Related papers: Nonlocal PDEs and Quantum Optics: Bound States and…
Non-self-adjoint second-order differential pencils on a finite interval with non-separated quasi-periodic boundary conditions and jump conditions are studied. We establish properties of spectral characteristics and investigate the inverse…
We study the asymptotic diffusion processes with (generally nonlocal) open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be…
In part I, the formalism for the description of open quantum systems (that are embedded into a common well-defined environment) by means of a non-Hermitian Hamilton operator $\ch$ is sketched. Eigenvalues and eigenfunctions are…
We provide the first classification of three-photon eigenstates in a finite periodic array of two-level atoms coupled to a waveguide. We focus on the strongly subwavelength limit and show the hierarchical structure of the eigenstates in the…
Applications that envisage utilizing the orbital angular momentum (OAM) at the single photon level assume that the OAM degrees of freedom that the photons inherit from the classical wave solutions are orthogonal. To test this critical…
In this work we study a general shape optimization problem where the state equation is given in terms of a nonlocal operator. Examples of the problems considered are monotone combinations of fractional eigenvalues. Moreover, we also analyze…
We construct quantum algorithms to compute physical observables of nonlinear PDEs with M initial data. Based on an exact mapping between nonlinear and linear PDEs using the level set method, these new quantum algorithms for nonlinear…
The bound states of two particles are studied in frames of non-relativistic quantum field model with current $\times$ current type interaction by analyzing the Bethe-Salpeter amplitudes. The Bethe-Salpeter equations are obtained in closed…
Two-photon coherent states are one of the main building pillars of non-linear and quantum optics. It is the basis for the generation of minimum-uncertainty quantum states and entangled photon pairs, applications not obtainable from standard…
We present a scheme for coherently manipulating quantum states of photons by incorporating multiple photonic modes in a system with long-range interactions. The presence of nonlocal photon-photon interactions destroys the energy or momentum…
We demonstrate suppression and enhancement of spontaneous parametric down- conversion via quantum interference with two weak fields from a local oscillator (LO). Pairs of LO photons are observed to upconvert with high efficiency for…
A method to calculate the bound states of three-atoms without resorting to an explicit partial wave decomposition is presented. The differential form of the Faddeev equations in the total angular momentum representation is used for this…
We experimentally measure the lower and upper bounds of concurrence for a set of two-qubit mixed quantum states using photonic systems. The measured concurrence bounds are in agreement with the results evaluated from the density matrices…
We study two interacting quantum particles forming a bound state in $d$-dimensional free space, and constrain the particles in $k$ directions to $(0,\infty)^k \times \mathbb{R}^{d-k}$, with Neumann boundary conditions. First, we prove that…
In this paper we exploit the phenomenon of two principal half eigenvalues in the context of fully nonlinear Lane-Emden type systems with possibly unbounded coefficients and weights. We show that this gives rise to the existence of two…
We analyze nonclassical correlations between outcomes of measurements conducted on two spatial radiation modes. These correlations cannot be simulated with statistical mixtures of coherent states or, more generally, with non-negative…
In this article, we study the impact of self-interaction and multiparticle states on sustaining negative energies in relativistic quantum systems. For physically reasonable models, one usually requires bounds on both magnitude and duration…
We justify supercritical geometric optics in small time for the defocusing semiclassical Nonlinear Schrodinger Equation for a large class of non-necessarily homogeneous nonlinearities. The case of a half-space with Neumann boundary…
In waveguide quantum electrodynamics systems, atomic radiation emission is shaped by the photonic environment and collective atom interactions, offering promising applications in quantum technologies. In particular, atom-photon bound…
The number resolution of solid-state artificial atoms is of fundamental interest for the study of quantum few-body systems, yet remains experimentally challenging. Quantum optical experiments offer a non-invasive approach which links up…