Plasmon assisted transmission of high dimensional orbital angular momentum entangled state

We present an experimental evidence that high dimensional orbital angular momentum entanglement of a pair of photons can be survived after a photon-plasmon-photon conversion. The information of spatial modes can be coherently transmitted by surface plasmons. This experiment primarily studies the high dimensional entangled systems based on surface plasmon with subwavelength structures. It maybe useful in the investigation of spatial mode properties of surface plasmon assisted transmission through subwavelength hole arrays.Comment: 7 pages,6 figure

Projection Measurement of the Maximally Entangled N-Photon State for a Demonstration of N-Photon de Broglie Wavelength

We construct a projection measurement process for the maximally entangled N-photon state (the NOON-state) with only linear optical elements and photodetectors. This measurement process will give null result for any N-photon state that is orthogonal to the NOON state. We examine the projection process in more detail for N=4 by applying it to a four-photon state from type-II parametric down-conversion. This demonstrates an orthogonal projection measurement with a null result. This null result corresponds to a dip in a generalized Hong-Ou-Mandel interferometer for four photons. We find that the depth of the dip in this arrangement can be used to distinguish a genuine entangled four-photon state from two separate pairs of photons. We next apply the NOON state projection measurement to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. A successful NOON state projection is demonstrated with the appearance of the four-photon de Broglie wavelength in the interference fringe pattern.Comment: 8 pages, 3 figures, new title, some content change, replaced Fig.

Bound states on the lattice with partially twisted boundary conditions

We propose a method to study the nature of exotic hadrons by determining the wave function renormalization constant $Z$ from lattice simulations. It is shown that, instead of studying the volume-dependence of the spectrum, one may investigate the dependence of the spectrum on the twisting angle, imposing twisted boundary conditions on the fermion fields on the lattice. In certain cases, e.g., the case of the $DK$ bound state which is addressed in detail, it is demonstrated that the partial twisting is equivalent to the full twisting up to exponentially small corrections

Two-photon Rabi-Hubbard and Jaynes-Cummings-Hubbard models: photon pair superradiance, Mott insulator and normal phases

We study the ground state phase diagrams of two-photon Dicke, the one-dimensional Jaynes-Cummings-Hubbard (JCH), and Rabi-Hubbard (RH) models using mean field, perturbation, quantum Monte Carlo (QMC), and density matrix renormalization group (DMRG) methods. We first compare mean field predictions for the phase diagram of the Dicke model with exact QMC results and find excellent agreement. The phase diagram of the JCH model is then shown to exhibit a single Mott insulator lobe with two excitons per site, a superfluid (SF, superradiant) phase and a large region of instability where the Hamiltonian becomes unbounded. Unlike the one-photon model, there are no higher Mott lobes. Also unlike the one-photon case, the SF phases above and below the Mott are surprisingly different: Below the Mott, the SF is that of photon {\it pairs} as opposed to above the Mott where it is SF of simple photons. The mean field phase diagram of the RH model predicts a transition from a normal to a superradiant phase but none is found with QMC.Comment: 14 pages, 14 figure

Two monotonic functions involving gamma function and volume of unit ball

In present paper, we prove the monotonicity of two functions involving the gamma function $\Gamma(x)$ and relating to the $n$-dimensional volume of the unit ball $\mathbb{B}^n$ in $\mathbb{R}^n$.Comment: 7 page

Geometries for Possible Kinematics

The algebras for all possible Lorentzian and Euclidean kinematics with $\frak{so}(3)$ isotropy except static ones are re-classified. The geometries for algebras are presented by contraction approach. The relations among the geometries are revealed. Almost all geometries fall into pairs. There exists $t \leftrightarrow 1/(\nu^2t)$ correspondence in each pair. In the viewpoint of differential geometry, there are only 9 geometries, which have right signature and geometrical spatial isotropy. They are 3 relativistic geometries, 3 absolute-time geometries, and 3 absolute-space geometries.Comment: 40 pages, 7 figure

Size, alloy and interface effects on Cu-based catalysts for enhancing electrochemical reduction of CO_{2}

The electrochemical reduction of CO2 (CO2RR) is a significant pathway for converting CO2 into valuable fuels and promoting the sustainability of energy and environment. In recent years, there has been a growing interest in copper-based CO2 conversion electrocatalysts due to their high activity and selectivity to generate various products from CO2 reduction. This review paper focuses on the systematic design of Cu-based CO2RR electrocatalysts, with a specific emphasis on size regulation, alloying strategies, and interface engineering. Furthermore, the stability, activity, catalytic performance, and underlying mechanisms of these Cu-based electrocatalysts are extensively discussed. Finally, the potential applications and existing challenges associated with copper-based electrocatalysts are summarized, aiming to guide the design of high-performance CO2RR electrocatalysts