Parity-deformed sl(2, R), su(2) and so(3) algebras: A basis for quantum optics and quantum communications applications

초록

Having in mind the significance of parity (reflection) in various areas of physics, the single-mode and two-mode Wigner algebras are considered adding to them a reflection operator. The associated deformed sl(2, R) algebra, sl(2, R) and the deformed so(3) algebra, so(3), are constructed for the widely used Jordan-Schwinger and Holstein-Primakoff realizations, commenting on various aspects and ingredients of the formalism for both single-mode and two-mode cases. Finally, due to its potential application in the study of qubit and qutrit systems, the parity-deformed so(3) representation is analyzed based on the isomorphy of so(3) and su(2). Related applications are discussed as well.

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