Related papers: Nonlocal PDEs and Quantum Optics: Bound States and…

Nonlinear interactions between single quantum particles are at the heart of any quantum information system, including analog quantum simulation and fault-tolerant quantum computing. This remains a particularly difficult problem for photonic…

Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…

We continue our study of the quantum optics of a single photon interacting with a system of two level atoms. In this work we investigate the case of a periodic arrangement of atoms. We provide a general structure theorem characterizing the…

We consider the possibility that photons of noncommutative QED can make bound states. Using the potential model, developed based on the constituent gluon picture of QCD glue-balls, arguments are presented in favor of existence of these…

Bound states of the pion--nucleus system are investigated in momentum space using a microscopic optical potential with inherent energy dependences and nonlocalities arising from elementary potential models. The wave equation and…

We study the rate of convergence for (variational) eigenvalues of several non-linear problems involving oscillating weights and subject to different kinds of boundary conditions in bounded domains.

The optical responses of solids are typically understood to be local in space. Whether locality holds for the optical response of a macroscopic quantum system has, however, been largely unexplored. Here, we use multidimensional coherent…

We consider atoms or molecules coupled to the quantized electromagnetic radiation field in a dipole approximation. We show the existence of ground states and resonance states in situations where the eigenvalues are degenerate and protected…

We discuss localized ground states of the periodic Gross-Pitaevskii equation in the framework of a quantum linear Schr\"odinger equation with effective potential determined in self-consistent manner. We show that depending on the…

The formation of bound states involving multiple particles underlies many interesting quantum physical phenomena, such as Efimov physics or superconductivity. In this work we show the existence of an infinite number of such states for some…

In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…

We report on high-resolution photoluminescence (PL) spectroscopic and microscopic study of laterally coupled InAs/GaAs self-assembled quantum dots by using a low-temperature near-field scanning optical microscope. We have observed slightly…

We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is a self-adjoint realisation of the kinetic-energy operator, with the specific realisation determined by…

We solve for the exact atom-field eigenstates of a single atom in a three dimensional spherical cavity, by mapping the problem onto the anisotropic Kondo model. The spectrum has a rich bound state structure in comparison with models where…

Moment based methods have produced efficient multiscale quantization algorithms for solving singular perturbation/strong coupling problems. One of these, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev. Lett.{\bf…

We study the existence of bound states in the continuum for a system of n two-level quantum emitters, coupled with a one-dimensional boson field, in which a single excitation is shared among different components of the system. The emitters…

We present experimental evidence of photon droplets in an attractive (focusing) nonlocal nonlinear medium. Photon droplets are self-bound, finite-sized states of light that are robust to size and shape perturbations due to a balance of…

Nonlinear optical phenomena are typically local. Here we predict the possibility of highly nonlocal optical nonlinearities for light propagating in atomic media trapped near a nano-waveguide, where long-range interactions between the atoms…

The model of a two-electron quantum dot, confined to move in a two dimensional flat space, in the presence of an external harmonic oscillator potential, is revisited for a specific purpose. Indeed, eigenvalues and eigenstates of the bound…

We study the nonlocality of arbitrary dimensional bipartite quantum states. By computing the maximal violation of a set of multi-setting Bell inequalities, an analytical and computable lower bound has been derived for general two-qubit…