In this paper we study approximate quasi-probability distribution functions of nonclassical states such as incoherent states, Kerr states, squeezed states and $k$ -photon coherent states in interacting Fock space.In this paper we study approximate quasi-probability distribution functions of nonclassical states such as incoherent states, Kerr states, squeezed states and $k$-photon coherent states in interacting Fock space.

Banach Center PublicationsJan 1, 20070 citations

Representations of coherent and squeezed states in af-deformed Fock space

R Roknizadeh, M K Tavassoly

We establish some of the properties of the states interpolating between number and coherent states denoted by | n ⟩ λ ; among them are the reproduction of these states by the action of an operator-valued function on | n ⟩ (the standard Fock space) and the fact that they can be regarded as f -deformed coherent bound states. In this paper we use them as the basis of our new Fock space which in this case is not orthogonal but normalized. Then by some special superposition of them we obtain new representations for coherent and squeezed states in the new basis. Finally the statistical properties of these states are studied in detail.We establish some of the properties of the states interpolating between number and coherent states denoted by | n ⟩ λ ; among them are the reproduction of these states by the action of an operator-valued function on | n ⟩ (the standard Fock space) and the fact that they can be regarded as f -deformed coherent bound states. In this paper we use them as the basis of our new Fock space which in this case is not orthogonal but normalized. Then by some special superposition of them we obtain new representations for coherent and squeezed states in the new basis. Finally the statistical properties of these states are studied in detail.

arXiv:math-ph/0405045Journal of Physics A Mathematical and GeneralMay 11, 200422 citations

Coherent and Squeezed States: Theoretical Aspects and Some Applications

Thomas Godsk Jørgensen

Jan 1, 19960 citations

Coherent state expansion of squeezed states

Петер Адам, József Janszky

Physics Letters ASep 1, 199021 citations

Representations of Coherent and Squeezed States in an Extended Two-parameters Fock Space

Mohammad Kazem Tavassoly, M.H. Lake

Recently a $f$ -deformed Fock space which is spanned by $|n>_λ$ has been introduced. These bases are indeed the eigen-states of a deformed non-Hermitian Hamiltonian. In this contribution, we will use a 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 an extended two-parameters bases $|n>_{λ_{1},λ_{2}}$ . These bases are now the eigen-states of a non-Hermitian Hamiltonian $H_{λ_{1},λ_{2}}=a^{\dagger}_{λ_{1},λ_{2}}a+1/2$ , where $a^{\dagger}_{λ_{1},λ_{2}}=a^{\dagger}+λ_{1}a + λ_{2}$ and $a$ are respectively, the deformed creation and ordinary bosonic annihilation operators. The bases $|n>_{λ_{1},λ_{2}}$ are non-orthogonal (squeezed states), but normalizable. Then, we deduce the new representations of coherent and squeezed states, in our two-parameters Fock space. Finally, we discuss the quantum statistical properties, as well as the non-classical properties of the obtained states, numerically.Recently a $f$-deformed Fock space which is spanned by $|n>_λ$ has been introduced. These bases are indeed the eigen-states of a deformed non-Hermitian Hamiltonian. In this contribution, we will use a 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 an extended two-parameters bases $|n>_{λ_{1},λ_{2}}$. These bases are now the eigen-states of a non-Hermitian Hamiltonian $H_{λ_{1},λ_{2}}=a^{\dagger}_{λ_{1},λ_{2}}a+1/2$, where $a^{\dagger}_{λ_{1},λ_{2}}=a^{\dagger}+λ_{1}a + λ_{2}$ and $a$ are respectively, the deformed creation and ordinary bosonic annihilation operators. The bases $|n>_{λ_{1},λ_{2}}$ are non-orthogonal (squeezed states), but normalizable. Then, we deduce the new representations of coherent and squeezed states, in our two-parameters Fock space. Finally, we discuss the quantum statistical properties, as well as the non-classical properties of the obtained states, numerically.

arXiv:1204.2680Apr 12, 20120 citations

In this paper we study approximate quasi-probability distribution functions of nonclassical states such as incoherent states, Kerr states, squeezed states and

k

-photon coherent states in interacting Fock space.

Recently a

f

-deformed Fock space which is spanned by

|n>_λ

has been introduced. These bases are indeed the eigen-states of a deformed non-Hermitian Hamiltonian. In this contribution, we will use a 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 an extended two-parameters bases

|n>_{λ_{1},λ_{2}}

. These bases are now the eigen-states of a non-Hermitian Hamiltonian

H_{λ_{1},λ_{2}}=a^{\dagger}_{λ_{1},λ_{2}}a+1/2

, where

a^{\dagger}_{λ_{1},λ_{2}}=a^{\dagger}+λ_{1}a + λ_{2}

and

a

are respectively, the deformed creation and ordinary bosonic annihilation operators. The bases

|n>_{λ_{1},λ_{2}}

are non-orthogonal (squeezed states), but normalizable. Then, we deduce the new representations of coherent and squeezed states, in our two-parameters Fock space. Finally, we discuss the quantum statistical properties, as well as the non-classical properties of the obtained states, numerically.