Splitting Of Energy Levels Research Articles

Nonlinear optical refractive index changes of GaAs/AlGaAs quantum dot under tangent-square potential

We investigate in detail the effects of some factors on the optical refractive index change (RICs) in GaAs/AlGaAs parabolic quantum dot (QD) with tangent-square potential (TSP) in our paper, such as the radius of quantum dot, the depth and width limit potential. In the first place, we increase the limit of tangent square potential in the z-direction of the system, which is based on the original parabolic QD, then the Schrödinger equation corresponding to the modified system is solved, and the expressions of different splitting energy levels and wave functions are obtained. At last, the numerical simulations indicate that these physical factors have a significant effect on the nonlinear optical performances of the tunable system.

Preparation of Tm3+ ion-doped BaZrO3 powder and its luminescence performance study

A series of Tm3+ ion doped BaZrO3 blue phosphors were synthesized by traditional hydrothermal method. The structure, morphology and luminescence properties of the synthesized materials were examined by X-ray diffraction (XRD), scanning electron microscopy (SEM), fourier transform infrared spectrum (FT-IR), size distribution and fluorescence spectrometer, respectively. The results show that the final products existed in a pure phase and with increasing of Tm3+ concentration, the grain size, lattice constants and lattice strain showed a trend of increase. In addition, by changing the supersaturation of the precursor solution, the spherical particle size can be carefully adjusted. When the doping molar fraction of Tm3+ was 5.0%, thebluemovementoftheinfrared absorption peakwasthemost, which was consistent with the theoretical calculations. Finally, based on the unique “probe” characteristics of Eu3+, it was confirmed that leading cause of energy level splitting was the reduction of the local symmetry of the matrix environment and the luminescence decrease should be attributed to the concentration quenching and lattice distortion.

Multichannel Six‐Wave Mixing with Spatial Multimode and Squeezing via Atomic Coherence

AbstractMultimode properties, based on nonlinear parametric processes, have potential research value on entanglement imaging. This paper studies the spatial and frequency multimode from dressing parametric‐amplified six‐wave mixing (PA‐SWM) process with three entangled signals. The S1 signal contains fifth‐order nonlinearity, the S2 signal contains electromagnetically induced absorption and fifth‐order nonlinearity, and the S3 signal contains Autler–Townes splitting (AT), second‐ and fifth‐order nonlinearity. The frequency multimode is attributed to dressing energy level splitting in spontaneous SWM (SSWM) process. The spatial multimode is due to frequency multimode and beam splitting via Kerr nonlinearity. In the spatial domain, it finds the optimal conditions of intensity difference squeezing (IDS) and spatial imaging along with their competitive relationship. On the one hand, the light spots with single spatial mode are contributed to the maximum IDS but not conducive to entanglement imaging; on the other hand, the light spots with multiple spatial modes are instrumental in entanglement imaging but not appropriate for the IDS. This research has potential applications in squeezed light sources for quantum metrology, and correlated imaging of spatial signals.

Modelling of the torsional IR spectra of the HSSSH, DSSSH, and DSSSD molecules

Equilibrium configurations of trans- and cis- conformers of the HSSSH molecule (trisulfane), as well as the vibrational spectra of both conformers, were calculated at the MP2/Aug-cc-pVTZ, level of theory in the harmonic and anharmonic approximations. A more accurate analysis of torsional vibrations of thiol groups was performed by constructing 2D surfaces of a) potential energy, b) kinetic coefficients, and c) dipole moment components as functions of torsional coordinates of S-H groups. The values of b) and c) were calculated at the MP2/Aug-cc-pVTZ level of theory while the values of a) were calculated at the B3LYP/Aug-cc-pVTZ, MP2/cc-pVTZ, MP2/Aug-cc-pVTZ, MP2/cc-pVQZ, MP2/CBS(T,Q) and CCSD(T)/Aug-cc-pVTZ levels of theory. The energies of the stationary torsional states of the trisulfane molecule conformers were determined by numerically solving the vibrational Schrödinger equation of restricted dimensionality. The frequencies of torsional vibrations of S-H groups, as well as the splittings of torsional energy levels in trans- and cis-conformers due to tunneling between equivalent configurations of the molecule, were determined. The calculated values of tunneling frequencies in the ground torsional state of HSSSH and DSSSD trans-conformers (2.3 * 10−22 and 7.5 * 10−27 cm−1, respectively) are of particular interest due to the fact that trisulfane is considered to be one of the best candidates for establishing the effect of violation of parity conservation law in chiral molecules.

