Representations of coherent and squeezed states in an extended two-parameter Fock space

Abstract

Recently an f-deformed Fock space which is spanned by |n〉λ was introduced. These bases are the eigenstates of a deformed non-Hermitian Hamiltonian. In this contribution, we will use rather new non-orthogonal basis vectors for the construction of coherent and squeezed states, which in special case lead to the earlier known states. For this purpose, we first generalize the previously introduced Fock space spanned by |n〉λ bases, to a new one, spanned by extended two-parameters bases |n〉λ1, λ2. These bases are now the eigenstates of a non-Hermitian Hamiltonian Hλ1,λ2 = a†λ1,λ2a+½, where a†λ1, λ2 and a are, respectively, the deformed creation and ordinary bosonic annihilation operators. The bases |n〉λ1, λ2 are non-orthogonal (squeezed states), but normalizable. Then, we deduce the new representations of coherent and squeezed states in our two-parameter Fock space. Finally, we discuss the quantum statistical properties, as well as the non-classical properties of the obtained states numerically.