replace toxic chromates for corrosion inhibition, in magnetic refrigeration, a variety of new materials, and their role in agriculture may expand. This review examines their role in sustainability, the environment, recycling, corrosion inhibition, crop production, animal feedstocks, catalysis, health, and materials, as well as considering future uses.

Cavity-Mediated Molecular Entanglement and Generation of Non-classical States of Light

The generation and control of entanglement in a quantum mechanical system are critical elements of nearly all quantum applications. Molecular systems are promising candidates, with numerous degrees of freedom able to be targeted. However, knowledge of intersystem entanglement mechanisms in such systems is limited. In this work, we demonstrate the generation of entanglement between vibrational degrees of freedom in molecules via strong coupling to a cavity mode driven by a weak coherent field. In a bimolecular system, we show that entanglement can be generated not only between the cavity and molecular system but also between molecules. This process also results in the generation of nonclassical states of light, providing potential pathways for harnessing entanglement in molecular systems.

Understanding Single-Molecule Magnet properties of lanthanide complexes from 4f orbital splitting

We present an approach for connecting the magnetic anisotropy of lanthanide mononuclear complexes with their f-orbital splitting for both idealized and real coordination environments. Our proposal is straightforward to apply and provides sensible estimations of the energy spacing of the ground multiplet for axial magnetic systems. This energy splitting controls Single-Molecule Magnet properties of lanthanide complexes, determining key parameters such as the demagnetization energy barrier (Ueff). Importantly, this approach is consistent with the current paradigm of oblate and prolate preferences for the distribution of the f-electron density, but delivers a finer description for ions belonging to the same group (e.g. the oblates TbIII and DyIII). The model provides simple explanations for some general trends observed experimentally (e.g. the low barriers for ErIII complexes in comparison to DyIII or the large barriers observed for cyclopentadienyl DyIII complexes in comparison with other ligands based on organometallic rings), contributing as a valuable tool to expand our description of ligand field effects in lanthanide-based SMMs.

Spectral and temporal atomic coherence interaction in Eu3+ : NaYF4 and Eu3+ : BiPO4

We investigate the spectral and temporal atomic coherence interaction based on out-of-phase fluorescence (FL) and spontaneous parametric four-wave mixing (SFWM) from the hexagonal phase of Eu3+ : NaYF4 and different phases of Eu3+ : BiPO4. Spectral and temporal interactions are interrelated and reduced by about 2 times due to two-photon nested dressing in contrast to the sum of each laser excitation. As the lifetime of photons increases, off-resonance profile cross-interaction decreases because cross-interaction reverses the signal at the near time gate position and keeps it consistent at the far time gate position. Moreover, the thermal phonon dressing at 300 K exhibits 6 times more eminent and obvious temporal interaction than that at 77 K. In a different phase of Eu3+ : BiPO4, there are three dark dips having stronger self-interaction; however, Eu3+ : NaYF4 has two dark dips as Eu3+ : BiPO4 has two phonon dressing. Further, the pure hexagonal phase of Eu3+ : BiPO4 demonstrates the strongest cross-interaction and longest coherent time under the dressing effect due to the smallest dressing phonon detuning and off-resonance profile cross-interaction at PMT2 because the angle quantization is the strongest. Such results can be used for designing novel quantum devices and have potential applications in quantum memory devices.

Future Paths in Cryogenic Single-Molecule Fluorescence Spectroscopy

In the last three decades, cryogenic single-molecule fluorescence spectroscopy has provided average-free understanding of the photophysics and of fundamental interactions at molecular scales. Furthermore, they propose original pathways and applications in the treatment and storage of quantum information. The ultranarrow lifetime-limited zero-phonon line acts as an excellent sensor to local perturbations caused either by intrinsic dynamical degrees of freedom, or by external perturbations, such as those caused by electric fields, elastic and acoustic deformations, or light-induced dynamics. Single aromatic hydrocarbon molecules, being sensitive to nanoscale probing at nanometer scales, are potential miniaturized platforms for integrated quantum photonics. In this Perspective, we look back at some of the past advances in cryogenic optical microscopy and propose some perspectives for future development.

