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arXiv · 1104.4452

Phase operators, phase states and vector phase states for SU(3) and SU(2,1)

Mohammed Daoud·Maurice Robert Kibler
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Abstract

This paper focuses on phase operators, phase states and vector phase states for the sl(3) Lie algebra. We introduce a one-parameter generalized oscillator algebra A(k,2) which provides a unified scheme for dealing with su(3) (for k < 0), su(2,1) (for k > 0) and h(4) x h(4) (for k = 0) symmetries. Finite- and infinite-dimensional representations of A(k,2) are constructed for k < 0 and k > 0 or = 0, respectively. Phase operators associated with A(k,2) are defined and temporally stable phase states (as well as vector phase states) are constructed as eigenstates of these operators. Finally, we discuss a relation between quantized phase states and a quadratic discrete Fourier transform and show how to use these states for constructing mutually unbiased bases.

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Mohammed Daoud, Maurice Robert Kibler. 2011-04-22. Phase operators, phase states and vector phase states for SU(3) and SU(2,1). https://doi.org/10.1063/1.3620414

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