Rare Earth Ions In Crystals Research Articles

Quantum computation of the lowest-energy Kramers states and magnetic g-factors of rare earth ions in crystals

Quantum computation of the lowest-energy Kramers states and magnetic g-factors of rare earth ions in crystals

A complete study on the temperature dependences of zero-field splitting b4 0 for Eu2+ and Gd3+ ions in CdF2 crystal

ABSTRACT This paper gives for the first time a complete equation to analyze the temperature dependence (or thermal variation) of spin-Hamiltonian parameter from low to high temperatures for transition metal and rare-earth ions in crystals. This equation includes not only the dynamic effect (only considered in previous papers) caused by electron–phonon interaction but also the static effect owing to lattice thermal expansion. Based on the complete equation, the thermal variations of zero-field splitting b4 0 from low to high temperatures for cubic Eu2+ and Gd3+ centers in CdF2 crystal are studied. The contributions due to static effect are estimated from the pressure dependence of zero-field splitting b4 0. The static parameters B (charactering the static effect) and the electron–phonon coupling parameters K (charactering the dynamic effect) for both systems are determined and the coefficients (B + K) in the complete equation are obtained. The results are discussed.

Ancilla-mediated qubit readout and heralded entanglement between rare-earth dopant ions in crystals

Owing to their long excited state lifetimes, rare-earth ions in crystals are widely used in quantum applications. To allow optical readout of the qubit state of individual ions, we propose to dope the crystal with an additional nearby ancilla ion with a shorter radiative lifetime. We show how a Bayesian analysis exhausts the information about the state of the qubit from the optical signal of the ancilla ion. We study the effects of incoherent processes and propose ways to reduce their effect on the readout. Finally, we extend the architecture to ions residing in two remote cavities, and we show how continuous monitoring of fluorescence signals from the two ancilla ions leads to entanglement of the qubit ions.

Giant spin-noise gain enables magnetic resonance spectroscopy of impurity crystals

Spin noise spectroscopy is a method of magnetic resonance widely used, nowadays, in atomic and semiconductor research. Classical objects of the EPR spectroscopy - dielectrics with paramagnetic impurities - seemed to be unsuitable for this technique because of large widths of allowed optical transitions and, therefore, low specific Faraday rotation (FR). We show, however, that the FR noise detected at the wavelength of a weak optical transition (with low regular FR) may increase by many orders of magnitude as its homogeneous width decreases. This spin-noise gain effect, numerically described by the ratio of the inhomogeneous linewidth to homogeneous, relates primarily to forbidden intraconfigurational transitions of impurity ions with unfilled inner electronic shells. Specifically, for the f-f transitions of rare-earth ions in crystals, this factor may reach 10$^8$. In this paper, we report on the first successful application of spin noise spectroscopy for detecting magnetic resonance of rare-earth ions in crystals.

Persistent atomic frequency comb based on Zeeman sub-levels of an erbium-doped crystal waveguide

Long-lived sub-levels of the electronic ground-state manifold of rare-earth ions in crystals can be used as atomic population reservoirs for photon echo-based quantum memories. We measure the dynamics of the Zeeman sub-levels of erbium ions that are doped into a lithium niobate waveguide, finding population lifetimes at cryogenic temperatures down to 0.7 K as long as seconds. Then, using these levels, we prepare and characterize atomic frequency combs (AFCs), which can serve as a memory for quantum light at 1532 nm wavelength. The results allow predicting a 0.1% memory efficiency, limited mainly by unwanted background absorption that we believe to be caused by excitation-induced erbium spin flips and frequency shifting due to two-level systems or non-equilibrium phonons. Hence, while it should be possible to create an AFC-based quantum memory in E r 3 + : T i 4 + : L i N b O 3 , improved crystal growth together with optimized AFC preparation will be required to make it suitable for applications in quantum communication.

Impurity fluorescence self-quenching in Nd3+: Gd3BWO9 crystalline powders: Experiment and analysis

We made precision measurements of fluorescence kinetics of crystalline Gd3BWO9: Nd3+ doped powders at room temperature by the method of gated single photon counting technique in a wide range of Nd3+ concentrations. The powders were synthesized with a high temperature solid-state reaction.We managed to describe the concentration dependence of the impurity fluorescence self-quenching kinetics curves with the constant microparameters of energy migration CDD = 2.97 nm6/ms and quenching energy transfer CDA = 0.43 nm6/ms. The microparameters were found with the direct fitting of the curves to the analytical formula of microscopic theory derived specifically for concentration fluorescence self-quenching accounting energy migration over donors. The obtained ratio of the values of the microparameters z = CDA/CDD = 0.145 indicates a hopping mechanism of fluorescence self-quenching of the 4F3/2 level of the Nd3+ ion. We developed a kinetic method to determine with high accuracy the concentrations of impurity rare-earth ions in crystals at low doping level, which is significantly higher than that for energy-dispersive X-ray spectroscopy (EDS) analysis. For arbitrary systems with fluorescence self-quenching, we obtained an analytical formula that allows us to calculate the value of the activator concentration at which the fluorescence brightness is maximum. For the studied Nd3+: Gd3BWO9 powder samples, the maximum brightness is realized at xmax≈2.98 at.%, which is in good agreement with the experimental value.

