Quadratic Shift Research Articles

Stark effect in MoSe<sub>2</sub> monolayer heterostructure

The effect of a vertical electric field on photoluminescence of a MoSe2 monolayer encapsulated with hexagonal boron nitride is investigated. In the spectra, there is a quadratic shift of the photoluminescence lines of excitons and trions from the applied potential difference, as well as a change in their intensity. It is found that the magnitude of the Stark shift significantly exceeds the theoretically predicted one. It is found that the energy distance between the trion and exciton lines in the spectra varies with the magnitude of the external field, which is due to the dependence of the density of free charge carriers in the monolayer on the field. This effect made it possible to determine the density of free charge carriers in the monolayer, which varies with the field and lies in the range from 0.3–3.4⋅1012 cm–2.

Liquid concentration sensing via weakly coupled point defects in a phononic crystal

A pair of weakly coupled point defects in a liquid–solid phononic crystal are employed for liquid concentration sensing. An exemplary case of methanol in ethanol is investigated. As the physical and chemical properties of the two constituents are very similar, sensing is a rather difficult task by other analytical means. The defects are formed by thin-walled polyethylene tubing filled with either the reference liquid (ethanol) or the mixture in a square phononic crystal composed of cylindrical steel rods in water. Finite-element method simulations for the dual defect system, which has a small form factor comparable to the acoustic wavelength in water, revealed that two sharp transmission peaks corresponding to the even and odd modes arising from symmetry lifting due to weak defect interaction behave in different manners as the methanol concentration is varied. Specifically, the even mode frequency exhibits a linear dependence on the concentration, whereas the odd mode is associated with a quadratic shift. Besides, a simple coupled mass-spring model is employed to analyze the observed peak behavior as a function of methanol concentration in ethanol. Accordingly, when the acoustic properties of the two liquids in a binary mixture vary in a parallel manner with temperature, the ratio of the resonance frequencies depends only on the concentration, thus offering a sensing scheme immune to temperature fluctuations. Furthermore, it is shown for a number of water-miscible liquids that the even and odd mode frequencies are representative of the dominant contents of the reference and the sample cells.

Universal scale laws for colors and patterns in imagery

Distribution of colors and patterns in images is observed through cascades that adjust spatial resolution and dynamics. Cascades of colors reveal the emergent universal property that Fully Colored Images (FCIs) of natural scenes adhere to the debated continuous linear log-scale law (slope −2.00±0.01) (L1). Cascades of discrete 2×2 patterns are derived from pixel square reductions onto the seven unlabeled rotation-free textures (0000, 0001, 0011, 0012, 0101, 0102, 0123). They exhibit an unparalleled universal entropy maximum of 1.74±0.013 at some dynamics regardless of spatial scale (L2). Patterns also adhere to the Integral Fluctuation Theorem (1.00±0.01) (L3), pivotal in studies of chaotic systems. Images with fewer colors exhibit quadratic shift and bias from L1 and L3 but adhere to L2. Randomized Hilbert fractal FCIs better match the laws than basic-to-AI-based simulations. Those results are of interest in Neural Networks, out-of-equilibrium physics, and spectral imagery.

Theoretical study on Stark effect of Rydberg atom in super low frequency electric field measurement

AbstractSuper low frequency electric field measurements are crucial in analysing electromagnetic compatibility, assessing equipment status, and other related fields. Rydberg atom‐based super low frequency electric field measurements are performed by observing the Stark shift in the spectrum of the Rydberg state. In a specific range of field strength (E < Eavoid, where Eavoid is the threshold to avoid crossing electric fields), the Rydberg atomic spectrum experiences a quadratic frequency shift in relation to the field strength, with the coefficient being determined by the atomic polarisability α. The authors establish a dynamic equation for the interaction between the external electric field and the atomic system, and present the Stark structure diagram of the Caesium Rydberg atom. The mathematical formulae for α and Eavoid in different Rydberg states are also obtained: α = A × (n*)6 + B × (n*)7 and Eavoid = C/(n*)5 + D/(n*)7, where A(B) = 2.2503 × 10−9(7.49,948 × 10−11) and C(D) = 1.68,868 × 108(2.45,991 × 109). The error of α and Eavoid compared with the experimental values does not exceed 8% and is even lower in the low Rydberg states. Accurately calculating the values of α and Eavoid is crucial in incorporating the Rydberg atom quantum coherence effect into super low frequency electric field measurements in new power systems.