Ultra-narrow inhomogeneous spectral distribution of telecom-wavelength vanadium centres in isotopically-enriched silicon carbide

Spin-active quantum emitters have emerged as a leading platform for quantum technologies. However, one of their major limitations is the large spread in optical emission frequencies, which typically extends over tens of GHz. Here, we investigate single V4+ vanadium centres in 4H-SiC, which feature telecom-wavelength emission and a coherent S = 1/2 spin state. We perform spectroscopy on single emitters and report the observation of spin-dependent optical transitions, a key requirement for spin-photon interfaces. By engineering the isotopic composition of the SiC matrix, we reduce the inhomogeneous spectral distribution of different emitters down to 100 MHz, significantly smaller than any other single quantum emitter. Additionally, we tailor the dopant concentration to stabilise the telecom-wavelength V4+ charge state, thereby extending its lifetime by at least two orders of magnitude. These results bolster the prospects for single V emitters in SiC as material nodes in scalable telecom quantum networks.

Accurate and Efficient Spin-Phonon Coupling and Spin Dynamics Calculations for Molecular Solids

Molecular materials are poised to play a significant role in the development of future optoelectronic and quantum technologies. A crucial aspect of these areas is the role of spin-phonon coupling and how it facilitates energy transfer processes such as intersystem crossing, quantum decoherence, and magnetic relaxation. Thus, it is of significant interest to be able to accurately calculate the molecular spin-phonon coupling and spin dynamics in the condensed phase. Here, we demonstrate the maturity of ab initio methods for calculating spin-phonon coupling by performing a case study on a single-molecule magnet and showing quantitative agreement with the experiment, allowing us to explore the underlying origins of its spin dynamics. This feat is achieved by leveraging our recent developments in analytic spin-phonon coupling calculations in conjunction with a new method for including the infinite electrostatic potential in the calculations. Furthermore, we make the first ab initio determination of phonon lifetimes and line widths for a molecular magnet to prove that the commonplace Born-Markov assumption for the spin dynamics is valid, but such "exact" phonon line widths are not essential to obtain accurate magnetic relaxation rates. Calculations using this approach are facilitated by the open-source packages we have developed, enabling cost-effective and accurate spin-phonon coupling calculations on molecular solids.

Molecular One- and Two-Qubit Systems with Very Long Coherence Times

General-purpose quantum computation and quantum simulation require multi-qubit architectures with precisely defined, robust interqubit interactions, coupled with local addressability. This is an unsolved challenge, primarily due to scalability issues. These issues often derive from poor control over interqubit interactions. Molecular systems are promising materials for the realization of large-scale quantum architectures, due to their high degree of positionability and the possibility to precisely tailor interqubit interactions. The simplest quantum architecture is the two-qubit system, with which quantum gate operations can be implemented. To be viable, a two-qubit system must possess long coherence times, the interqubit interaction must be well defined and the two qubits must also be addressable individually within the same quantum manipulation sequence. Here results are presented on the investigation of the spin dynamics of chlorinated triphenylmethyl organic radicals, in particular the perchlorotriphenylmethyl (PTM) radical, a mono-functionalized PTM, and a biradical PTM dimer. Extraordinarily long ensemble coherence times up to 148 µs are found at all temperatures below 100 K. Two-qubit and, importantly, individual qubit addressability in the biradical system are demonstrated. These results underline the potential of molecular materials for the development of quantum architectures.

