Density Matrix Elements Research Articles

Novel Quantum States of Exciton-Floquet Composites: Electron-Hole Entanglement and Information.

Coulomb exchange between distinct electron-hole modes, i.e., exciton and Floquet states, in two-dimensional semiconductors is explored. Coherent ultrafast mixing of the exciton and Floquet states under weak optical pumping is investigated through a theoretical description of time-resolved and angle-resolved photoemission spectroscopy (tr-ARPES) in an extended Haldane model that includes the electron-hole Coulomb interaction. Two branches of novel quantum states are found in the form of bosonic exciton-Floquet composites, which result from exchange coupling due to the Coulomb interaction. Furthermore, tr-ARPES could be directly employed for the density matrix element of the biparticle subsystem of photoelectron and hole, and electron-hole entanglement and information could be further explored. This finding suggests a unique platform to study the buildup and dephasing of novel exciton-Floquet composites and to resolve the information carried by them, which would enable the pursuit of new reconfigurable devices based on two-dimensional semiconductors.

Quantifying coherence with principal diagonal elements of density matrix

Quantifying coherence with principal diagonal elements of density matrix

A Low-Order Permutationally Invariant Polynomial Approach to Learning Potential Energy Surfaces Using the Bond-Order Charge-Density Matrix: Application to Cn Clusters for n = 3-10, 20.

A representation for learning potential energy surfaces (PESs) in terms of permutationally invariant polynomials (PIPs) using the Hartree-Fock expression for electronic energy is proposed. Our approach is based on the one-electron core Hamiltonian weighted by the configuration-dependent elements of the bond-order charge density matrix (CDM). While the previously reported model used an s-function Gaussian basis for the CDM, the present formulation is expanded with p-functions, which are crucial for describing chemical bonding. Detailed results are demonstrated on linear and cyclic Cn clusters (n = 3-10) trained on extensive B3LYP/aug-cc-pVTZ data. The described method facilitates PES learning by reducing the root mean squared error (RMSE) by a factor of 5 relative to the s-function formulation and by a factor of 20 relative to the conventional PIP approach. This is equivalent to using CDM and an sp basis with a PIP of order M to achieve the same RMSE as with the conventional method with a PIP of order M + 2. Implications for large-scale problems are discussed using the case of the PES of the C20 fullerene in full permutational symmetry.

Controllable optical effects in Landau-quantized graphene

This paper investigates the manipulation and control of optical properties in a Y-configured four-level Landau-Quantized Graphene system. Through a comprehensive analysis of the density matrix elements, we explore the influence of various system parameters, including control field intensities, detunings, and decay rates, on the optical response of the graphene sample. Our findings unveil compelling phenomena such as optical transparency, sub- and superluminal light propagation, and the emergence of multiple absorption peaks and transparency windows. Specifically, we examine the impact of decay rates on the absorption characteristics of graphene, revealing that higher decay rates diminish the effectiveness of Electromagnetically Induced Transparency (EIT) and slow light in the system. Furthermore, by systematically varying system parameters, we demonstrate the controllability of achieving either single or double EIT through manipulation of control field intensities and detunings. These results open promising avenues for applications in optical communications and quantum information processing, where precise control over graphene's optical properties is critical.

Beyond a Richardson-Gaudin Mean-Field: Slater-Condon Rules and Perturbation Theory.

Richardson-Gaudin states provide a basis of the Hilbert space for strongly correlated electrons. In this study, optimal expressions for the transition density matrix elements between Richardson-Gaudin states are obtained with a cost comparable with the corresponding reduced density matrix elements. Analogues of the Slater-Condon rules are identified based on the number of near-zero singular values of the RG state overlap matrix. Finally, a perturbative approach is shown to be close in quality to a configuration interaction of Richardson-Gaudin states while being feasible to compute.

Analyzing the Nuclear Structure of 13O-13B and 13N-13C Mirror Nuclei

In the context of the shell model, electromagnetic transitions were used to analyze the nuclear structure of a mirror nucleus with the same mass number, A = 13. The shell model investigation was performed by calculating the root mean square (rms) for the proton, neutron, matter and charge radii, occupancies, the excitation energies, as well as electromagnetic moments, using the elements of a body density matrix of the PSDMOD two-body effective interactions carried out in the psdpn-shell model space. The present results adopted the harmonic oscillator's single particle eigen functions and Hartree-Fock approximation. In addition, the effect of core polarization was added using the effective charge and effective g factors to calculate electromagnetic moments. To acquire a fair analysis of the information, the core polarization has to be present. The outcomes were compared with experimental data

