Véronique Hussin

Higher-order SUSY, linearized nonlinear Heisenberg algebras and coherent states

Using an iterative construction of the first-order intertwining technique, we find k-parametric families of exactly solvable anharmonic oscillators whose spectra consist of a part isospectral to the oscillator plus k additional levels at arbitrary positions below E0 = ½. It is seen that the `natural ladder operators for these systems give place to polynomial nonlinear algebras, and it is shown that these algebras can be linearized. The coherent states construction is performed in the nonlinear and linearized cases.

A simple generation of exactly solvable anharmonic oscillators

Abstract An elementary finite difference algorithm shortens the Darboux method, permitting an easy generation of families of anharmonic potentials almost isospectral to the harmonic oscillator. Against common belief, it is possible to associate a SUSY partner to a given Hamiltonian H using a factorization energy greater than the ground state energy of H. The explicit 3-SUSY partners of the oscillator potential are found and discussed.

Coherent states for Hamiltonians generated by supersymmetry

Coherent states are derived for one-dimensional systems generated by supersymmetry from an initial Hamiltonian with a purely discrete spectrum for which the levels depend analytically on their subindex. It is shown that the algebra of the initial system is inherited by its SUSY partners in the subspace associated with the isospectral part or the spectrum. The technique is applied to the harmonic oscillator, infinite well and trigonometric Poschl–Teller potentials.

General sets of coherent states and the Jaynes–Cummings model

General sets of coherent states are constructed for quantum systems admitting a nondegenerate infinite discrete energy spectrum. They are eigenstates of an annihilation operator and satisfy the usual properties of standard coherent states. The application of such a construction to the quantum optics Jaynes–Cummings model leads to a new understanding of the properties of this model.

Generalized and Gaussian coherent states for the Morse potential

In this paper, we consider the one-dimensional anharmonic oscillator, which represents well the anharmonic vibrations in diatomic molecules. For the description of the associate potential we use the Morse potential, which gives a good approximation of the experimentally observed vibrational modes of molecules and hence contributes to the realistic description of the spectrum of diatomic molecules. The generalized and Gaussian coherent states are thus constructed and compared in terms of the localization of the particle in those states. We apply these results to the example of the sodium chloride molecule, 1H35Cl.

Squeezed coherent states and the one-dimensional Morse quantum system

The Morse potential one-dimensional quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to the one of the harmonic oscillator using ladder operators. The properties of these states are analysed with respect to the localization in position, minimal Heisenberg uncertainty relation, the statistical properties and illustrated with examples using the finite number of states in a well-known diatomic molecule.

Classification of the quantum deformations of the superalgebra gl(1|1)

We present a classification of the possible quantum deformations of the supergroup and its Lie superalgebra . In each case, the (super)commutation relations and the Hopf structures are explicitly computed. For each R-matrix, one finds two inequivalent co-products whether one chooses an unbraided or a braided framework while the corresponding structures are isomorphic as algebras. In the braided case, one recovers the classical algebra for suitable limits of the deformation parameters but this is no longer true in the unbraided case.

Comments of the definitions of coherent states for the SUSY harmonic oscillator

We insist on the possibility of regarding coherent states for the supersymmetric harmonic oscillator equivalently in three different ways, just as in the usual bosonic case.

Entangled squeezed states in noncommutative spaces with minimal length uncertainty relations

We provide an explicit construction of entangled states in a noncommutative space with nonclassical states, particularly with the squeezed states. Noncommutative systems are found to be more entangled than the usual quantum mechanical systems. The noncommutative parameter provides an additional degree of freedom in the construction by which one can raise the entanglement of the noncommutative systems to fairly higher values beyond the usual systems. Despite of having classical-like behaviour, coherent states in noncommutative space produce little amount of entanglement and therefore they possess slight nonclassicality as well, which are not true for the coherent states of ordinary harmonic oscillator.

Noncommutative

We construct the photon-added coherent states of a noncommutative harmonic oscillator associated to a