Direct determination of high-order transverse ligand field parameters via µSQUID-EPR in a Et4N[160GdPc2] SMM

The development of quantum technologies requires a thorough understanding of systems possessing quantum effects that can ultimately be manipulated. In the field of molecular magnetism, one of the main challenges is to measure high-order ligand field parameters, which play an essential role in the relaxation properties of SMMs. The development of highly advanced theoretical calculations has allowed the ab-initio determination of such parameters; however, currently, there is a lack of quantitative assessment of how good the ab-initio parameters are. In our quest for technologies that can allow the extraction of such elusive parameters, we develop an experimental technique that combines the EPR spectroscopy and µSQUID magnetometry. We demonstrate the power of the technique by performing EPR-µSQUID measurement of a magnetically diluted single crystal of Et₄N[GdPc₂], by sweeping the magnetic field and applying a range of multifrequency microwave pulses. As a result, we were able to directly determine the high-order ligand field parameters of the system, enabling us to test theoretical predictions made by state-of-the-art ab-initio methods.

Bioexcitons by Design: How Do We Get There?

Biological pigment-protein complexes (PPCs) exhibit a remarkable ability to tune the optical properties of biological excitons (bioexcitons) through specific pigment-protein interactions. While such fine-tuning allows natural systems (e.g., photosynthetic proteins) to carry out their native functions with near-optimal performance, native function itself is often suboptimal for applications such as biofuel production or quantum technology development. This perspective offers a look at near-term prospects for the rational reoptimization of PPC bioexcitons for new functions using site-directed mutagenesis. The primary focus is on the "structure-spectrum" challenge of understanding the relationships between structural features and spectroscopic properties. While recent examples demonstrate that site-directed mutagenesis can be used to tune nearly all key bioexciton parameters (e.g., site energies, interpigment couplings, and electronic-vibrational interactions), critical challenges remain before we achieve truly rational design of bioexciton properties.

Modular Approach to Creating Functionalized Surface Arrays of Molecular Qubits

The quest for developing quantum technologies is driven by the promise of exponentially faster computations, ultrahigh performance sensing, and achieving thorough understanding of many-particle quantum systems. Molecular spins are excellent qubit candidates because they feature long coherence times, are widely tunable through chemical synthesis, and can be interfaced with other quantum platforms such as superconducting qubits. A present challenge for molecular spin qubits is their integration in quantum devices, which requires arranging them in thin films or monolayers on surfaces. However, clear proof of the survival of quantum properties of molecular qubits on surfaces has not been reported so far. Furthermore, little is known about the change in spin dynamics of molecular qubits going from the bulk to monolayers. Here, a versatile bottom-up method is reported to arrange molecular qubits as functional groups of self-assembled monolayers (SAMs) on surfaces, combining molecular self-organization and click chemistry. Coherence times of up to 13 µs demonstrate that qubit properties are maintained or even enhanced in the monolayer.

Highly Tunable 4-Phosphoryl Pyrazolone Receptors for Selective Rare-Earth Separation

Highly selective rare-earth separation has become increasingly important due to the indispensable role of these elements in various cutting-edge technologies including clean energy. However, the similar physicochemical properties of rare-earth elements (REEs) render their separation very challenging, and the development of new selective receptors for these elements is potentially of very considerable economic and environmental importance. Herein, we report the development of a series of 4-phosphoryl pyrazolone receptors for the selective separation of trivalent lanthanum, europium, and ytterbium as the representatives of light, middle, and heavy REEs, respectively. X-ray crystallography studies were employed to obtain solid-state structures across 11 of the resulting complexes, allowing comparative structure-function relationships to be probed, including the effect of lanthanide contraction that occurs along the series from lanthanum to europium to ytterbium and which potentially provides a basis for REE ion separation. In addition, the influence of ligand structure and lipophilicity on lanthanide binding and selectivity was systematically investigated via n-octanol/water distribution and liquid-liquid extraction (LLE) studies. Corresponding stoichiometry relationships between solid and solution states were well established using slope analyses. The results provide new insights into some fundamental lanthanide coordination chemistry from a separation perspective and establish 4-phosphoryl pyrazolone derivatives as potential practical extraction reagents for the selective separation of REEs in the future.