Employing quasidegenerate optical modes for chiral sensing

Chiral molecules cannot be superposed with their own mirror image. This yields two enantiomers of opposite handedness that are made out of the same building blocks, but interact differently with their environment. Hence, chiral sensing is of utmost importance for biology, chemistry, and life sciences. However, the impact of the handedness and chirality is very weak in most sensing schemes. Nevertheless, it has been demonstrated recently that chirality may result in strong coupling between resonant states with high quality factors. This is achieved by spectrally overlapping two quasibound states in the continuum in a periodic array of nanostructures. We demonstrate that this requires neither quasibound states in the continuum nor periodic arrays, which is exemplified for three achiral systems: a sphere with equal permittivity and permeability, a single core-shell structure, and a dielectric metasurface. For such achiral systems, we have shown previously that isolated resonant states exhibit a quadratic energy shift in the Pasteur parameter. However, for quasidegenerate states, we observe, using the rigorous resonant-state expansion and full-wave simulations, a linear energy shift and linear splitting in the presence of a chiral medium or molecule. Thus, the splitting is more sensitive to low concentrations of chiral molecules, which paves the way for novel chiral sensing schemes. Published by the American Physical Society 2024

Characterizations of entire solutions for the system of Fermat-type binomial and trinomial shift equations in ℂ n#

Abstract In this article, we investigate the existence and the precise form of finite-order transcendental entire solutions of some system of Fermat-type quadratic binomial and trinomial shift equations in C n {{\mathbb{C}}}^{n} . Our results are the generalizations of the results of [H. Y. Xu, S. Y. Liu, and Q. P. Li, Entire solutions for several systems of nonlinear difference and partial differential-difference equations of Fermat-type, J. Math. Anal. Appl. 483 (2020), 123641, 1–22, DOI: https://doi.org/10.1016/j.jmaa.2019.123641.] and [H. Y. Xu and Y. Y. Jiang, Results on entire and meromorphic solutions for several systems of quadratic trinomial functional equations with two complex variables, RACSAM 116 (2022), 8, DOI: https://doi.org/10.1007/s13398-021-01154-9.] to a large extent. Most interestingly, as a consequence of our main result, we have shown that the system of quadratic trinomial shift equation has no solution when it reduces to a system of quadratic trinomial difference equation. In addition, some examples relevant to the content of the article have been exhibited.

Shift symmetries and duality web in gauge theories

Using a generalised Noether prescription we are able to extract all the currents and their conservation laws in space dependent shift symmetric theories. Various identities among the currents in the matter sector are found that form the basis for revealing a dual picture when the full interacting theory is considered by coupling to gauge fields. The coupling is achieved in terms of vector fields by adhering to a modified minimal prescription which is also supported by an iterative Noether scheme. Further, this scheme shows that couplings can also be introduced using higher rank tensor gauge fields that have appeared in recent discussions on fractons. We reveal a connection among these descriptions (using vector or tensor fields) through certain duality maps that relate the various fields (gauge, electric and magnetic) in the two cases. A correspondence is established among the Gauss' law, Faraday's law and Ampere's law. Explicit calculations are provided for linear and quadratic shift symmetric lagrangians.

Multistate interferometric measurement of the nonlinear ac Stark shift

We demonstrate measurement of quadratic AC Stark shifts between Zeeman sublevels in an $^{87}$Rb Bose--Einstein condensate using a multi-state atomic interferometer. The interferometer can detect a quadratic shift without being affected by relatively large state-independent shifts, thereby improving the measurement precision. We measure quadratic shifts in the total spin $F = 2$ state due to the light being near-resonant to the D$_1$ line. The agreement between the measured and theoretical detuning dependences of the quadratic shifts confirms the validity of the measurement. We also present results on the suppression of nonlinear spin evolution using near-resonant dual-color light pulses with opposite quadratic shifts.

