Related papers: Jacobi photonic lattices and their SUSY partners
Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the…
Supersymmetric (SUSY) optical structures display a number of intriguing properties that can lead to a variety of potential applications, ranging from perfect global phase matching to highly efficient mode conversion and novel multiplexing…
We present a two-dimensional array of nearest-neighbor coupled waveguides that is the optical analog of a quantum optomechanical system. We show that the quantum model predicts the appearance of effective column isolation, diagonal-coupling…
We propose the use of photonic crystal structures to design subwavelength optical lattices in two dimensions for ultracold atoms by using both Guided Modes and Casimir-Polder forces. We further show how to use Guided Modes for…
Integrated Jx photonic lattices, inspired by the quantum harmonic oscillator and due to their equidistant eigenvalue spectrum, have been proven extremely useful for various applications, such as perfect imaging and coherent transfer of…
We present a class of waveguide arrays that is the classical analog of a quantum harmonic oscillator where the mass and frequency depend on the propagation distance. In these photonic lattices refractive indices and second neighbor…
Cholesky factorization provides photonic lattices that are the isospectral partners or the square root of other arrays of coupled waveguides. The procedure is similar to that used in supersymmetric quantum mechanics. However, Cholesky…
We show that supersymmetry can provide a versatile platform in synthesizing a new class of optical structures with desired properties and functionalities. By exploiting the intimate relationship between superpatners, one can systematically…
The concept of supersymmetry developed in particle physics has been applied to various fields of modern physics. In quantum mechanics, the supersymmetric systems refer to the systems involving two supersymmetric partner Hamiltonians, whose…
We present the general ideas on SuperSymmetric Quantum Mechanics (SUSY-QM) using different representations for the operators in question, which are defined by the corresponding bosonic Hamiltonian as part of SUSY Hamiltonian and its…
A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant…
Coherent states and their generalisations, displaced Fock states, are of fundamental importance to quantum optics. Here we present a direct observation of a classical analogue for the emergence of these states from the eigenstates of the…
We propose a way of generating optical lattices embedded in photonic crystals. By setting up extended modes in photonic crystals, ultracold atoms can be mounted in different types of field intensity distributions. This novel way of…
We consider polynomial deformations of Lie superalgebras and their representations. For the class A(n-1,0) ~ sl(n/1), we identify families of superalgebras of quadratic and cubic type, consistent with Jacobi identities. For such deformed…
Quantum Hamilton-Jacobi formalism is used to give a proof for Gozzi's criterion that for eigenstates of the supersymmetric partners, corresponding to same energy, the difference in the number of nodes is equal to one when supersymmetry…
We study the cooperative optical coupling between regularly spaced atoms in a one-dimensional waveguide using decompositions to subradiant and superradiant collective excitation eigenmodes, direct numerical solutions, and analytical…
We revisit electromagnetic field propagation through tight-binding arrays of coupled photonic waveguides, with properties independent of the propagation distance, and recast it as a symmetry problem. We focus our analysis on photonic…
We propose to use a continuous supersymmetric (SUSY) transformation of a dielectric permittivity profile in order to design a photonic mode sorter. The iso-spectrality of the SUSY transformation ensures that modes of the waveguide preserve…
A novel approach is proposed to analyze a rather vast counter-rotating Hamiltonian interaction in the context of cavity quantum electrodynamics. The method relies upon the supersymmetric mapping of the corresponding rotating interaction and…
A ladder structure of operators is presented for the Jacobi polynomials, J_n^(a,b)(x), with parameters n, a and b integers, showing that they are related to the unitary irreducible representation of SU(2,2) with quadratic Casimir…