Shortwave Infrared Luminescence of Tetravalent Chromium and Divalent Nickel: Phosphor Design Principles and Applications

Shortwave infrared radiations (SWIR, 900–1700 nm) emitting inorganic luminescent materials are key components for multiple applications, which range from optical communication and anticounterfeiting purposes to chemical and medical diagnosis. The blue light excitable SWIR phosphors activated with the transition metal ions Cr4+/Ni2+ are considered prospective light sources for an upcoming compact modern device using phosphor converter technology. In this review, the crystal field theory and Tanabe-Sugano diagram are briefly discussed to understand the splitting of energy levels and the concurrent effect. Several possible strategies to achieve and enhance the luminescence efficiency of Cr4+/Ni2+ SWIR emission are disclosed as is the reported chemical system. Finally, the domains for the potential practical application of SWIR phosphors are introduced. This review will provide information on the recent advances and the luminescence mechanism of Cr4+/Ni2+-activated SWIR phosphors and will also assist researchers in developing next-generation SWIR phosphors and exploring new applications.

Collective radiance of giant atoms in non-Markovian regime

We investigate the non-Markovian dynamics of two giant artificial atoms interacting with a continuum of bosonic modes in a one-dimensional (1D) waveguide. Based on the diagrammatic method, we present the exact analytical solutions, which predict the rich phenomena of collective radiance. For the certain collective states, the decay rates are found to be far beyond that predicted in the the Dicke model and standard Markovian framework, which indicates the occurrence of super-superradiance. The superadiance-to-subradiance transition could be realized by adjusting the exchange symmetry of giant atoms. Moreover, there exists multiple bound states in continuum (BICs), with photons/phonons bouncing back and forth in the cavity-like geometries formed by the coupling points. The trapped photons/phonons in the BICs can also be re-released conveniently by changing the energy level splitting of giant atoms. The mechanism relies on the joint effects of the coherent time-delayed feedback and the interference between the coupling points of giant atoms. This work fundamentally broadens the fields of giant atom collective radiance by introducing non-Markovianity. It also paves the way for a clean analytical description of nonlinear open quantum system with more complex retardation.

Oxynitride K2Ba6.72Si16O40-1.5yNy:0.28Eu2+ phosphor with high thermal stability realized by crystal field engineering.

Extensive research has gone into modifying the chemical composition of phosphors to achieve desirable optical properties. Here, oxynitride phosphors K2Ba6.72Si16O40-1.5yNy:0.28Eu2+ were synthesized by introducing N3- (y) into a K2Ba6.72Si16O40:0.28Eu2+ lattice. An uneven shrinking of the cell parameters a, b, and c was observed through a combination of X-ray diffraction studies and Rietveld refinements. This shrinking caused a large centroid shift (εc) and splitting of the 5d energy level (εcfs), thus inducing the broadening of the excitation spectra (104 → 127 nm, y = 0 → y = 12) and the red shift of the emission spectra (501 → 543 nm, y = 0 → y = 12). The modified series of samples have a broad excitation spectrum, suitable of use in UV, near-UV, and blue light-emitting LEDs. In addition, the optimal sample, K2Ba6.72Si16O31N6:0.28Eu2+, benefits from an increased activation energy and thermal stability.

Impact of the organic cation on the band-edge emission of two-dimensional lead-bromide perovskites.

