Rare Earth Ions In Solids Research Articles

Fast Wide‐Field Quantum Sensor Based on Solid‐State Spins Integrated with a SPAD Array

AbstractAchieving fast, sensitive, and parallel measurement of a large number of quantum particles is an essential task in building large‐scale quantum platforms for different quantum information processing applications such as sensing, computation, simulation, and communication. Current quantum platforms in experimental atomic and optical physics based on CMOS sensors and charged coupled device cameras are limited by either low sensitivity or slow operational speed. Here an array of single‐photon avalanche diodes is integrated with solid‐state spin defects in diamond to build a fast wide‐field quantum sensor, achieving a frame rate up to 100 kHz. The design of the experimental setup to perform spatially resolved imaging of quantum systems is presented. A few exemplary applications, including sensing DC and AC magnetic fields, temperature, strain, local spin density, and charge dynamics, are experimentally demonstrated using a nitrogen‐vacancy ensemble diamond sample. The developed photon detection array is broadly applicable to other platforms such as atom arrays trapped in optical tweezers, optical lattices, donors in silicon, and rare earth ions in solids.

Spectral Broadening of a Single Er3+ Ion in a Si Nanotransistor

Single rare-earth ions in solids show great potential for quantum applications, including single photon emission, quantum computing, and high-precision sensing. However, homogeneous linewidths observed for single rare-earth ions are orders of magnitude larger than the sub-kilohertz linewidths observed for ensembles in bulk crystals. The spectral broadening creates a significant challenge for achieving entanglement generation and qubit operation with single rare-earth ions, so it is critical to investigate the broadening mechanisms. We report a spectral broadening study on a single Er$^{3+}$ ion in a Si nano-transistor. The Er-induced photoionisation rate is found to be an appropriate quantity to represent the optical transition probability for spectroscopic studies, and the single ion spectra display a Lorentzian lineshape at all optical powers in use. Spectral broadening is observed at relatively high optical powers and is caused by spectral diffusion on a fast time scale.

Proposal for transduction between microwave and optical photons using Er167 -doped yttrium orthosilicate

Efficient transduction devices that reversibly convert optical and microwave quantum signals into each other are essential for integrating different technologies. Rare-earth ions in solids, and in particular Erbium ions, with both optical and microwave addressable transitions are promising candidates for designing transducers. We propose a microwave-to-optical quantum transducer scheme based on the dark state protocol in $\mathrm{^{167}Er}$ doped into yttrium orthosilicate (YSO) at zero external magnetic fields. Zero-field operation is beneficial for superconducting resonators that can incur extra losses in magnetic fields. By calculating the fidelity and efficiency of the transducer, considering the most important imperfections, we show that an efficient conversion is possible with a high fidelity. We also investigate the microwave transitions of $\mathrm{^{167}Er}$:YSO that can be used for the transducer protocol.

Probing strong coupling between a microwave cavity and a spin ensemble with Raman heterodyne spectroscopy

Rare-earth ions in solids are under active investigation for quantum microwave-optical signal converters. Here, light passed through an Er:YSO crystal sitting in a driven microwave resonator develops modulation due to three-wave mixing in the erbium dopants. Strong coupling between the microwave cavity and the spins causes modulation when the microwaves are resonant with the spin-cavity polaritons rather than the spins. This work extends the rare-earth microwave-optical conversion to both millikelvin temperatures and isotopically pure dopants.

Microwave to optical photon conversion via fully concentrated rare-earth-ion crystals

Most investigations of rare earth ions in solids for quantum information have used rare earth ion doped crystals. Here we analyse the conversion of quantum information from microwave photons to optical frequencies using crystals where the rare earth ions, rather than being dopants, are part of the host crystal. The potential of large ion densities and small linewidths makes such systems very attractive in this application. We show that, as well as high efficiency, large bandwidth conversion is possible. In fact, the collective coupling between the rare earth ions and the optical and microwave cavities is large enough that the limitation on the bandwidth of the devices will instead be the spacing between magnon mode modes in the crystal.

