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

Generalized squeezed states

Kevin Zelaya, Sanjib Dey, Véronique Hussin

arXiv:1810.02947Physics Letters AOct 5, 201830 citations

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

Mohammad Kazem Tavassoly, M.H. Lake

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 〉 λ 1 , λ 2 . These bases are now the eigenstates of a non-Hermitian Hamiltonian H λ 1 ,λ 2 = a † λ 1 ,λ 2 a +½, where a † λ 1 , 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-parameter Fock space. Finally, we discuss the quantum statistical properties, as well as the non-classical properties of the obtained states numerically.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 〉 λ 1 , λ 2 . These bases are now the eigenstates of a non-Hermitian Hamiltonian H λ 1 ,λ 2 = a † λ 1 ,λ 2 a +½, where a † λ 1 , 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-parameter Fock space. Finally, we discuss the quantum statistical properties, as well as the non-classical properties of the obtained states numerically.

Chinese Physics CAug 1, 20121 citation

Modeling Generalized Squeezed States

Skylar Turner, Brian R. La Cour

Bulletin of the American Physical SocietyMar 19, 20210 citations

General two-mode squeezed states

R. F. Bishop, Apostol Vourdas

The European Physical Journal BDec 1, 198839 citations

Tuneable Hybrid and Multimode Squeezed States of Light

Christian Drago

Gaussian quantum states of light have many applications in quantum technologies. Two of the most widely used Gaussian quantum states of light are the single- and two-mode squeezed states. In this thesis, we propose the generation of a hybrid of these two states, which has both properties of single- and two-mode squeezed states. We then extend our method to the generation of multimode squeezed states which posses N-partite entanglement. Our states are defined using Gaussian frequency modes, and our method relies on a nonlinear-optical process called spontaneous parametric downconversion. We shape the joint spectral amplitude of the generated light in two ways, by spectrally engineering the light incident on the crystal and by the engineering of the nonlinear crystal to have desired properties. We first use our method to generate tuneable hybrid squeezed states and then extend it to multimode squeezed states. We then investigate design considerations for the nonlinear crystal and study the effect of fabrication errors. The tuneable hybrid and multimode squeezed states are localized in both frequency and time, making them ideal for a variety of quantum information protocols. We expect that the states will be used to generalize many quantum information protocols to their multimode counterparts, such as, multi-parameter quantum metrology, multi-channel quantum imaging and multi-partite teleportation. Our work will therefore broaden the applicability of optics for the development of quantum technologies.Gaussian quantum states of light have many applications in quantum technologies. Two of the most widely used Gaussian quantum states of light are the single- and two-mode squeezed states. In this thesis, we propose the generation of a hybrid of these two states, which has both properties of single- and two-mode squeezed states. We then extend our method to the generation of multimode squeezed states which posses N-partite entanglement. Our states are defined using Gaussian frequency modes, and our method relies on a nonlinear-optical process called spontaneous parametric downconversion. We shape the joint spectral amplitude of the generated light in two ways, by spectrally engineering the light incident on the crystal and by the engineering of the nonlinear crystal to have desired properties. We first use our method to generate tuneable hybrid squeezed states and then extend it to multimode squeezed states. We then investigate design considerations for the nonlinear crystal and study the effect of fabrication errors. The tuneable hybrid and multimode squeezed states are localized in both frequency and time, making them ideal for a variety of quantum information protocols. We expect that the states will be used to generalize many quantum information protocols to their multimode counterparts, such as, multi-parameter quantum metrology, multi-channel quantum imaging and multi-partite teleportation. Our work will therefore broaden the applicability of optics for the development of quantum technologies.

Sep 3, 20200 citations

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.