Quantum Mimicry With Inorganic Chemistry

Quantum objects, such as atoms, spins, and subatomic particles, have important properties due to their unique physical properties that could be useful for many different applications, ranging from quantum information processing to magnetic resonance imaging. Molecular species also exhibit quantum properties, and these properties are fundamentally tunable by synthetic design, unlike ions isolated in a quadrupolar trap, for example. In this comment, we collect multiple, distinct, scientific efforts into an emergent field that is devoted to designing molecules that mimic the quantum properties of objects like trapped atoms or defects in solids. Mimicry is endemic in inorganic chemistry and featured heavily in the research interests of groups across the world. We describe a new field of using inorganic chemistry to design molecules that mimic the quantum properties (e.g. the lifetime of spin superpositions, or the resonant frequencies thereof) of other quantum objects, "quantum mimicry." In this comment, we describe the philosophical design strategies and recent exciting results from application of these strategies.

Towards Luminescent Vanadium(II) Complexes with Slow Magnetic Relaxation and Quantum Coherence

Molecular entities with doublet or triplet ground states find increasing interest as potential molecular quantum bits (qubits). Complexes with higher multiplicity might even function as qudits and serve to encode further quantum bits. Vanadium(II) ions in octahedral ligand fields with quartet ground states and small zero-field splittings qualify as qubits with optical read out thanks to potentially luminescent spin-flip states. We identified two V²⁺ complexes [V(ddpd)₂ ]²⁺ with the strong field ligand N,N'-dimethyl-N,N'-dipyridine-2-yl-pyridine-2,6-diamine (ddpd) in two isomeric forms (cis-fac and mer) as suitable candidates. The energy gaps between the two lowest Kramers doublets amount to 0.2 and 0.5 cm^-1 allowing pulsed EPR experiments at conventional Q-band frequencies (35 GHz). Both isomers possess spin-lattice relaxation times T₁ of around 300 μs and a phase memory time T_M of around 1 μs at 5 K. Furthermore, the mer isomer displays slow magnetic relaxation in an applied field of 400 mT. While the vanadium(III) complexes [V(ddpd)₂ ]³⁺ are emissive in the near-IR-II region, the [V(ddpd)₂ ]²⁺ complexes are non-luminescent due to metal-to-ligand charge transfer admixture to the spin-flip states.

Photon-Phonon Atomic Coherence Interaction of Nonlinear Signals in Various Phase Transitions Eu3+: BiPO4

We report photon-phonon atomic coherence (cascade- and nested-dressing) interaction from the various phase transitions of Eu³⁺: BiPO₄ crystal. Such atomic coherence spectral interaction evolves from out-of-phase fluorescence to in-phase spontaneous four-wave mixing (SFWM) by changing the time gate. The dressing dip switch and three dressing dips of SFWM result from the strong photon-phonon destructive cross- and self-interaction for the hexagonal phase, respectively. More phonon dressing results in the destructive interaction, while less phonon dressing results in the constructive interaction of the atomic coherences. The experimental measurements of the photon-phonon interaction agree with the theoretical simulations. Based on our results, we proposed a model for an optical transistor (as an amplifier and switch).

Silver Nanoparticle Chains for Ultra-Long-Range Plasmonic Waveguides for Nd3+ Fluorescence