Quantum technologies with optically interfaced solid-state spins

Spins of impurities in solids provide a unique architecture to realize quantum technologies. A quantum register of electron and nearby nuclear spins in the lattice encompasses high-fidelity state manipulation and readout, long-lived quantum memory, and long-distance transmission of quantum states by optical transitions that coherently connect spins and photons. These features, combined with solid-state device engineering, establish impurity spins as promising resources for quantum networks, information processing and sensing. Focusing on optical methods for the access and connectivity of single spins, we review recent progress in impurity systems such as colour centres in diamond and silicon carbide, rare-earth ions in solids and donors in silicon. We project a possible path to chip-scale quantum technologies through sustained advances in nanofabrication, quantum control and materials engineering.

EPR study of ceria nanoparticles containing different concentration of Ce3+ ions

The electron paramagnetic resonance of Ce3+ ions in ceria is a rather controversial issue. In this report we analyze the EPR line with g ∼1.97 in the absorption spectra of ceria powders, which has been assigned in many studies to Ce3+ ions. Such an assignment is not in agreement with the experimental data nor with the theory of spin-lattice relaxation of rare earth ions in solids. Our statement is supported by our experimental results based on EPR spectroscopy of nanocrystalline ceria, synthesized in various ways, as well as by magnetization measurements of as-prepared and vacuum-annealed ceria nanoparticles. The possible model of the paramagnetic center, which is assigned to the EPR line with g ∼1.97 in ceria, is an electron trapped near the surface Ce3+/Ce4+ redox pair.

Protecting a Diamond Quantum Memory by Charge State Control.

In recent years, solid-state spin systems have emerged as promising candidates for quantum information processing. Prominent examples are the nitrogen-vacancy (NV) center in diamond, phosphorus dopants in silicon (Si:P), rare-earth ions in solids, and VSi-centers in silicon-carbide. The Si:P system has demonstrated that its nuclear spins can yield exceedingly long spin coherence times by eliminating the electron spin of the dopant. For NV centers, however, a proper charge state for storage of nuclear spin qubit coherence has not been identified yet. Here, we identify and characterize the positively charged NV center as an electron-spin-less and optically inactive state by utilizing the nuclear spin qubit as a probe. We control the electronic charge and spin utilizing nanometer scale gate electrodes. We achieve a lengthening of the nuclear spin coherence times by a factor of 4. Surprisingly, the new charge state allows switching of the optical response of single nodes facilitating full individual addressability.

Full-profile fitting of emission spectrum to determine transition intensity parameters of Yb3 +:GdTaO4**Project supported by the National Natural Science Foundation of China (Grant Nos. 51172236, 51502292, 51272254, 51102239, 61205173, and 61405206).

The Judd–Ofelt theoretic transition intensity parameters of luminescence of rare-earth ions in solids are important for the quantitative analysis of luminescence. It is very difficult to determine them with emission or absorption spectra for a long time. A “full profile fitting” method to obtain in solids with its emission spectrum is proposed, in which the contribution of a radiative transition to the emission spectrum is expressed as the product of transition probability, line profile function, instrument measurement constant and transition center frequency or wavelength, and the whole experimental emission spectrum is the sum of all transitions. In this way, the emission spectrum is expressed as a function with the independent variables intensity parameters , full width at half maximum (FWHM) of profile functions, instrument measurement constant, wavelength, and the Huang–Rhys factor S if the lattice vibronic peaks in the emission spectrum should be considered. The ratios of the experimental to the calculated energy lifetimes are incorporated into the fitting function to remove the arbitrariness during fitting and other parameters. Employing this method obviates measurement of the absolute emission spectrum intensity. It also eliminates dependence upon the number of emission transition peaks. Every experiment point in emission spectra, which usually have at least hundreds of data points, is the function with variables and other parameters, so it is usually viable to determine and other parameters using a large number of experimental values. We applied this method to determine twenty-five of Yb3+ in GdTaO4. The calculated and experiment energy lifetimes, experimental and calculated emission spectrum are very consistent, indicating that it is viable to obtain the transition intensity parameters of rare-earth ions in solids by a full profile fitting to the ions’ emission spectrum. The calculated emission cross sections of Yb3+:GdTaO4 also indicate that the F–L formula gives larger values in the wavelength range with reabsorption.

