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M. Kibler

Publications and source records attributed to M. Kibler.

At least 19 recordsLinked to original sources
arXiv2008

Generalized spin bases for quantum chemistry and quantum information

Symmetry adapted bases in quantum chemistry and bases adapted to quantum information share a common characteristics: both of them are constructed from subspaces of the representation space of the group SO(3) or its double group (i.e., spinor group) SU(2). We exploit this fact for generating spin bases of relevance for quantum systems with cyclic symmetry and equally well for quantum information and quantum computation. Our approach is based on the use of generalized Pauli matrices arising from a polar decomposition of SU(2). This approach leads to a complete solution for the construction of mutually unbiased bases in the case where the dimension d of the considered Hilbert subspace is a prime number. We also give the starting point for studying the case where d is the power of a prime number. A connection of this work with the unitary group U(d) and the Pauli group is brielly underlined.

quant-ph↗
arXiv2001

On Two Approaches to Fractional Supersymmetric Quantum Mechanics

Two complementary approaches of N = 2 fractional supersymmetric quantum mechanics of order k are studied in this article. The first one, based on a generalized Weyl-Heisenberg algebra W(k) (that comprizes the affine quantum algebra Uq(sl(2)) with q to k = 1 as a special case), apparently contains solely one bosonic degree of freedom. The second one uses generalized bosonic and k-fermionic degrees of freedom. As an illustration, a particular emphasis is put on the fractional supersymmetric oscillator of order k.

math-ph↗
arXiv1999

A System of Interest in Spectroscopy: The qp-Rotor System

A rotor system, having the symmetry afforded by the two-parameter quantum algebra Uqp(u(2)), is investigated in this communication. This system is useful in rotational spectroscopy of molecules and nuclei. In particular, it is shown to lead to a model (viz., the qp-rotor model) for describing (via an energy formula and a qp-deformation of E2 reduced transition probabilities) rotational bands of deformed and superdeformed nuclei.

nucl-th↗
arXiv1998

Symmetry Adaptation in Two-Photon Spectroscopy

Symmetry adaptation techniques are applied to the determination of the intensity of two-photon transitions for transition ions in finite symmetry environments. We treat the case of intra-configurational transitions with some details and briefly report some results on inter-configurational transitions. In particular, for intra-configurational transitions, we describe a model which takes into account the following ingredients: symmetry, second- plus third- order mechanisms, S-, L- and J-mixings.

physics.atm-clus↗
arXiv1998

Two-Photon Laser Spectroscopy of Transition Ions in Crystals: Inter- Configurational Transitions

Symmetry adaptation techniques are applied to the determination of the intensity of two-photon absorption transitions, between Stark levels of configurations with opposite parities, for transition ions in finite symmetry environments. The equivalence between third-order mechanisms and second- plus first-order mechanisms is clearly established. A compact formula is derived for the intensity of a two-photon transition between two levels with well-defined symmetries. A set of (selection) rules which controls the number of intensity parameters for inter-configurational transitions is given. The formalism is illustrated with the case of an ion with 4f configuration in tetragonal symmetry.

physics.atm-clus↗
arXiv1998

Symmetry Adaptation and Two-Photon Spectroscopy of Ions in Molecular or Solid-State Finite Symmetry

Finite symmetry adaptation techniques are applied to the determination of the intensity strength of two-photon transitions for ions with one partly-filled shell nl in crystalline environments of symmetry G. We treat the case of intra- configurational transitions as well as the case of inter-configurational transitions. In both cases, the Wigner-Racah algebra of the chain O(3) > G allows to extract the polarization dependence from the intensity. The reported results are valid for any strength of the crystalline field.

physics.atm-clus↗
arXiv1998

Sum Rules for Multi-Photon Spectroscopy of Ions in Finite Symmetry

Models describing one- and two-photon transitions for ions in crystalline environments are unified and extended to the case of parity-allowed and parity- forbidden p-photon transitions. The number of independent parameters for characterizing the polarization dependence is shown to depend on an ensemble of properties and rules which combine symmetry considerations and physical models.

