Para-Bose oscillator algebras of odd orders: x-representations and Wigner functions for coherent and cat states and their photon-added and photon-subtracted counterparts
Department of Theoretical Physics and Astrophysics, Faculty of Physics, University of Tabriz, P. O. Box 51666-16471, Tabriz, Iran
Accepted: 25 September 2022
Published online: 31 October 2022
The expansion coefficients for the Glauber-type coherent states of a para-Bose algebra of odd order are expressed in terms of the Laguerre polynomials of order in . It allows us to use one of the generating functions of the Laguerre polynomials to obtain the x-representation of the coherent states in terms of the J-Bessel functions. This, in turn, makes it possible to evaluate x-representations of the even and odd cat states as well as the m-photon-added and m-photon-subtracted coherent and cat states of the para-Bose oscillator algebra of odd order . Finally, with the help of these x-representations, we are able to examine Wigner functions and observe the non-classical behaviors via negative values for the probability distribution functions in phase space.
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