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Journal of Physics A Mathematical and General

New coherent states of the Lie superalgebra osp (1/2,R)

Le‐Man Kuang, Xin Chen

Published Mar 7, 1994• 3 citations
Publisher

Abstract

A new kind of coherent states (CSs) for Lie superalgebra osp(l/2,R) are introduced. Some properties of these states are discussed. It is shown that they can encompass the Glauber CSs, su(1,1) CSs and squeezed states within a common formalism. The D-algebra differential operator realization of the osp(1/2,R) generators on the CSs and their diagonal projectors are constructed.

DOI
10.1088/0305-4470/27/5/003

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Physica Scripta•Aug 22, 2008•3 citations
A new kind of coherent states (CSs) for Lie superalgebra osp(l/2,R) are introduced. Some properties of these states are discussed. It is shown that they can encompass the Glauber CSs, su(1,1) CSs and squeezed states within a common formalism. The D-algebra differential operator realization of the osp(1/2,R) generators on the CSs and their diagonal projectors are constructed.
The superalgebra eigenstates (SAES) concept is introduced and then applied to find the SAES associated to the sh(2/2) superalgebra, also known as Heisenberg–Weyl Lie superalgebra. This implies to solve a Grassmannian eigenvalue superequation. Thus, the sh(2/2) SAES contain the class of supercoherent states associated to the supersymmetric harmonic oscillator and also a class of supersqueezed states associated to the osp(2/2) + ⊃ sh(2/2) superalgebra, where osp(2/2) denotes the orthosymplectic Lie superalgebra generated by the set of operators formed from the quadratic products of the Heisenberg–Weyl Lie superalgebra generators. The properties of these states are investigated and compared with those of the states obtained by applying the group-theoretical technics. Moreover, new classes of generalized supercoherent and supersqueezed states are also obtained. As an application, the superHermitian and η–pseudo–superHermitian Hamiltonians without a defined Grassmann parity and isospectral to the harmonic oscillator are constructed. Their eigenstates and associated supercoherent states are calculated.
Two new types of coherent states associated with the Cλ-extended oscillator, where Cλ is the cyclic group of order λ, are introduced. The first ones include as special cases both the Barut-Girardello and the Perelomov su(1,1) coherent states for λ = 2, as well as the annihilation-operator coherent states of the Cλ-extended oscillator spectrum generating algebra for higher λ values. The second ones, which are eigenstates of the Cλ-extended oscillator annihilation operator, extend to higher λ values the paraboson coherent states, to which they reduce for λ = 2. All these states satisfy a unity resolution relation in the Cλ-extended oscillator Fock space (or in some subspace thereof). They give rise to Bargmann representations of the latter, wherein the generators of the Cλ-extended oscillator algebra are realized as differential-operatorvalued matrices (or differential operators). The statistical and squeezing properties of the new coherent states are investigated over a wide range of parameters and some interesting nonclassical features are exhibited. 1 1
Generalized coherent states associated with SU(1,1) Lie algebra are reviewed. A state is called intelligent if it satisfies the strict equality in the Heisenberg uncertainty relation. The eigenvalue problem satisfied by intelligent states (IS) is solved. The IS associated with SU(1,1) Lie algebra are investigated. We have constructed some realizations for our results of IS, and some applications are discussed. Some nonclassical properties such as Glauber second-order correlation function, photon number distribution and squeezing are investigated.