Liquid Sensor Based on Interaction between Decoupled Waveguides and a Cavity with Transverse Offset in a Phononic Crystal

A liquid sensor employing a cavity in the form of a point defect with a transverse offset along the normal bisector of a barrier at the center of a linear waveguide in a two-dimensional phononic crystal, which gives rise to two decoupled waveguides, is proposed. The phononic crystal consists of cylindrical steel rods with 2.0 mm radius in water, arranged with 4.2 mm lattice constant in the square lattice. Linear waveguides are formed by removing a single row from the phononic crystal, whereas the point defect is formed by substituting a single cylindrical steel rod by a polyethylene tubing comprising the analyte of interest. The cavity acts as a cross-bridge between the waveguides through the interaction of the linear defect mode in the input waveguide with the point defect mode, which in turn interacts with the output waveguide mode. Finite-element method simulations reveal that at frequencies around 200 kHz, a sharp peak with a quality factor of the order of 1000 occurs in the transmission spectrum of the system, where resonant transmission occurs. In case of determining the ratio of methanol in ethanol as an instance, it is found that the peak frequency exhibits a quadratic shift with the molar ratio of methanol. On the other hand, the transmission value decreases exponentially with increasing methanol ratio at the frequency of 196.19 kHz, which is the peak frequency for pure ethanol. The proposed sensing scheme can be utilized in many applications such as the identification of fake beverages and in high-throughput concentration measurements in the industry.

Observation of Nonlinearity of Generalized King Plot in the Search for New Boson

We measure isotope shifts for neutral Yb isotopes on an ultranarrow optical clock transition S10−P03 with an accuracy of a few hertz. Combined with one of the recently reported isotope-shift measurements of Yb+ on two optical transitions, the result allows us to construct the King plots—a set of scaled isotope shifts data on two different optical transitions plotted in two-dimensional plane. When only the leading-order terms of isotope shifts are taken into account, a King plot should exhibit a linear relation as a result of elimination of the leading nuclear-size dependence. Extremely large nonlinearity unexplainable by a quadratic field shift is revealed, which was proposed previously as a source of the observed nonlinearity of the King plot. We further construct the generalized King plot with three optical transitions so that we can eliminate the contribution arising from a higher-order effect within the standard model. Our analysis of the generalized King plot shows a deviation from linearity at the 3σ level, indicating that there exist at least two higher-order contributions in the measured isotope shifts. Under reasonable assumptions, we obtain the upper bound of the product of the couplings for a new boson, mediating a force between electrons and neutrons—|yeyn|/(ℏc)<1×10−10 for the mass less than 1 keV—with the 95% confidence level, providing an important step toward probing new physics via isotope-shift spectroscopy.2 MoreReceived 18 October 2021Accepted 16 March 2022DOI:https://doi.org/10.1103/PhysRevX.12.021033Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectronic structure of atoms & moleculesElectronic transitionsHypothetical particle physics modelsNuclear charge distributionPhysical SystemsAtomsHypothetical particlesTechniquesPrecision measurementsSpectroscopyAtomic, Molecular & OpticalParticles & Fields

Evidence for Nonlinear Isotope Shift in Yb^{+} Search for New Boson.

We measure isotope shifts for five Yb^{+} isotopes with zero nuclear spin on two narrow optical quadrupole transitions ^{2}S_{1/2}→^{2}D_{3/2}, ^{2}S_{1/2}→^{2}D_{5/2} with an accuracy of ∼300 Hz. The corresponding King plot shows a 3×10^{-7} deviation from linearity at the 3σ uncertainty level. Such a nonlinearity can indicate physics beyond the Standard Model (SM) in the form of a new bosonic force carrier, or arise from higher-order nuclear effects within the SM. We identify the quadratic field shift as a possible nuclear contributor to the nonlinearity at the observed scale, and show how the nonlinearity pattern can be used in future, more accurate measurements to separate a new-boson signal from nuclear effects.