Organic-inorganic low-dimensional layered metal-halide perovskites are semiconductors in which the optoelectronic properties can be tuned by the material composition and the design of the layered architecture. While the electronic band structure is mainly determined by the inorganic octahedra lattice, the binding and conformation of the organic cations induces related lattice distortions that can break the symmetry and lead to the splitting of the exciton energy levels, and influence the dielectric confinement. Furthermore, organic-induced lattice deformations lead to offsets in k-space (where k is the wavevector) that go along with the exciton energy level splitting. Hence, the electronic transitions between these levels require the momentum contribution of phonons, and contributions of phonons in the exciton recombination dynamics result in thermal broadening of the emission linewidth. In this work, we investigate the band-edge emission of two-dimensional Ruddlesden-Popper lead-bromide perovskites synthesized with different organic cations that vary in their binding head group and their alkyl chain length. We find several peaks in the low-temperature photoluminescence spectra, and the number of peaks in the band-edge emission and their decay dynamics depend strongly on the type of organic cation in the material, which we relate to the difference in the inorganic lattice distortions that the cations induce. For two-dimensional layered perovskites with mainly in-plane distortions, induced by short primary ammonium molecules, we find a two-fold splitting of the band edge emission at low temperatures. If also out-of-plane distortions are present, as for the long-chain primary ammoniums, a three-fold splitting is observed. Interestingly, the low-energy peaks of the split series merge into the highest energy peak with increasing temperature. Thermal broadening analysis of the temperature-dependent photoluminescence linewidth in the structures with out-of-plane distortions yields energies that are larger than those reported for the inorganic lattice phonons. This indicates the involvement of either high-frequency oscillations involving the organic cations, or the broadening might be related to higher order phonon scattering processes in the excitonic recombination process. The strong directionality of the phonon modes in the octahedral lattice could promote the involvement of multiple electron-phonon scattering processes in the exciton relaxation dynamics, for example involving modes with orthogonal directionality.

Electron energy spectrum of the spherical GaAs/AlxGa1-xAs quantum dot with several impurities on the surface

The model of a spherical quantum dot with several donor impurities on its surface is suggested. The electron energy spectra are studied as a function of the quantum dot radius and the number of impurities. Several cases of the location of impurities on the quantum dot surface are considered. The plane wave functions method has been applied to calculate the electron energy spectrum. The splitting of electron energy levels is analyzed in the cases of different number of impurities. It is shown that the electron energy splitting depends on both the number of impurities on the surface and on their location. The electron binding energy is defined too.

Splitting of the atomic hydrogen 21-cm line induced by gravitational waves from a supermassive black hole binary

We investigate the characteristic of the hyperfine splitting of a ground-state hydrogen atom subjected to a field of a gravitational wave. In our consideration, hydrogen atoms are in the source’s local wave zone. The interaction between the atoms and the gravitational wave induces the shifts of some energy levels in the hyperfine structure, computed by the first-order perturbation theory. The splitting of energy levels leads to more than one hyperfine transition. Our analysis suggests that a gravitational wave emitted by supermassive black hole binaries could be strong enough to induce a significant effect on the hyperfine splitting. This radio-wave spectrum provides the gravitational-wave signature and thus offers a way of identifying the merger of supermassive black hole binaries.

Tailoring afterglow properties of polychromatic long-persistent LiMg Sr4--2(BO3)3: y Eu2+ phosphor by codoping with Dy3+ or Nd3+

Herein, redshifted long persistent LiMgxSr4-x-2y(BO3)3: y Eu2+, Dy3+(Nd3+) phosphors are successfully prepared in a reducing atmosphere using a high-temperature solid-state process. The emission of phosphors displays redshift characteristics between 633 and 660 nm with an increase in the concentration of Mg2+ substitution, primarily attributed to enhanced energy level splitting of Eu2+ after Mg2+ replacement. The afterglow performance of LiMg0.6Sr3.4-2y (BO3)3: y Eu2+, Dy3+ (Nd3+) samples is enhanced with increase in concentrations of the doped rare-earth ions. An optimal concentration of 6%, the best afterglow performance was achieved because high concentration traps with suitable energy levels were developed; this was confirmed using afterglow measurements and thermoluminescence tests. The Nd3+ codoped phosphor shows improved afterglow performance compared with the Dy3+ codoped phosphor at the same doping concentration, which can be attributed to Nd3+ can easily be incorporated into the borate lattice that generates electron traps with high concentration.