The Dynamics of the Hubbard Model Through Stochastic Calculus and Girsanov Transformation

As a typical quantum many body problem, we consider the time evolution of density matrix elements in the Bose-Hubbard model. For an arbitrary initial state, these quantities can be obtained from an SDE or stochastic differential equation system. To this SDE system, a Girsanov transformation can be applied. This has the effect that all the information from the initial state moves into the drift part, into the mean field part, of the transformed system. In the large N limit with g=UN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g=UN$$\\end{document} fixed, the diffusive part of the transformed system vanishes and as a result, the exact quantum dynamics is given by an ODE system which turns out to be the time dependent discrete Gross Pitaevskii equation. For the two site Bose-Hubbard model, the GP equation reduces to the mathematical pendulum and the difference of expected number of particles at the two lattice sites is equal to the velocity of that pendulum which is either oscillatory or it can have rollovers which then corresponds to the self trapping or insulating phase. As a by-product, we also find an equivalence of the mathematical pendulum with a quartic double well potential. Collapse and revivals are a more subtle phenomenom, in order to see these the diffusive part of the SDE system or quantum corrections have to be taken into account. This can be done with an approximation and collapse and revivals can be reproduced, numerically and also through an analytic calculation. Since expectation values of Fresnel or Wiener diffusion processes, we write the density matrix elements exactly in this way, can be obtained from parabolic second order PDEs, we also obtain various exact PDE representations. The paper has been written with the goal to come up with an efficient calculation scheme for quantum many body systems and as such the formalism is generic and applies to arbitrary dimension, arbitrary hopping matrices and, with suitable adjustments, to fermionic models.

Dipole momenta and compositeness of the τ lepton at Belle II

The large number of τ leptons available at the Belle II experiment makes it possible to study their properties and the extent of their compositeness. We propose a strategy that relies on three observables defined in terms of elements of the polarization density matrix of the produced τ pairs, which we obtain via quantum tomography. We find that these observables can explore values of the magnetic dipole moment down to 6.3×10−4, which is 2 orders of magnitude better than the current experimental limit, constrain the electromagnetic radius below 4.3×10−3 fm, and exclude an electric dipole moment larger than 1.7×10−17 e cm. The quoted limits are at the 95% confidence level (CL) and are obtained for a benchmark integrated luminosity of 1 ab−1 and a Monte Carlo estimate of the statistical sensitivity. Published by the American Physical Society 2024

Polarization and coherence properties of a partially coherent elegant Laguerre–Gaussian vortex beam in turbulent plasma

The analytical expressions for the cross-spectral density matrix elements of the partially coherent elegant Laguerre–Gaussian (eLG) vortex beam propagating through anisotropic turbulent plasma were derived based on the extended Huygens-Fresnel principle and used to study the changes in the polarization degree and the coherence degree of the partially coherent eLG vortex beam in the turbulent plasma. The numerical results show that the polarization degree of a partially coherent eLG vortex beam reaches a specific value (which is equal to the degree of polarization in the source plane) after a long propagation distance in the turbulent plasma. Moreover, this value is independent of the beam order, topological charge, correlation coefficient, wavelength of the source plane, anisotropy parameter, refractive index fluctuation variance, and outer and inner scales of the turbulent plasma. The results also show that with increasing distance, the coherence degree first decreases from unity and then oscillates around zero. However, this oscillation gradually disappears after traveling a long distance. Our results intuitively present the beam polarization and coherence properties through anisotropic hypersonic turbulence, which can be useful for optical communication in hypersonic turbulent environments.

Evaluation of neutron cross sections of 48Ti based on the Unified-Monte-Carlo-B method* *Supported by the National Key Research and Development (R&D) Program (2022YFA1602403) and Continuous Support Basic Scientific Research Project BJ010261223282

A cross section evaluation of neutron induced reactions on 48Ti is undertaken using the Unified Monte Carlo-B (UMC-B) approach. The evaluation concentrates on estimating the covariance and the use of the UMC-B allows avoiding the deficiencies of linear regression brought by the traditional least squares method. Eight main neutron and charged particle emission reactions from n+48Ti in the fast neutron energy region below 20 MeV are studied in this work. The posterior probability density function (PDF) of each neutron cross section is obtained in a UMC-B Bayesian approach by convoluting the model PDFs sampled based on model parameters and the likelihood functions for the experimental data. Nineteen model parameters including level density, pair corrections, optical model and Kalbach matrix element parameter are stochastically sampled with the assumption of normal distributions to estimate the model uncertainty. The Cholesky factorization approach is applied to consider potential parameter correlations. Finally, the posterior covariance matrices are generated using the UMC-B generated weights. The new evaluated results are compared with the CENDL-3.2, ENDF/B-VIII.0, JEFF-3.3, TENDL-2021 and JENDL-5 evaluations and differences are discussed.