Nonlinear isotope-shift effects in Be-like, B-like, and C-like argon

Violation of linearity of the King plot is investigated for a chain of partially stripped argon isotopes. The nonlinearity originates within the Standard Model from subtle contributions to the isotope shifts from next-to-leading order effects, which have never been systematically studied so far. In light atoms these nonlinear effects are dominated by the quadratic nuclear recoil ($\propto 1/M^2$ where $M$ is the nuclear mass). Large-scale relativistic calculations of the linear and quadratic mass shift and the field shift are performed for the $2P$ fine-structure transitions in Be-like, B-like, and C-like argon ions. Nonlinearities of the King plots from 5 to 30 kHz are found, which is four orders of magnitude larger than previous estimates in comparable systems. Accurate calculations of these effects are vital for identification of possible nonlinearities originating from physics beyond the Standard Model.

Exciton Polarization and Renormalization Effect for Optical Modulation in Monolayer Semiconductors

The ideal quantum confinement structure of monolayer semiconductors offers prominent optical modulation capabilities that are mediated by enhanced many-body interactions. Herein, we establish an electrolyte-gating method for tuning the luminescence properties that are in transition metal dichalcogenide (TMDC) monolayers. We fabricate electric double-layer capacitors on TMDC/graphite heterostructures to investigate electric-field- and carrier-density-dependent photoluminescence. The exciton peak energy initially shows a slight quadratic red shift of ∼1 meV without carrier accumulations, which is caused by the quantum-confined Stark effect. In contrast, the exciton resonance exhibits a larger red shift up to 10 meV with the accumulated carrier density above 1013 cm-2. These results indicate that the optical transitions can be largely modulated by the carrier density control in S- and Se-based TMDCs, as triggered by the doping-induced band gap renormalization effect. To further inspire this modulation capability, we also apply our method to electrolyte-based TMDC light-emitting devices. Biasing solely in electrolyte-induced p-i-n junctions yields pronounced red shifts up to 40 meV for exciton and trion electroluminescence. Consequently, our approach reveals that the doping effects in the high-carrier-density regimes are potentially significant for efficient optical modulation in monolayer semiconductors.

Theory of nonreciprocal spin-wave excitations in spin Hall oscillators with Dzyaloshinskii-Moriya interaction

A two-dimensional analytical model for the description of the excitation of nonreciprocal spin waves by spin current in spin-Hall oscillators in the presence of the interfacial Dzyaloshinskii-Moriya interaction (i-DMI) is developed. The theory allows one to calculate the threshold current for the excitation of spin waves, as well as the frequencies and spatial profiles of the excited spin wave modes. It is found, that the frequency of the excited spin waves exhibits a quadratic red shift with the i-DMI strength. At the same time, in the range of small and moderate values of the i-DMI constant, the averaged wave number of the excited spin waves is almost independent of the i-DMI, which results in a rather weak dependence on the i-DMI of the threshold current of the spin wave excitation. The obtained analytical results are confirmed by the results of micromagnetic simulations.

Double‐clad fiber Michelson interferometer for measurement of temperature and refractive index

AbstractAn all‐fiber Michelson interferometer based on double‐clad fiber (DCF) is proposed for temperature and refractive index (RI) sensing. The sensor is formed by continuous splicing between single mode fiber, multimode fiber, and DCF. Temperature measurement is achieved by monitoring the dip wavelength shift of the interferometer spectra resulting from thermo‐optic effect on core and first cladding of DCF. RI measurement is established from the power change in spectra due to the Fresnel's reflection at the DCF tip. Experimental result on 18.5 mm sensor manifests that temperature and RI responses are distinguishable. For instance, power level at 1540.5 nm exhibits quadratic shift to RI changes while unaffected to temperature changes. Dip wavelengths of sensor spectra demonstrate linear shift to temperature changes while unaffected by RI changes. The proposed sensor is cost effective as sensor fabrication only requires conventional splicing. Sensor capability to distinguish temperature and RI parameters makes it practical for broad range applications including for biomedical and food industries.

Effects of mass defect in atomic clocks

We consider some implications of the mass defect on the frequency of atomic transitions. We have found that some well-known frequency shifts (such as gravitational and quadratic Doppler shifts) can be interpreted as consequences of the mass defect, i.e., without the need for the concept of time dilation used in special and general relativity theories. Moreover, we show that the inclusion of the mass defect leads to previously unknown shifts for clocks based on trapped ions..