Long aliphatic chain derivatives of trigonal lanthanide complexes.

The trigonal lanthanide complexes LnL (H3L = tris(((3-formyl-5-methylsalicylidene)amino)ethyl)amine) contain three pendant aldehyde groups and are known to react with primary amines. Reacting LnL (Ln = Yb, Lu) with 1-octadecylamine yields the novel aliphatic lanthanide complexes LnL18 (H3L18 = tris(((3-(1-octadecylimine)-5-methylsalicylidene)amino)ethyl)amine) where the three aldehyde groups are transformed to 1-octadecylimine groups. Herein the syntheses, structural characterisation and magnetic properties of LnL18 are presented. The crystal structure of YbL18 shows that the reaction of YbL with 1-octadecylamine leads to only very subtle perturbations in the first coordination sphere of Yb(III), with the Yb(III) ion retaining its heptacoordination and similar bond lengths and angles to the ligand. The three octadecyl chains in each complex were found to direct crystal packing into lipophilic arrays of van der Waals interaction-driven hydrocarbon stacking. The static magnetic properties of YbL18 were compared to those of the non-derivatised complex YbL. The energy level splitting of the 2F7/2 ground multiplet was found, by emission spectroscopy, to be very similar between the derivatised and non-derivatised complexes. A.c. magnetic susceptibility measurements on YbL18 and YbL diluted at 4.8% and 4.2% into the diamagnetic hosts LuL18 and LuL, respectively, revealed that the spin-lattice relaxation of both complexes is governed by a low temperature direct process and a high temperature Raman process. In the high temperature regime, the derivatised complex was also found to have faster spin-lattice relaxation, which is likely due to the increased number of phonons in the octadecyl chains.

Quantum Electrodynamic Behavior of Chlorophyll in a Plasmonic Nanocavity.

Plasmonic nanocavities have been used as a novel platform for studying strong light-matter coupling, opening access to quantum chemistry, material science, and enhanced sensing. However, the biomolecular study of cavity quantum electrodynamics (QED) is lacking. Here, we report the quantum electrodynamic behavior of chlorophyll-a in a plasmonic nanocavity. We construct an extreme plasmonic nanocavity using Au nanocages with various linker molecules and Au mirrors to obtain a strong coupling regime. Plasmon resonance energy transfer (PRET)-based hyperspectral imaging is applied to study the electrodynamic behaviors of chlorophyll-a in the nanocavity. Furthermore, we observe the energy level splitting of chlorophyll-a, similar to the cavity QED effects due to the light-matter interactions in the cavity. Our study will provide insight for further studies in quantum biological electron or energy transfer, electrodynamics, the electron transport chain of mitochondria, and energy harvesting, sensing, and conversion in both biological and biophysical systems.

Tunable absorptance by the magnetic field in multilayer black phosphorene dielectric structures

The magnetic field effect on the interband optical conductivity of black phosphorene (BP) is considered in the investigation of the absorptance of BP-based multilayer dielectric structures using the transfer matrix method. The BP interband optical conductivity is anisotropic and shows multi-peaks in the presence of the magnetic field because of the splitting of energy levels. The peak position of the absorptance is tuned via the magnetic field strength. In the energy region (0.5 eV - 1.7 eV), the maximum absorptance in the armchair direction is larger than that in the zigzag (ZZ) direction which depends on the angle of incidence and the dielectric structure. But the increased rate of the maximum absorptance in the presence of a magnetic field in the ZZ direction is quite obvious and increased about 10 times. An increased number of BP/Si layers makes the optical absorption in both directions much stronger.

Circularly Polarized Photoluminescence of Chiral 2D Halide Perovskites at Room Temperature.