physics.atm-clus↗
arXiv1998

Symmetry Adaptation Techniques in n-Photon Absorption Spectroscopy

We present some recent progress achieved in the application of symmetry adaptation techniques to n-photon absorption spectroscopy of rare earth ions in finite symmetry. More specifically, this work is concerned with the determination of the intensity of n-photon transitions between Stark levels (rather than J levels) of an ion in an environment with a given symmetry. The role of symmetry is taken into account through the use of initial and final state vectors characterized by irreducible representations of the (double) group for the ion site symmetry. Two distinct situations are considered, viz., the case of parity-allowed and parity-forbidden n-photon transitions.

physics.atm-clus↗
arXiv1998

Two-Photon Spectroscopy of Transition-Metal Ions in Cubical Symmetry

Symmetry adaptation techniques are applied to the determination of intensities of intra-configurational two-photon transitions for transition-metal ions in cubical symmetry. This leads to a simple model giving the polarization dependence of intensities of two-photon (electric dipolar) transitions between Stark levels of the configuration 3dN (N = even or odd).

physics.atm-clus↗
arXiv1998

Classical Trajectories for two Ring-Shaped Potentials

This paper deals with the classical trajectories for two super-integrable systems: a system known in quantum chemistry as the Hartmann system and a system of potential use in quantum chemistry and nuclear physics. Both systems correspond to ring-shaped potentials. They admit two maximally super-integrable systems as limiting cases, viz, the isotropic harmonic oscillator system and the Coulomb-Kepler system in three dimensions. The planarity of the trajectories is studied in a systematic way. In general, the trajectories are quasi-periodic rather than periodic. A constraint condition allows to pass from quasi-periodic motions to periodic ones. When written in a quantum mechanical context, this constraint condition leads to new accidental degeneracies for the two systems studied.

quant-ph↗
arXiv1998

Intensity of Two-Photon Absorption Transitions for Ni2+ in MgO

The parity-allowed two-photon transitions between the ground state 3A2(T2) of the configuration 3d8 in cubical symmetry and the excited states of the same configuration are obtained via a simple model. This model is developed in a symmetry adapted framework by using second-order mechanisms and ionic wave-functions. It is applied to the recent experimental results obtained by McClure and co-workers for Ni2+ in MgO.

physics.atm-clus↗
arXiv1998

On Generalized Super-Coherent States

A set of operators, the so-called k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of an algebra arising from two non-commuting quon algebras. The deformation parameters q and 1/q for these quon algebras are roots of unity with q to the power k being equal to 1. The case k = 2 corresponds to fermions and the case k going to infinity to bosons. Generalized coherent states (connected to the k-fermionic states) and super-coherent states (involving a k-fermionic sector and a purely bosonic sector) are investigated.

quant-ph↗
arXiv1997

An Alternative Basis for the Wigner-Racah Algebra of the Group SU(2)

The Lie algebra of the classical group SU(2) is constructed from two quon algebras for which the deformation parameter is a common root of unity. This construction leads to (i) a not very well-known polar decomposition of the ladder generators of the SU(2) Lie algebra and to (ii) an alternative to the (J,M) quantization scheme, viz., the (J,alpha) quantization scheme. The key ideas for developing the Wigner-Racah algebra of the group SU(2) in the (J,alpha) scheme are given. In particular, some properties of the coupling and recoupling coefficients as well as the Wigner-Eckart theorem in the (J,alpha) scheme are briefly discussed.

math-ph↗
arXiv1997

On a Generalized Oscillator: Invariance Algebra and Interbasis Expansions

This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian and cylindrical bases as well as the cylindrical and spherical bases for D=3. These interbasis expansion coefficients are found to be analytic continuations to real values of their arguments of the Clebsch-Gordan coefficients for the group SU(2). For D=2, the superintegrable character for the generalized oscillator system is investigated from the points of view of a quadratic invariance algebra.

quant-ph↗