Probing VCMA in MTJs with in-plane magnetization

Voltage controlled magnetic anisotropy (VCMA) is a novel method to switch magnetizations in low-power and ultra-fast applications based on magnetic tunnel junctions (MTJs). Here we explore the ferromagnetic resonance (FMR) technique to probe VCMA in situations where other methods cannot be applied. We quantify VCMA in CoFeB/MgO/CoFeB MTJ nanopillars with in-plane magnetizations where our FMR method is unique in providing direct information about VCMA. We observe a quadratic shift of the FMR resonance field when a voltage bias is applied across the MTJ. The VCMA energy corresponding to the quadratic shift varies with an energy factor of 8.2μJ/m2 for 1 V2/nm2. These results are important for understanding magnetodynamics in MTJ-based applications with in-plane magnetizations.

Higher-Order Dispersion, Stability, and Waveform Invariance in Nonlinear Monoatomic and Diatomic Systems

Recent studies have presented first-order multiple time scale approaches for exploring amplitude-dependent plane-wave dispersion in weakly nonlinear chains and lattices characterized by cubic stiffness. These analyses have yet to assess solution stability, which requires an analysis incorporating damping. Furthermore, due to their first-order dependence, they make an implicit assumption that the cubic stiffness influences dispersion shifts to a greater degree than the quadratic stiffness, and they thus ignore quadratic shifts. This paper addresses these limitations by carrying-out higher-order, multiple scales perturbation analyses of linearly damped nonlinear monoatomic and diatomic chains. The study derives higher-order dispersion corrections informed by both quadratic and cubic stiffness and quantifies plane wave stability using evolution equations resulting from the multiple scales analysis and numerical experiments. Additionally, by reconstructing plane waves using both homogeneous and particular solutions at multiple orders, the study introduces a new interpretation of multiple scales results in which predicted waveforms are seen to exist over all space and time, constituting an invariant, multiharmonic wave of infinite extent analogous to cnoidal waves in continuous systems. Using example chains characterized by dimensionless parameters, numerical studies confirm that the spectral content of the predicted waveforms exhibits less growth/decay over time as higher-order approximations are used in defining the simulations' initial conditions. Thus, the study results suggest that the higher-order multiple scales perturbation analysis captures long-term, nonlocalized invariant plane waves, which have the potential for propagating coherent information over long distances.

Unusual quantum confined Stark effect and Aharonov-Bohm oscillations in semiconductor quantum rings with anisotropic effective masses

The effects of external electric and magnetic fields on the energy spectrum of quantum rings made out of a bidimensional semiconductor material with anisotropic band structures are investigated within the effective-mass model. The interplay between the effective-mass anisotropy and the radial confinement leads to wave functions that are strongly localized at two diametrically opposite regions where the kinetic energy is lowest due to the highest effective mass. We show that this quantum phenomenon has clear consequences on the behavior of the energy states in the presence of applied in-plane electric fields and out-of-plane magnetic fields. In the former, the quantum confined Stark effect is observed with either linear or quadratic shifts, depending on the direction of the applied field. As for the latter, the usual Aharonov-Bohm oscillations are not observed for a circularly symmetric confining potential, however they can be reinstated if an elliptic ring with an appropriate aspect ratio is chosen.

The Zeeman splitting of bulk 2H-MoTe2 single crystal in high magnetic field

A high magnetic field magneto-optical spectrum is utilized to study the A exciton of bulk 2H-MoTe2 single crystal. A clear Zeeman splitting of the A exciton is observed under high magnetic fields up to 41.68 T, and the g-factor (−2.09 ± 0.08) is deduced. Moreover, a high magnetic field enables us to obtain the quadratic diamagnetic shifts of the A exciton (0.486 μeV T−2). Accordingly, the binding energy, reduced mass, and radius of the A exciton were obtained by using both two and three dimensional models. Compared with other transition metal dichalcogenides (TMDs), the A exciton of bulk 2H-MoTe2 has a relatively small binding energy and larger exciton radius, which provide fundamental parameters for comprehensive understanding of excitons in TMDs as well as their future applications.