Related papers: Optical matrix elements in tight-binding models wi…
We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum…
We discuss the general matrix elements of the squeezing operator between number eigenstates of a harmonic oscillator (which may also represent a quantized mode of the electromagnetic radiation). These matrix elements have first been used by…
A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given.…
We propose a tight binding model for the quantum spin Hall system on triangular optical lattice and we determined the edge state spectrum which contains gap traversing states as the hallmark of $\mathds{Z}_{2}$ topological insulator. The…
The quantum superposition principle has been extensively utilized in the quantum mechanical description of the bonding phenomenon. It explains the emergence of delocalized molecular orbitals and provides a recipe for the construction of…
We study interacting bosons in a two dimensional bipartite optical lattice. By focusing on the regime where the first three excited bands are nearly degenerate we derive a three orbital tight-binding model which captures the most relevant…
Recently experiments have shown very significant spin activity in biological molecules such as DNA, proteins, oligopeptides and aminoacids. Such molecules have in common their chiral structure, time reversal symmetry and the absence of…
Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms…
A collective spin model is used to describe two species of mutually interacting ultracold bosonic atoms confined to a toroidal trap. The system is modeled by a Hamiltonian that can be split into two components, a linear part and a quadratic…
We study cold atoms in an optical lattice with synthetic spin-orbit coupling in the Mott-insulator regime. We calculate the parameters of the corresponding tight-binding model using Peierls substitution and "localized Wannier states method"…
We have investigated a wide range of nonclassical behavior exhibited by a tripartite cavity optomechanical system comprising a two-level atom placed inside a Fabry-P\'{e}rot type optical cavity with a vibrating mirror attached to one end.…
Ultracold atoms placed in a tight cigar-shaped trap are usually described in terms of the Lieb-Liniger model. We study the extensions of this model which arise when van der Waals interaction between atoms is taken into account. We find that…
We provide a methodology to understand materials with complex bonding patterns, and apply it to the example of heteroanionic and lone pair materials. We build a tight-binding model based on Wannier functions fitted on density functional…
The study of transverse optical pattern formation has been studied extensively in nonlinear optics, with a recent experimental interest in studying the phenomenon using cold atoms, which can undergo real-space self-organization. Here, we…
We show how mapping techniques inherent to $N^{2}$-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the…
In the study of orbital angular momentum (OAM), the focus has been predominantly on the intra-atomic contribution. However, recent research has begun to shift towards exploring the inter-atomic contribution to OAM dynamics. In this paper,…
We propose a method to perform precision measurements of the interaction parameters in systems of N ultra-cold spin 1/2 atoms. The spectroscopy is realized by first creating a coherent spin superposition of the two relevant internal states…
To manipulate orbital angular momentum (OAM) carried by light beams, there is a great interest in designing various optical elements from the deep-ultraviolet to the microwave. Normally, the OAM variation introduced by optical elements can…
Photon carries linear momentum and angular momentum simultaneously. Within the light-matter interaction process, exchange of linear momentum results in optical forces, whereas exchange of angular momentum leads to optical torques. Use of…
The goal of this paper is to relate the capacitance matrix formalism to the tight-binding approximation. By doing so, we open the way to the use of mathematical techniques and tools from condensed matter theory in the mathematical and…