Indications for the Substantial Predominance of Short-Range Effects on Inelastic Coulomb Form Factors for Various States in the 26Mg Nucleus

Short-range effects on C2, C3, as well as C4 form factors in the 26Mg nucleus, were examined. The charge density distribution in this nucleus was also tested by means of one and two body fragments of cluster enlargement in cooperation with single-particle wave functions of harmonic potential. The correlation of Jastrow form was employed to inset the influence of short-range into the two body fragment of cluster enlargement. The nucleus of 26Mg was assumed to own a 16O-core with (A-16) nucleons dispersed over the sd-model space. The form factors in 26Mg nucleus ascend from the core-polarization and model space involvements. The form of Tassie model, subject to the charge density, was used to determine the transition density of core polarization. The one body density matrix elements required for determining the transition density of model space for various transitions in 26Mg were found via carrying out shell model computations using the OXBASH program with the universal-sd interaction of Wildenthal. The present calculations were subjected to the oscillator and correlation parameters symbolized by and respectively. These parameters are self-sufficiently generated for every specific nucleus by fitting between the calculated and observed elastic form factors. For determining the charge density, elastic form factors and inelastic Coulomb form factors for dissimilar excited states in 26Mg, one value is needed for and This study shows indications for the substantial predominance of short-range influences on current computations, where considering these influences look to be requisite for carrying out a distinguished adjustment in calculated results which ultimately leads to a remarkable explication of the data throughout all the considered momentum transfers.

Dynamical evolution of the two-qubit system with Ising spin-chain environment

In this article, we study the evolution of the two-qubit system with Ising spin-chain environment by choosing the Lindblad equation to describe this process. First, we expand the Hamiltonian of a two-qubit system with its eigenstates and give the Lindblad equation for the evolution of the two-qubit system with Ising spin-chain as the environment. Compared with directly calculating the differential equation between elements of density matrix, we choose a method to solve the Lindblad equation with a smaller calculation dimension. Finally, by constructing an operator solution with operators, we obtain the dynamics of the two-qubit system with Ising spin-chain environment.

Polarization properties of partially coherent mixed dislocation beams transmitting in biological tissues

<sec> <b>Objective</b> The optical information change of beams acting on biological tissue can get an insight into the new optical effects of tissue, and even can provide a theoretical basis for developing biphotonic medical diagnosis and therapy technologies. Polarization technology is also widely used in the field of biological detection due to its advantages of non-contact, rich information and without staining markers. In this work, the polarization behaviors of partially coherent screw-linear edge mixed dislocation beam transmitting in biological tissue are analyzed and explored. Simultaneously, in order to more clearly and more intuitively understand a mixed dislocation beam, both the normalized intensities and phase distributions at source plane for different parameters <i>a</i> and <i>b</i> are also discussed. We hope that the obtained results will provide theoretical and experimental foundation for expanding the application of singularity beams in biological tissue imaging technology.</sec><sec> <b>Method</b> By combining the Schell term with the field distribution of the screw-linear edge mixed dislocation beam at the source plane, and based on the generalized Huygens-Fresnel principle, the analytical expressions of the cross-spectral density matrix elements of partially coherent screw-linear edge dislocation beam propagating in biological tissues are derived. Adopting the unified theory of coherence and polarization, the polarization behaviors of the beams can be investigated in detail.</sec><sec> <b>Results</b> At the source plane, the intensity has a non axisymmetric distribution, and there exists a coherent vortex with a topological charge size of 1 and a linear edge dislocation. The sign of <i>a</i> is related to the rotation direction of the phase singularity. The larger the value of <i>b</i>, the farther the linear edge dislocation is from the origin. At the source plane, the degree of polarization and ellipticity between the two identical points are independent of the four parameters: dimensionless parameter <i>a</i>, off-axis distance of edge dislocation <i>b</i>, spatial self-correlation length <i>σ</i><sub><i>yy</i></sub>, and spatial mutual-correlation length <i>σ</i><sub><i>xy</i></sub>, the orientation angle is only independent of <i>a</i> and <i>σ</i><sub><i>xy</i></sub>; the polarization of two different points is independent of <i>a</i> and <i>b</i>, but is related to <i>σ</i><sub><i>yy</i></sub> and <i>σ</i><sub><i>xy</i></sub>. In transmission, the polarization degrees and ellipticity of two different points fluctuate greatly and the orientation angle displays less fluctuation. Finally, all the polarization state parameters tend to be their corresponding values, respectively.</sec><sec> <b>Conclusions</b> The results show that when <i>b</i> is smaller, the linear edge dislocation is paraxial and plays an important role in the polarization state change; when <i>b</i> is larger, the polarization state changes of the screw-linear edge mixed dislocation beam will tend to be the pattern of spiral beams. The absolute value of the difference between <i>σ</i><sub><i>yy</i></sub> and <i>σ</i><sub><i>xy</i></sub> is also one of main factors influencing the polarization state. The sign of <i>a</i> does not affect the change in polarization state, but its magnitude can influe the change of speed. Due to more complex factors determining the correlation fluctuations between different points in the light field, the changes of two different points are more sensitive than those of the two identical points in shallow biological tissue. Beams with different parameters can be selected for different application requirements.</sec>