Chiral halide perovskites have attracted considerable attention because of their chiroptical, second-harmonic generation, and ferroelectricity properties and their potential application in chiroptoelectronics and chiral spintronics. However, the fundamental research of these properties is insufficient. In this work, chiral perovskites were synthesized using precursor solutions with various stoichiometric ratios ⟨n⟩. The chiral perovskite film prepared from the solution with ⟨n⟩ = 1 is composed of (R-/S-/rac-MBA)2PbBr4, whereas the films prepared from the solutions with ⟨n⟩ larger than 1 are a mixture of (R-/S-/rac-MBA)2(CsMA)n-1PbnBr3n+1 with n = 1 and large n values. A photoluminescence quantum yield of approximately 90 was obtained. Symmetric circular dichroism (CD) spectra were observed without an external magnetic field. Under various magnetic fields, magnetic field-induced CD features are superimposed with the intrinsic chirality-induced CD features. For the ⟨n⟩ = 1 chiral perovskite film, the energy level splitting induced by chiral molecules are a few 10 μeV, whereas the energy level splitting induced by magnetic fields are at the range of ∼-250 to ∼250 μeV. Circularly polarized photoluminescence spectra were observed at room temperature and associated with the spin-preserved energy funneling from highly energetic phases to the lower energetic phases.

Zeeman Effect in Centrosymmetric Antiferromagnetic Semiconductors Controlled by an Electric Field.

Centrosymmetric antiferromagnetic semiconductors, although abundant in nature, seem less promising than ferromagnets and ferroelectrics for practical applications in semiconductor spintronics. As a matter of fact, the lack of spontaneous polarization and magnetization hinders the efficient utilization of electronic spin in these materials. Here, we propose a paradigm to harness electronic spin in centrosymmetric antiferromagnets via Zeeman spin splitting of electronic energy levels-termed as the spin Zeeman effect-which is controlled by an electric field. By symmetry analysis, we identify 21 centrosymmetric magnetic point groups that accommodate such a spin Zeeman effect. We further predict by first principles that two antiferromagnetic semiconductors, Fe_{2}TeO_{6} and SrFe_{2}S_{2}O, are excellent candidates showcasing Zeeman splittings as large as ∼55 and ∼30 meV, respectively, induced by an electric field of 6 MV/cm. Moreover, the electronic spin magnetization associated to the splitting energy levels can be switched by reversing the electric field. Our Letter thus sheds light on the electric-field control of electronic spin in antiferromagnets, which broadens the scope of application of centrosymmetric antiferromagnetic semiconductors.

Exploring the Charge Dynamics and Energy Loss in Printable Mesoscopic Perovskite Solar Cells

AbstractPrintable mesoscopic perovskite solar cells (p‐MPSCs) show great potential for commercialization, but little research has been devoted to understanding the dynamics of photogenerated carriers in this type of cell, limiting their further performance improvements. Herein, two techniques with complementary time scales were used, namely transient absorption spectroscopy (TAS) and time‐resolved photoluminescence spectroscopy (TRPL), to quantify the processes of carrier recombination, diffusion, and extraction in p‐MPSCs. It is found that the carrier diffusion in mesoscopic samples should not be neglected at the time scale monitored by TRPL, and thus the diffusion‐recombination model is more suitable compared to the simplified carrier recombination model usually used in interpreting the data of TAS and TRPL. As a result, the calculated carrier diffusion length within the perovskite filled in the mesoscopic scaffold is up to 5.48 µm. This also demonstrates that the hole transport layer is not necessary for p‐MPSCs. In addition, the relationship between the maximum quasi‐Fermi energy level splitting and the bulk recombination coefficient within perovskite is determined through calculations. This study takes an important step toward establishing the relationship between the mesoscopic structure, carrier dynamics, and device performance of p‐MPSCs.