Multidimensional Purcell effect in an ytterbium-doped ring resonator

A silicon nitride ring resonator with implanted ytterbium ions offers a means for greatly enhanced ion–light interactions in an integrated optics platform. Rare-earth ions in solids are of particular interest for quantum information storage and processing because of the long coherence times of the 4f states1. In the past few years, substantial progress has been made by using ensembles of ions2,3,4,5,6 and single ions7,8,9,10. However, the weak optical transitions within the 4f manifold pose a great challenge to the optical interaction with a single rare-earth ion on a single-photon level. Here, we demonstrate a ninefold enhanced ion–light interaction (Purcell effect11) in an integrated-optics-based, fibre-coupled silicon nitride (Si3N4) ring resonator with implanted ytterbium ions (Yb3+). We unveil the one-, two- and three-dimensional contributions to the Purcell factor as well as the temperature-dependent decoherence and depolarization of the ions. The results indicate that this cavity quantum electrodynamics (QED) system has the potential of interfacing single rare-earth ions with single photons on a chip.

Optical measurement of the effect of electric fields on the nuclear spin coherence of rare-earth ions in solids.

We show that the coherence properties of the nuclear spin states of rare-earth ions in solids can be manipulated by small applied electric fields. This was done by measuring the Stark effect on the nuclear quadrupole transitions of (151)Eu in Y(2)SiO(5) (YSO) using a combination of Raman heterodyne optical detection and Stark modulated quadrupole echoes to achieve high sensitivity. The measured Stark coefficients were 0.42 and 1.0 Hz cm/V for the two quadrupole transitions at 34.54 and 46.20 MHz, respectively. The long decoherence time of the nuclear spin states (25 ms) allowed us to make the measurements in very low electric fields of ∼ 10 V/cm, which produced 100% modulation of the nuclear spin echo, and to measure Stark shifts of ∼ 1 Hz or 20 ppm of the inhomogeneous linewidth.

Vacuum ultraviolet luminescence of wide band-gap solids studied using time-resolved spectroscopy with synchrotron radiation

Some highlights of the time-resolved vacuum ultraviolet (VUV) luminescence spectroscopy of solids using synchrotron radiation (SR) are outlined, including studies of the unique phenomenon crossluminescence (CL) and the contribution of time-resolved VUV spectroscopy to the understanding of 5d–4f transitions of rare earth ions in solids. The main properties of CL studied at different SR sources are described and some unclear aspects of CL are pointed out. The results of recent studies of some CL-active nanosize materials are presented. We describe the time-resolved experiments which led to the discovery of 5d–4f luminescence in the deep VUV region (near 10 eV) of Gd3+ and Lu3+ ions incorporated into some wide band-gap fluoride hosts. The results of high-resolution (Δλ ∼ 0.5 Å) studies of 5d–4f emission and 4f–5d excitation spectra of Gd3+ and Lu3+, which allowed the detailed analysis of electron–lattice coupling in these systems, are presented. Possible new developments in the femtosecond time-resolved spectroscopy of solids with a free electron laser are discussed.