Insight into the thermal shifts of ten fluorescence peaks Y1–Y10 for Sm3+ ions in Y3Al5O12 crystal

The observed linear thermal shifts of ten fluorescence peaks Y1–Y10 from room temperature to about 1000 K for Y3Al5O12:Sm3+ (grown by the Czochralski method) were investigated by considering both the static effect owing to lattice thermal expansion and the dynamic effect stemming from electron–phonon interaction. The static effects were acquired by using the pressure dependences of these fluorescence peak positions. The static effects for the ten fluorescence peaks resulted in thermal blue shift, but the dynamic effects for all peaks except Y7 led to thermal red shift. The observed nature of thermal shift (i.e. red or blue) of a fluorescence peak was due to competition between the static and dynamic effects. Based on an approximate treatment, the static parameter A (characterizing the static effect) and electron–phonon coupling parameter αʹ (characterizing the dynamic effect) for these fluorescence peaks were estimated in the case where thermal shift curves from low temperature to near or higher than room temperature were not measured. Parameters A for all fluorescence peaks and αʹ for all peaks except Y7 were comparable in sign and magnitude with those of the sharp luminescence peaks of other rare earth ions in crystals and so were deemed to be reasonable. The causes of the exception for αʹ of Y7 spectral peak (including the very large observed thermal blue shift of this peak) remain unclear.

Deformation Broadening and the Fine Structure of Spectral Lines in Optical Spectra of Dielectric Crystals Containing Rare-Earth Ions

The procedure of calculation of the spectral line shape in optical spectra of rare-earth ions in crystals with the inclusion of random deformations of an elastically anisotropic crystal lattice caused by point defects is developed. The distribution function of components of the random strain tensor in the case of a low defect concentration is obtained as the generalized six-dimensional Lorentz distribution. The distribution function parameters are represented by the integral functional of the strain tensor components on a sphere of unit radius containing an isotropic point defect in its center. The numerical calculations of the strain tensors induced by point defects and the parameters of the distribution functions of random strains in LiLuF4 and LaAlO3 crystals have been performed. The calculated envelope with the doublet structure corresponding to the Γ2(3H4) → Γ34(3H5) singlet–doublet transition in the absorption spectrum of Pr3+ ions in the LiLuF4 crystal agrees well with the data of the measurements.

Деформационное уширение и тонкая структура спектральных линий в оптических спектрах диэлектрических кристаллов, содержащих редкоземельные ионы

AbstractThe procedure of calculation of the spectral line shape in optical spectra of rare-earth ions in crystals with the inclusion of random deformations of an elastically anisotropic crystal lattice caused by point defects is developed. The distribution function of components of the random strain tensor in the case of a low defect concentration is obtained as the generalized six-dimensional Lorentz distribution. The distribution function parameters are represented by the integral functional of the strain tensor components on a sphere of unit radius containing an isotropic point defect in its center. The numerical calculations of the strain tensors induced by point defects and the parameters of the distribution functions of random strains in LiLuF_4 and LaAlO_3 crystals have been performed. The calculated envelope with the doublet structure corresponding to the Γ_2(^3 H _4) → Γ_34(^3 H _5) singlet–doublet transition in the absorption spectrum of Pr^3+ ions in the LiLuF_4 crystal agrees well with the data of the measurements.

Determination of the g-factors measured by EPR based on theoretical crystal field and superposition model analyses for lanthanide-based magnetically concentrated crystals – case study: double tungstates and molybdates

ABSTRACTThe methods developed for theoretical determination of g-factors measured by electron paramagnetic resonance (EPR) for single transition ions are extended to lanthanide-based magnetically concentrated crystals. The crystal field (CF) and superposition model (SPM) analyses are employed for optoelectronic materials: double tungstates and molybdates. Using the crystallographic data for Nd3+ ions in RbNd(WO4)2 and Yb3+ ions in KYb(MoO4)2 as input for SPM modelling, the CF parameters (CFPs) are predicted for the respective ions. The matrix for g tensor is calculated by the complete diagonalisation method. By matching three principal g values (gxx, gyy, gzz) to those measured by EPR, three adjustable SPM intrinsic parameters:, and are obtained. The reliability of the related CFPs is verified by comparative analysis of available data. The results demonstrate that the methods suitable for single lanthanide ions in crystal can be successfully applied to magnetically concentrated systems. The predicted g tensor anisotropy enables consideration of EPR linewidths arising from dipolar broadening in ALn(MO4)2 (A = alkali ions, Ln = lanthanide ions, M = W or Mo) systems based on the moment method, which requires accurate g-factors. The model parameters determined here may be utilised for SPM/CFP calculations for Nd3+ and Yb3+ ions in single-molecule magnets and single-ion magnets.

