Imaging constituent quark shape of proton with exclusive vector meson production at HERA

We show within proton hot spot picture that the exclusive vector meson production in electron-proton deeply inelastic scattering is sensitive to the individual width of the constituent quarks of the proton. For comparison, we calculate the exclusive $J/\Psi$ production cross-sections in three cases, $\mathrm{B_u} \geq \mathrm{B_d}$, $\mathrm{B_u} < \mathrm{B_d}$ and $\mathrm{B_u}\neq\mathrm{B^{\prime}_u}\neq\mathrm{B_d}$, where the $\mathrm{B_u}$, $\mathrm{B^{\prime}_u}$ and $\mathrm{B_d}$ denote the widths of two up quarks and down quark. We find that only results calculated with $\mathrm{B_u} \geq \mathrm{B_d}$ can give a reasonable description of the exclusive $J/\Psi$ production cross-section data at HERA. To test that our results are independent of the details of the model, we retain the average width of the three constituent quarks unchanged and compute the exclusive $J/\Psi$ production cross-sections with contribution weight by setting different proportional coefficients ($\mathrm{W_u}$ and $\mathrm{W_d}$) for the up and down quarks, respectively. It shows that the results calculated with $\mathrm{W_u}\geq\mathrm{W_d}$ can well reproduce the exclusive $J/\Psi$ production data at HERA, while the opposite case cannot describe the HERA data. These interesting findings seem to indicate that the up quark has more gluons around it than the down quark at high energy although the spatial distribution of gluons fluctuates event-by-event . To ensure the relevant results independent of the species of the vector meson, we also calculate the $\rho$ production cross-sections with the same group of parameters used in the exclusive $J/\Psi$ production and compare the predictions with the HERA data. It shows that all the results computed in the exclusive $\rho$ productions are consistent with the findings obtained in the exclusive $J/\Psi$ productions.Comment: 12 pages, 6 figure

Information-Theoretic Measure of Genuine Multi-Qubit Entanglement

We consider pure quantum states of N qubits and study the genuine N-qubit entanglement that is shared among all the N qubits. We introduce an information-theoretic measure of genuine N-qubit entanglement based on bipartite partitions. When N is an even number, this measure is presented in a simple formula, which depends only on the purities of the partially reduced density matrices. It can be easily computed theoretically and measured experimentally. When N is an odd number, the measure can also be obtained in principle.Comment: 5 pages, 2 figure

Anisotropic Electron-Hole Excitation and Large Linear Dichroism in Two-Dimensional Ferromagnet CrSBr with In-Plane Magnetization

The observation of magnetic ordering in atomically thin CrI$_3$ and Cr$_2$Ge$_2$Te$_6$ monolayers has aroused intense interest in condensed matter physics and material science. Studies of van de Waals two-dimensional (2D) magnetic materials are of both fundamental importance and application interest. In particular, exciton-enhanced magneto-optical properties revealed in CrI$_3$ and CrBr$_3$ monolayers have expanded the understanding of exciton physics in 2D materials. Unlike CrI$_3$ and CrBr$_3$ with out-of-plane magnetization, CrSBr has an in-plane magnetic moment, therefore, providing a good opportunity to study the magnetic linear dichroism and high-order magneto-optical effects. Here, based on the many-body perturbation method within density-functional theory, we have studied quasiparticle electronic structure, exciton, and optical properties in CrSBr monolayer. Strongly bounded exciton has been identified with the first bright exciton located at 1.35 eV, in good agreement with an experiment of photoluminescence (Nat. Mater. \textbf{20}, 1657 (2021)). Strong contrast in the optical absorption is found between the electric fields lying along the in-plane two orthogonal directions. In accordance with a typical and realistic experimental setup, we show that the rotation angle of linear polarized light, either reflected or transmitted, could be comparable with those revealed in black phosphorene. Such large linear dichroism arises mainly from anisotropic in-plane crystal structure. The magnetic contribution from the off-diagonal component of dielectric function to the linear dichroism in CrSBr is negligible. Our findings not only have revealed excitonic effect on the optical and magneto-optical properties in 2D ferromagnet CrSBr, but also have shown its potential applications in 2D optics and optoelectronics.Comment: 47 pages, 24 figure