Quantum error correction in a solid-state hybrid spin register

Error correction is important in classical and quantum computation. Decoherence caused by the inevitable interaction of quantum bits with their environment leads to dephasing or even relaxation. Correction of the concomitant errors is therefore a fundamental requirement for scalable quantum computation. Although algorithms for error correction have been known for some time, experimental realizations are scarce. Here we show quantum error correction in a heterogeneous, solid-state spin system. We demonstrate that joint initialization, projective readout and fast local and non-local gate operations can all be achieved in diamond spin systems, even under ambient conditions. High-fidelity initialization of a whole spin register (99 per cent) and single-shot readout of multiple individual nuclear spins are achieved by using the ancillary electron spin of a nitrogen-vacancy defect. Implementation of a novel non-local gate generic to our electron-nuclear quantum register allows the preparation of entangled states of three nuclear spins, with fidelities exceeding 85 per cent. With these techniques, we demonstrate three-qubit phase-flip error correction. Using optimal control, all of the above operations achieve fidelities approaching those needed for fault-tolerant quantum operation, thus paving the way to large-scale quantum computation. Besides their use with diamond spin systems, our techniques can be used to improve scaling of quantum networks relying on phosphorus in silicon, quantum dots, silicon carbide or rare-earth ions in solids.

Impurity trapped exciton states related to rare earth ions in crystals under high hydrostatic pressure

Emission related to rare earth ions in solids takes place usually due to 4fn → 4fn and 4fn−15d1 → 4fn internal transitions. In the case of band to band excitation the effective energy transfer from the host to optically active impurity is required. Among other processes one of the possibilities is capturing of the electron at excited state and hole at the ground state of impurity. Localization of electron or hole at the dopand site creates a long range Coulomb potential that attracts the second carrier which then occupies the localized Rydberg-like states. Such a system can be considered as impurity trapped exciton. Usually impurity trapped exciton is a short living phenomenon which decays non-radiatively leaving the impurity ion in the excited state. However, in several compounds doped with Eu2+ the impurity trapped exciton states become stable and contribute to the radiative processes though anomalous luminescence that appears apart of the 4f7 → 4f7 and 4f75d1 → 5f7 emission. In this contribution pressure effect on energies of the 4fn−15d1→5fn transitions in Ln doped oxides and fluorides as well as influence of pressure on the energy of impurity trapped exciton states is discussed. The latest results on high pressure investigations of luminescence related to Pr3+, and Eu2+ in different lattices are reviewed.

Excited states dynamics under high pressure in lanthanide-doped solids

Emission related to rare earth ions in solids takes place usually due to 4fn→4fn and 4fn−15d1→4fn internal transitions. In the case of band to band excitation the effective energy transfer from the host to optically active impurity is required. Among other processes one of the possibilities is capturing of the electron at the excited state and the hole at the ground state of impurity. The latest results on high pressure investigations of luminescence related to Pr3+ and Eu2+ in different lattices are briefly reviewed. The influence of pressure on anomalous luminescence and 4fn−15d1→4fn luminescence in BaSrF2:Eu2+ and LiBaF3:Eu2+ systems and Pr3+ 4fn→4fn emission quenching is presented and discussed. A theoretical model describing the impurity-trapped exciton as a system where a hole is localized at the impurity and an electron is captured by Coulomb potential at Rydberg-like states is developed. The results show the importance of local lattice relaxation for the creation of stable impurity-trapped exciton states. The ligands shifts create a potential barrier that controls the effect of mixing between the Rydberg-like electron and localized electron wave functions.

The simple model and its application to interpretation and assignment of 4 f–5 d transition spectra of rare-earth ions in solids

The simple model for 4 f–5 d transition spectra of rare-earth ions in crystals is reviewed. We summarize successful applications to the 4 f–5 d spectra of Nd 3+, Sm 3+ , Eu 3+, Eu 2+, Tb 3+, Ho 3+, Er 3+ ions in various crystals. Some unsolved issues are also mentioned and discussed briefly.

First-principles analysis method for the multiplet structures of rare-earth ions in solids

A first-principles fully relativistic multielectron method based on molecular orbital (MO) theory is applied to the analysis for the 4f5d configurations of Pr3+-doped LaF3, LiYF4 (YLF), and CaF2 crystals. The formation of MOs between the Pr 5d orbitals and the ligand fluorine 2p orbitals is considered using a (PrF11)8− and (PrF8)5− molecular models. The energy of the lowest level of 4f5d configuration decreases in the order LaF3, LiYF4, and CaF2 (Oh symmetry). The high energy in Pr3+:LaF3 is ascribed to the smaller ligand-field splitting due to the large coordination number. The analysis of many-electron wave functions shows the mixtures between the spin-orbit splitting of the 4f-level MOs and the ligand-field splitting of the 5d-level MOs. Configuration interaction with one-electron excitations gives transition probability to the originally forbidden two-electron excitations, which produce satellite structures in spectra.