Plasmonic waveguides have been shown to be a promising approach to confine and transport electromagnetic energy beyond the diffraction limit. However, ohmic losses generally prevent their integration at micrometric or millimetric scales. Here, we present a gain-compensated plasmonic waveguide based on the integration of linear chains of Ag nanoparticles on an optically active Nd³⁺-doped solid-state gain medium. By means of dual confocal fluorescence microscopy, we demonstrate long-range optical energy propagation due to the near-field coupling between the plasmonic nanostructures and the Nd³⁺ ions. The subwavelength fluorescence guiding is monitored at distances of around 100 µm from the excitation source for two different emission ranges centered at around 900 nm and 1080 nm. In both cases, the guided fluorescence exhibits a strong polarization dependence, consistent with the polarization behavior of the plasmon resonance supported by the chain. The experimental results are interpreted through numerical simulations in quasi-infinite long chains, which corroborate the propagation features of the Ag nanoparticle chains at both excitation (λ_exc = 590 nm) and emission wavelengths. The obtained results exceed by an order of magnitude that of previous reports on electromagnetic energy transport using linear plasmonic chains. The work points out the potential of combining Ag nanoparticle chains with a small interparticle distance (~2 nm) with rare-earth-based optical gain media as ultra-long-range waveguides with extreme light confinement. The results offer new perspectives for the design of integrated hybrid plasmonic-photonic circuits based on rare-earth-activated solid-state platforms.

Computational Insights into Electronic Excitations, Spin-Orbit Coupling Effects, and Spin Decoherence in Cr(IV)-Based Molecular Qubits

The great success of point defects and dopants in semiconductors for quantum information processing has invigorated a search for molecules with analogous properties. Flexibility and tunability of desired properties in a large chemical space have great advantages over solid-state systems. The properties analogous to point defects were demonstrated in the Cr(IV)-based molecular family, Cr(IV)(aryl)₄, where the electronic spin states were optically initialized, read out, and controlled. Despite this kick-start, there is still a large room for enhancing properties crucial for molecular qubits. Here, we provide computational insights into key properties of the Cr(IV)-based molecules aimed at assisting the chemical design of efficient molecular qubits. Using the multireference ab initio methods, we investigate the electronic states of Cr(IV)(aryl)₄ molecules with slightly different ligands, showing that the zero-phonon line energies agree with the experiment and that the excited spin-triplet and spin-singlet states are highly sensitive to small chemical perturbations. By adding spin-orbit interaction, we find that the sign of the uniaxial zero-field splitting (ZFS) parameter is negative for all considered molecules and discuss optically induced spin initialization via non-radiative intersystem crossing. We quantify (super)hyperfine coupling to the ⁵³Cr nuclear spin and to the ¹³C and ¹H nuclear spins, and we discuss electron spin decoherence. We show that the splitting or broadening of the electronic spin sub-levels due to superhyperfine interaction with ¹H nuclear spins decreases by an order of magnitude when the molecules have a substantial transverse ZFS parameter.

Theoretical Insights into the Geometrical Evolution, Photoelectron Spectra, and Vibrational Properties of YGe n - (n = 6-20) Anions: From Y-Linked to Y-Encapsulated Structures

The structural evolution behavior of germanium anionic clusters doped with the rare-earth metal yttrium, YGe _n ^- (n = 6-20), has been investigated using a mPW2PLYP density functional scheme and an ABCluster structure searching technique. The results reveal that with increasing cluster size n, the structure evolution pattern is from the Y-linked framework (n = 10-14), where Y serves as a linker (the Y atom bridges two germanium subclusters), to the Y-encapsulated framework (n = 15-20), where the Y atom is located in the center of the Ge cage. The simulated PES spectra show satisfying agreement with the experimental PES spectra for n = 12-20, which reveals that the global minimum structures reported here are reliable. In particular, the anionic YGe₁₆ ^- nanocluster is found to be the most stable structure in the size range of n = 6-20 through analyzes of the relative stability, highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap, spherical jellium model, and isochemical shielding surface. Moreover, spectral properties such as infrared and Raman spectra were reported. In addition, the UV-vis spectra of the YGe₁₆ ^- nanocluster are in good agreement with solar energy distribution, showing that such substances serve as multifunctional building blocks to be potentially used in optoelectronic devices or solar energy converters.