Characterization ofYb3+171:YVO4for photonic quantum technologies

Rare-earth ions in crystals are a proven solid-state platform for quantum technologies in the ensemble regime and attractive for new opportunities at the single ion level. Among the trivalent rare earths, ${}^{171}\mathrm{Yb}^{3+}$ is unique in that it possesses a single 4f excited-state manifold and is the only paramagnetic isotope with a nuclear spin of 1/2. In this work, we present measurements of the optical and spin properties of $^{171}$Yb$^{3+}$:YVO$_4$ to assess whether this distinct energy level structure can be harnessed for quantum interfaces. The material was found to possess large optical absorption compared to other rare-earth-doped crystals owing to the combination of narrow inhomogeneous broadening and a large transition oscillator strength. In moderate magnetic fields, we measure optical linewidths less than 3 kHz and nuclear spin linewidths less than 50 Hz. We characterize the excited-state hyperfine and Zeeman interactions in this system, which enables the engineering of a $\Lambda$-system and demonstration of all-optical coherent control over the nuclear spin ensemble. Given these properties, $^{171}$Yb$^{3+}$:YVO$_4$ has significant potential for building quantum interfaces such as ensemble-based memories, microwave-to-optical transducers, and optically addressable single rare-earth-ion spin qubits.

Controlling rare-earth ions in a nanophotonic resonator using the ac Stark shift

On-chip nanophotonic cavities will advance quantum information science and measurement because they enable efficient interaction between photons and long-lived solid-state spins, such as those associated with rare-earth ions in crystals. The enhanced photon-ion interaction creates new opportunities for all-optical control using the ac Stark shift. Toward this end, we characterize the ac Stark interaction between off-resonant optical fields and Nd$^{3+}$-ion dopants in a photonic crystal resonator fabricated from yttrium orthovanadate (YVO$_4$). Using photon echo techniques, at a detuning of 160 MHz we measure a maximum ac Stark shift of 2$\pi\times$12.3 MHz per intra-cavity photon, which is large compared to both the homogeneous linewidth ($\Gamma_h =$100 kHz) and characteristic width of isolated spectral features created through optical pumping ($\Gamma_f \approx$3 MHz). The photon-ion interaction strength in the device is sufficiently large to control the frequency and phase of the ions for quantum information processing applications. In particular, we discuss and assess the use of the cavity enhanced ac Stark shift to realize all-optical quantum memory and detection protocols. Our results establish the ac Stark shift as a powerful added control in rare-earth ion quantum technologies.

A general way of analyzing EPR spectroscopy for a pair of magnetically equivalent lanthanide ions in crystal: A case study of BaY2F8:Yb3+ crystal

Electron paramagnetic resonance (EPR) is an important tool to study the complex interactions (e.g., exchange and magnetic dipole-dipole interactions) for a pair of lanthanide (Ln) ions in crystals. How to analyze these EPR spectra and obtain the strength of each interaction is a challenge for experimentalists. In this work, a general way of calculating the EPR lines for two magnetically equivalent Ln ions is given by us to solve this problem. In order to explain their EPR spectra and obtain exchange interaction parameters Ji (i = x, y, z) between them, we deduce the analytic formulas for computing the angular dependent EPR lines for such Ln pairs under the condition of weak coupling (|Ji| ≪ hv, where v is the microwave frequency in the EPR experiment) and set up the spin-Hamiltonian energy matrix that should be diagonalized to obtain these lines if intermediate (|Ji| ∼ hv) and strong (|Ji| > hv) couplings are encountered. To verify our method, the experimental EPR spectra for the Yb3+ doped BaY2F8 crystal are considered by us and the EPR lines from the isolated Yb3+ ion and Yb3+-Yb3+ pair with distance R equal to 0.371 nm are identified clearly. Moreover, exchange interaction parameters (Jx ≈ –0.04 cm–1, Jy ≈ –0.24 cm–1, and Jz ≈ –0.1 cm–1) for such a pair are also determined by our calculations. This case study demonstrates that the theoretical method given in this work would be useful and could be applied to understand interactions between Ln ions in crystals.