Multiphonon relaxation of excited rare-earth ions in ionic matrices

A theory of multiphonon relaxation for rare-earth ions in ionic crystals and glasses is presented. The theory is based on the static coupling scheme. The electron-vibration coupling is assumed to be linear with respect to the relative ligand rare-earth displacements. The multiphonon transitions are induced by higher-order lattice anharmonicity of the ionic motions. The probability of multiphonon transitions could be related to the IR multiphonon spectrum. A simplified form of the general expression is proposed. The electronic part of the expression obtained has exactly the same form as the corresponding expression in the well-known Judd-Ofelt theory for optical transitions between multiplets of rare-earth ions in solids.

High-resolution laser spectroscopy of rare-earth doped insulators: a personal perspective

I offer some reflections on the past three decades of high-resolution spectroscopy of rare-earth ions in solids which was ushered in by the development of tunable lasers in the mid 1970s. A brief review is given of some of the accomplishments in the area of spectral hole-burning and coherent transient spectroscopy, emphasizing work with which the author has been associated. Spectral hole-burning has been characterized by a richness of mechanisms. These include population storage in nuclear-spin and electron-spin Zeeman sub-levels, hyperfine and superhyperfine levels and metastable optical levels with corresponding hole lifetimes from many hours to microseconds. In addition, persistent hole-burning has been seen in disordered materials and in those showing photo-ionization or photo-chemistry following excitation into zero-phonon lines. This has made hole-burning a generally useful technique for the measurement of magnetic and electric dipole moments, hyperfine interactions, spin relaxation and thermally induced line-broadening. Photon-echoes have proven to be the prime source of coherence-time information and coherence times as long as several milliseconds corresponding to optical resonance widths of less than 100 Hz have been reported. Tables summarizing these results and providing references to original work are included.

Observation of sub-kilohertz resonance in Rf-Optical double resonance experiment in rare earth ions in solids

We have observed kilohertz and sub-kilohertz resonance structures in RF-optical double resonance experiments of rare-earth-doped solids, when the frequency of the RF ® eld is scanned across the hyper® ne transitions while monitoring the resonant optical absorption of a CW laser. The ea ect is observed only when the laser spectral width is broad compared to the hyper® ne structure. The observed line widths are apparently free of the inhomogeneous widths of hyper® ne levels and the line shape has peculiar double peak structure. The ea ect is modelled with a resonance involving three atomic levels interacting with three electromagnetic ® elds, two optical and one RF, in a triangular ordelta' con® guration. While the ordinary optical- RF two-® eld resonance is limited by spin inhomogeneous width, the simul- taneous excitation of three coupled transitions leads to narrow and highly nonlinear resonance structures that are not averaged by the inhomogeneous distribution of hyper® ne transition. We have observed a peculiarly narrow resonance structure in the course of optical-RF double resonance experiment of rare earth ions in solids. The reso- nance is characterized by a sharp doublepeak structure in the absorption spectrum as the RF frequency is scanned across the hyper® ne transition, with the few kilohertz width of the transparency hole at least an order of magnitude narrower than the spin inhomogeneous width. The ea ect is evident only when the laser bandwidth is larger than the hyper® ne level splittings. A theoretical model is presented based on the assumption that the optical ® elds of a noisy laser simul- taneously couples an optically excited state with two hyper® ne levels of the ground state, which in turn are acted on by the RF ® eld. A quantum interference ea ect among the three coupled transitions creates sharp fringes in the frequency domain that are not averaged out by ensemble average over the inhomogeneousbroadening of the optical or spin transitions. The model is found to be consistent with the main features of the experimental observations. Various quantum interference ea ects in atomic transitions have recently been research topics of great interest, because of the rich and often counter-intuitive