Tapered Optical Fibers Coated with Rare-Earth Complexes for Quantum Applications

Crystals and fibers doped with rare-earth (RE) ions provide the basis for most of today's solid-state optical systems, from lasers and telecom devices to emerging potential quantum applications such as quantum memories and optical to microwave conversion. The two platforms, doped crystals and doped fibers, seem mutually exclusive, each having its own strengths and limitations, the former providing high homogeneity and coherence and the latter offering the advantages of robust optical waveguides. Here we present a hybrid platform that does not rely on doping but rather on coating the waveguide-a tapered silica optical fiber-with a monolayer of complexes, each containing a single RE ion. The complexes offer an identical, tailored environment to each ion, thus minimizing inhomogeneity and allowing tuning of their properties to the desired application. Specifically, we use highly luminescent Yb3+[Zn(II)MC (QXA)] complexes, which isolate the RE ion from the environment and suppress nonradiative decay channels. We demonstrate that the beneficial optical transitions of the Yb3+ are retained after deposition on the tapered fiber and observe an excited-state lifetime of over 0.9 ms, on par with state-of-the-art Yb-doped inorganic crystals.

Structural evolution, photoelectron spectra and vibrational properties of anionic GdGe n - (n = 5-18) nanoalloy clusters: a DFT insight

The structural growth of Gd-doped germanium anionic nanoclusters, GdGe_n⁻ (n = 5–18), has been explored via quantum chemistry calculations using the mPW2PLYP method and an unprejudiced structural searching technique known as ABCluster. The optimized geometries exhibited that when n = 10–14, the structural evolution favors the Gd-linked configuration where the Gd atom as a connector bridges two Ge subgroups, while the Gd atom is encapsulated in a closed cage-like Ge frame when n = 15–18. The properties like magnetic moment, charge transfer, relative stability, HOMO–LUMO gap, photoelectron spectra, and infrared and Raman spectra have been predicted. The information of these spectra could provide extra approaches to experimentally determine the electronic structures and equilibrium configuration of these compounds. The largest spin magnetic moment of 7 μ_B is attained via half-filled 4f states. The GdGe₁₆⁻ nanocluster is determined to be a superatom because its total valence of 75 electrons can be distributed to the orbital sequence of 1S²1P⁶(4f⁷)1D¹⁰1F¹⁴2S²2P²1G¹⁸2P⁴2D¹⁰, which complies with not only Hund's rule, but also the spherical jellium model. Particularly, its UV-Vis spectra match well with solar energy distribution. Such materials act as nano multifunctional building units potentially used in solar energy converters or ultra-highly sensitive near-infrared photodetectors.

The structural evolution, electronic and vibrational properties of GdGe_n⁻ (n=5-18) nanoclusters were studied by quantum chemical calculations, which revealed GdGe₁₆⁻ nanocluster is a superatom to the orbital of 1S²1P⁶(4f⁷)1D¹⁰1F¹⁴2S²2P²1G¹⁸2P⁴2D¹⁰.

Deterministic Relation between Optical Polarization and Lattice Symmetry Revealed in Ion-Doped Single Microcrystals

Rare-earth ion doped crystals are of great significance for microsensing and quantum information, while the ions in the crystals emit light with spontaneous partial polarization, which is, though believed to be originated from the crystal lattice structure, still lacking a deterministic explanation that can be tested with quantitative accuracy. We report experimental evidence showing the profound physical relation between the polarization degree of light emitted by the doped ion and the lattice symmetry by demonstrating, with high precision, that the lattice constant ratio c/a directly quantifies the macroscopic effective polar angle of the electric and magnetic dipoles, which essentially determines the linear polarization degree of the emission. Based on this result, we further propose a pure optical technology to identify the three-dimensional orientation of a rod-shaped single microcrystal using the polarization-resolved microspectroscopy. Our results, demonstrating the physical origin of light polarization in ion-doped crystals, allow work toward on-demand polarization control with crystallography and provide a versatile platform for polarization-based microscale sensing in dynamical systems.