Coherent control of electron-nuclear states of rare-earth ions in crystals using radio-frequency and microwave radiation

We have demonstrated electron-electron and electron-nuclear spin manipulations of Gd3+ ion in CaWO4 crystal. The results suggest that the studied system is perspective for multiqubit implementation in quantum computing.

Optical spectroscopy of random deformations in elastically-anisotropic crystals containing rare-earth ions

We present the results of studies of spectral effects in the optical high-resolution (0.01 cm-1) spectra of rare-earth ions in crystals caused by random deformations of a crystal lattice. Low-temperature polarized transmission spectra in a broad spectral range (5000–15000 cm −1 ) were taken for tetragonal single crystals ABO4 (A=Y, Lu; B=V, P) containing impurity Tm 3+ ions with concentrations 0.2 and 1.0 at.%. A specific fine structure of singlet-doublet transitions in the Tm3+ ions was observed. We demonstrate a possibility to estimate a concentration of intrinsic lattice defects from the analysis of the measurement data, by making use of an analytical expression derived in the present work for the distribution function of random lattice strains induced by point defects in the elastically-anisotropic continuum.

Investigations of hyperfine and isotope structures in optical spectra of crystals with rare-earth ions

This is a review of works on hyperfine and isotope structures in the spectra of rare-earth ions in crystals that have been performed at the Laboratory of Fourier Spectroscopy of the Institute for Spectroscopy, Russian Academy of Sciences. The applicability of these studies to the development of optical quantum memory is discussed.

Spectroscopic detection of single Pr3+ ions on the 3H4−1D2 transition

Rare earth ions in crystals exhibit narrow spectral features and hyperfine-split ground states with exceptionally long coherence times. These features make them ideal platforms for quantum information processing in the solid state. Recently, we reported on the first high-resolution spectroscopy of single ions in yttrium orthosilicate nanocrystals via the transition at a wavelength of 488 nm. Here we show that individual praseodymium ions can also be detected on the more commonly studied transition at 606 nm. In addition, we present the first measurements of the second-order autocorrelation function, fluorescence lifetime, and emission spectra of single ions in this system as well as their polarization dependencies on both transitions. Furthermore, we demonstrate that by a proper choice of the crystallite, one can obtain narrower spectral lines and, thus, resolve the hyperfine levels of the excited state. We expect our results to make single-ion spectroscopy accessible to a larger scientific community.

Single molecule fluorescence resonance energy transfer scanning near-field optical microscopy: potentials and challenges.

A few years ago, single molecule Fluorescence Resonance Energy Transfer Scanning Near-Field Optical Microscope (FRET SNOM) images were demonstrated using CdSe semiconductor nanocrystal-dye molecules as donor-acceptor pairs. Corresponding experiments reveal the necessity to exploit much more photostable fluorescent centers for such an imaging technique to become a practically used tool. Here we report the results of our experiments attempting to use nitrogen vacancy (NV) color centers in nanodiamond (ND) crystals, which are claimed to be extremely photostable, for FRET SNOM. All attempts were unsuccessful, and as a plausible explanation we propose the absence (instability) of NV centers lying close enough to the ND border. We also report improvements in SNOM construction that are necessary for single molecule FRET SNOM imaging. In particular, we present the first topographical images of single strand DNA molecules obtained with fiber-based SNOM. The prospects of using rare earth ions in crystals, which are known to be extremely photostable, for single molecule FRET SNOM at room temperature and quantum informatics at liquid helium temperatures, where FRET is a coherent process, are also discussed.

Decay times of radiative and non-radiative transitions in rare-earth ions

We present a theoretical method for evaluation of decay times of both radiative and non-radiative transitions in rare-earth ions in crystals and glasses. Relying on one experimentally known lifetime and known parameters of electrostatic and spin–orbit interaction, the fluorescence spectra can be modelled for various pumping wavelengths providing new insights into dynamical processes of fluorescence.

Influence of excited configurations on the intensities of electric-dipole transitions of rare-earth ions

The theory of induced electric-dipole transitions of rare-earth ions in crystals and glasses is improved by taking into account the third-order effects of perturbation theory with respect to the energies of virtual excitations of 4f electrons to the 5d states. Since the energy regions of excited 4f N − 15d states are usually superimposed with the charge-transfer bands, the effects caused by a virtual transfer of an electron from the outer shells of ions of the surroundings (ligands) to the unfilled 4f N shells are also considered. The Pr3+, Sm3+, and Eu3+ ions are considered as examples. It is found that some difficulties inherent in the Judd-Ofelt calculation scheme are successfully overcome. The agreement of the calculated results with the experimental data improves.