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Abstract
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Using the parity deformed Heisenberg algebra (RDHA), we first establish associated
coherent states (RDCSs) for a pseudo-harmonic oscillator (PHO) system that are defined
as eigenstates of a deformed annihilation operator. Such states can be expressed
as superposition of an even and odd Wigner cat states.35 The RDCSs minimize a corresponding
uncertainty relation, and resolve an identity condition through a positive
definite measure which is explicitly derived. We introduce a class of single-mode excited
coherent states (PARDCS) of the PHO through “m” times application of deformed creation
operators to RDCS. For the states thus constructed, we analyze their statistical
properties such as squeezing and sub-Poissonian statistics as well as their uncertainty
relations.
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