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Physical Review A

Para-Bose oscillator as a deformed Bose oscillator

S. Chaturvedi, Venkatraman Srinivasan

Published Dec 1, 1991• 31 citations
Publisher

Abstract

We show that a single para-Bose oscillator may be regarded as a deformed Bose oscillator. We construct a nonlinear realization of the single-mode para-Bose algebra in terms of a single boson. This is in contrast to the Green decomposition that expresses a single para-Bose oscillator in terms of p anticommuting bosons. We also construct an operator canonically conjugate to the para-Bose annihilation operator that permits us to carry over familiar constructions to the para-Bosonic case.

DOI
10.1103/physreva.44.8024

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Journal of Physics A Mathematical and General•Oct 7, 1992•4 citations
We show that a single para-Bose oscillator may be regarded as a deformed Bose oscillator. We construct a nonlinear realization of the single-mode para-Bose algebra in terms of a single boson. This is in contrast to the Green decomposition that expresses a single para-Bose oscillator in terms of p anticommuting bosons. We also construct an operator canonically conjugate to the para-Bose annihilation operator that permits us to carry over familiar constructions to the para-Bosonic case.
A unified view of general multimode oscillator algebras with Fock-like representations is presented. It extends a previous analysis of the single-mode oscillator algebras. The expansion of the [Formula: see text] operators is extended to include all normally ordered terms in creation and annihilation operators, and we analyze their action on Fock-like states. We restrict ourselves to the algebras compatible with number operators. The connection between these algebras and generalized statistics is analyzed. We demonstrate our approach by considering the algebras obtainable from the generalized Jordan-Wigner transformation, the para-Bose and para-Fermi algebras, the Govorkov “paraquantization” algebra and generalized quon algebra.
We present the truncated (or [Formula: see text]-deformed) para-Bose oscillator algebra of order [Formula: see text], with [Formula: see text] being a half-integer, along with its [Formula: see text]-dimensional Fock representation. The model reduces to the truncated simple harmonic oscillator and the conventional para-Bose oscillator algebras in the limiting cases where the parameters [Formula: see text] and [Formula: see text] approach zero and infinity, respectively. A Fock–Bargmann realization is constructed in such a way that the creation operator is expressed as a function of both deformation parameters [Formula: see text] and [Formula: see text]. Two-component orthogonal cat states are formulated through suitable superpositions of even and odd parity states within the Fock representation space. The corresponding positive-definite measures over the entire complex plane are derived in terms of Meijer’s [Formula: see text]-functions parameterized by [Formula: see text] and [Formula: see text]. In addition, the nonclassical properties of the even and odd cat states are analyzed, including the manifestation of sub-Poissonian statistics, photon antibunching effect, and quadrature squeezing. We further investigate how the parameters [Formula: see text] and [Formula: see text] individually influence the enhancement or suppression of entanglement in the associated quasi-Bell states.