The Petz (lite) recovery map for the scrambling channel

Abstract We study properties of the Petz recovery map in chaotic systems, such as the Hayden–Preskill setup for evaporating black holes and the Sachdev–Ye–Kitaev (SYK) model. Since these systems exhibit the phenomenon called scrambling, we expect that the expression of the recovery channel $\mathcal {R}$ gets simplified, given by just the adjoint $\mathcal {N}^{\dagger }$ of the original channel $\mathcal {N}$ which defines the time evolution of the states in the code subspace embedded into the physical Hilbert space. We check this phenomenon in two examples. The first one is the Hayden–Preskill setup described by Haar random unitaries. We compute the relative entropy $S(\mathcal {R}\left[\mathcal {N}[\rho ]\right] ||\rho )$ and show that it vanishes when the decoupling is archived. We further show that the simplified recovery map is equivalent to the protocol proposed by Yoshida and Kitaev. The second example is the SYK model where the 2D code subspace is defined by an insertion of a fermionic operator, and the system is evolved by the SYK Hamiltonian. We check the recovery phenomenon by relating some matrix elements of an output density matrix $\langle{T}|\mathcal {R}[\mathcal {N}[\rho ]]|{T^{\prime }}\rangle$ to Rényi-two modular flowed correlators, and show that they coincide with the elements for the input density matrix with small error after twice the scrambling time.

Generalized spin σ-SCF method.

We introduce a generalization of the σ-SCF method to approximate noncollinear spin ground and excited single-reference electronic states by minimizing the Hamiltonian variance. The new method is based on the σ-SCF method, originally proposed by Ye et al. [J. Chem. Phys. 147, 214104 (2017)], and provides a prescription to determine ground and excited noncollinear spin states on an equal footing. Our implementation was carried out utilizing an initial simulated annealing stage followed by a mean-field iterative self-consistent approach to simplify the cumbersome search introduced by generalizing the spin degrees of freedom. The simulated annealing stage ensures a broad exploration of the Hilbert space spanned by the generalized spin single-reference states with random complex element-wise rotations of the generalized density matrix elements in the simulated annealing stage. The mean-field iterative self-consistent stage employs an effective Fockian derived from the variance, which is utilized to converge tightly to the solutions. This process helps us to easily find complex spin structures, avoiding manipulating the initial guess. As proof-of-concept tests, we present results for Hn (n = 3-7) planar rings and polyhedral clusters with geometrical spin frustration. We show that most of these systems have noncollinear spin excited states that can be interpreted in terms of geometric spin frustration. These states are not directly targeted by energy minimization methods, which are meant to converge to the ground state. This stresses the capability of the σ-SCF methodology to find approximate noncollinear spin structures as mean-field excited states.

Coherence as an indicator to discern electromagnetically induced transparency and Autler–Townes splitting

Electromagnetically induced transparency (EIT) and Autler–Townes splitting (ATS) are generally characterized and distinguished by the width of the transparency created in the absorption profile of a weak probe in presence of a strong control field. This often leads to ambiguities, as both phenomena yield similar spectroscopic signatures. However, an objective method based on Akaike’s information criterion (AIC) test offers a quantitative way to discern the two regimes when applied on the probe absorption profile. The obtained transition value of control field strength was found to be higher than the value given by pole analysis of the corresponding off-diagonal density matrix element. By contrast, we apply the test on ground state coherence and the measured coherence quantifier, which yields a distinct transition point around the predicted value even in presence of noise. Our test accurately captures the transition between two regimes, indicating that a proper measure of coherence is essential for making such distinctions.