Interaction frames in solid-state NMR: A case study for chemical-shift-selective irradiation schemes

Interaction frames play an important role in describing and understanding experimental schemes in magnetic resonance. They are often used to eliminate dominating parts of the spin Hamiltonian, e.g., the Zeeman Hamiltonian in the usual (Zeeman) rotating frame, or the radio-frequency-field (rf) Hamiltonian to describe the efficiency of decoupling or recoupling sequences. Going into an interaction frame can also make parts of a time-dependent Hamiltonian time independent like the rf-field Hamiltonian in the usual (Zeeman) rotating frame. Eliminating the dominant term often allows a better understanding of the details of the spin dynamics. Going into an interaction frame can also reduces the energy-level splitting in the Hamiltonian leading to a faster convergence of perturbation expansions, average Hamiltonian, or Floquet theory. Often, there is no obvious choice of the interaction frame to use but some can be more convenient than others. Using the example of frequency-selective dipolar recoupling, we discuss the differences, advantages, and disadvantages of different choices of interaction frames. They always include the complete radio-frequency Hamiltonian but can also contain the chemical shifts of the spins and may or may not contain the effective fields over one cycle of the pulse sequence.

Systematical site investigation and temperature sensing in Pr3+-doped M3RE4O9 (M = Sr and Ba; RE = Sc, Y, Lu)

Site engineering is an important modulation strategy for adjusting the physicochemical properties of lanthanide luminescent ions and shows growing applications in the optoelectronic field. Herein, we explored the influence of changing M2+ (or RE3+) ions on the occupation preference of Pr3+ ions and related crystal-field splittings in Pr3+:M3RE4O9 (M = Sr and Ba; RE = Sc, Y, Lu). The obtained results indicated that Pr3+ ions possess two kinds of doping sites (M2+ (Site Ⅰ) and RE3+ (Site Ⅱ)) in Pr3+:Ba3Lu4O9 and Pr3+:Ba3Y4O9, while only occupying Site Ⅰ in Pr3+:Sr3Sc4O9 and Pr3+:Ba3Sc4O9. The variation of RE3+ ions has little impact on the crystal-field splitting of both the two types of Pr3+ luminescent sites, and by contrast, replacing M2+ ones influences the energy-level splitting of the 3H4 multiplet of Site Ⅰ obviously. Moreover, we found that the host emission of M3RE4O9 stemming from intrinsic oxygen defects shows an apparent thermally induced fluorescence quenching phenomenon. And based on the defect and Site Ⅱ emissions, both Pr3+:Ba3Lu4O9 and Pr3+:Ba3Y4O9 exhibit excellent temperature sensing performance, yielding maximum relative sensitivity (Sr) of 8.40%·K−1 (132K) and 7.89%·K−1 (129K), respectively. This work enriches the site engineering strategy in Pr3+-based optical functional materials and broadens the relevant application in temperature sensing.

Precise determination of the low-energy electronuclear Hamiltonian of LiY1−xHoxF4

We use complementary optical spectroscopy methods to directly measure the lowest crystal-field energies of the rare-earth quantum magnet LiY$_{1-x}$Ho$_{x}$F$_{4}$, including their hyperfine splittings, with more than 10 times higher resolution than previous work. We are able to observe energy level splittings due to the $^6\mathrm{Li}$ and $^7\mathrm{Li}$ isotopes, as well as non-equidistantly spaced hyperfine transitions originating from dipolar and quadrupolar hyperfine interactions. We provide refined crystal field parameters and extract the dipolar and quadrupolar hyperfine constants ${A_J=0.02703\pm0.00003}$ $\textrm{cm}^{-1}$ and ${B= 0.04 \pm0.01}$ $\textrm{cm}^{-1}$, respectively. Thereupon we determine all crystal-field energy levels and magnetic moments of the $^5I_8$ ground state manifold, including the (non-linear) hyperfine corrections. The latter match the measurement-based estimates. The scale of the non-linear hyperfine corrections sets an upper bound for the inhomogeneous line widths that would still allow for unique addressing of a selected hyperfine transition. e.g. for quantum information applications. Additionally, we establish the far-infrared, low-temperature refractive index of LiY$_{1-x}$Ho$_{x}$F$_{4}$.