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Abstract
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The construction of nonlinear coherent states via a unitary displacement operator is possible only
for a few quantum-mechanical systems. In this paper, we define two non-unitary and a unitary displacement
operators with the help of corresponding f-deformed bosonic annihilation and creation operators. While
the action of the non-unitary displacement type operators on the vacuum state of field results in two
new families of nonlinear coherent states (NLCSs), the unitary displacement operator reproduces Wigner-
Heisenberg coherent states of the Gilmore-Perelomov type.We prove that the introduced NLCSs satisfy the
resolution of the identities through positive definite measures. We also examine the non-classical properties
of the obtained NLCSs by evaluating Klyshko’s criterion, Mandel’s parameter, quadrature squeezing and
Wigner quasi-probability distribution function, in detail. Finally, we propose a simple scheme for the
physical generation of the introduced NLCSs of the Gilmore-Perelomov type.
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