Separation of metric in Wick's theorem.

In quantum chemistry, Wick's theorem is an important tool to reduce products of fermionic creation and annihilation operators. It is especially useful in computations employing reference states. The original theorem has been generalized to tackle multiconfigurational wave functions or nonorthogonal orbitals. One particular issue of the resulting structure is that the metric and density matrices are intertwined despite their different origin. Here, an alternative, rather general tensorial formulation of Wick's theorem is proposed. The main difference is the separation of the metric-the coefficients at normal-ordered operators become products of an n-electron density matrix element and the Pfaffian of a matrix formed by orbital overlaps. Different properties of the formalism are discussed, including the use of density cumulants, the particle-hole symmetry, and applications to transition density matrices, i.e., the case of different bra and ket reference states. The metric-separated version of Wick's theorem provides a platform for the derivation of various quantum chemical methods, especially those complicated by non-trivial reference states and nonorthogonality issues.

Average Intensity of a Laguerre—Gaussian Vector Vortex Beam through Inhomogeneous Atmospheric Turbulence

We investigate the evolution properties of a partially coherent Laguerre–Gaussian vector vortex (LGVV) beam through inhomogeneous atmospheric turbulence. Analytical formulae for the elements of a cross-spectral density matrix of a partially coherent LGVV beam propagating in turbulence are derived with the help of the extended Huygens–Fresnel principle. Our outcomes demonstrate that the normalized initial profile of a partially coherent beam with concentric dark rings gradually evolves into a Gaussian-like beam profile in turbulence. We also find that the beam is emitted at a large zenith angle and quickly converts to a Gaussian-like beam. Furthermore, it is also shown that a propagation beam with a large topological charge has a stronger ability to resist atmospheric turbulence. In order to confirm our numerical results, we combine the complex screen method and multi-phase screen method to simulate the propagation of a partially coherent LGVV beam in atmospheric turbulence. It is indicated that the simulation results are in good agreement with theoretical predictions. Our results will pave the way for the development of free-space optical communications and remote sensing.

High-frequency transport properties of a 2D electron gas with spin-orbit interaction under magnetic field driven topological transition

We study the transport properties of a two-dimensional electron system with an essential spin-orbit interaction under topological phase transition due to changing in-plane magnetic field. We have analyzed the contribution of diagonal and off-diagonal components of density matrix with respect to number of spin zone in the high-frequency conductivity. Analytical formulas for the conductivity tensor have been obtained. A numerical analysis giving full enough representation about the dependence of the conductivity on frequency and magnetic field is presented. We have shown that the contribution of the off-diagonal elements of density matrix is the greater than the higher the frequency of the alternating electromagnetic field. It has been established that for magnetic field value at which the minimum electron energy of upper spin zone exceeds the Fermi energy, the conductivity as a function of magnetic field change in discrete step.

First measurement of prompt and non-prompt D⁎+ vector meson spin alignment in pp collisions at [formula omitted] TeV

This letter reports the first measurement of spin alignment, with respect to the helicity axis, for D⁎+ vector mesons and their charge conjugates from charm-quark hadronisation (prompt) and from beauty-meson decays (non-prompt) in hadron collisions. The measurements were performed at midrapidity (|y|<0.8) as a function of transverse momentum (pT) in proton–proton (pp) collisions collected by ALICE at the centre-of-mass energy s=13TeV. The diagonal spin density matrix element ρ00 of D⁎+ mesons was measured from the angular distribution of the D⁎+→D0(→K−π+)π+ decay products, in the D⁎+ rest frame, with respect to the D⁎+ momentum direction in the pp centre of mass frame. The ρ00 value for prompt D⁎+ mesons is consistent with 1/3, which implies no spin alignment. However, for non-prompt D⁎+ mesons an evidence of ρ00 larger than 1/3 is found. The measured value of the spin density element is ρ00=0.455±0.022(stat.)±0.035(syst.) in the 5<pT<20GeV/c interval, which is consistent with a Pythia 8 Monte Carlo simulation coupled with the EvtGen package, which implements the helicity conservation in the decay of D⁎+ meson from beauty mesons. In non-central heavy-ion collisions, the spin of the D⁎+ mesons may be globally aligned with the direction of the initial angular momentum and magnetic field. Based on the results for pp collisions reported in this letter it is shown that alignment of non-prompt D⁎+ mesons due to the helicity conservation coupled to the collective anisotropic expansion may mimic the signal of global spin alignment in heavy-ion collisions.