Two-Photon Algebra Eigenstates: A Unified Approach to Squeezing

Abstract

We use the concept of the algebra eigenstates that provides a unified description of the generalized coherent states (belonging to different sets) and of the intelligent states associated with a dynamical symmetry group. The formalism is applied to the two-photon algebra and the corresponding algebra eigenstates are studied by using the Fock-Bargmann analytic representation. This formalism yields a unified analytic approach to various types of single-mode photon states generated by squeezing and displacing transformations.

To appear in Annals of Physics, REVTeX with AMSsymbols, 27 pages, no figures. More information on http://www.technion.ac.il/~brif/science.html

Cited by in corpus (21)

• Multiphoton Quantum Optics and Quantum State Engineering
• Exact Solvability of the two-photon Rabi Hamiltonian
• SU(2) and SU(1,1) algebra eigenstates: A unified analytic approach to coherent and intelligent states
• Robertson Intelligent States
• Energy-Sensitive and "Classical-like" Distances Between Quantum States
• Decoherence and thermalization dynamics of a quantum oscillator
• (1+1) Schrodinger Lie bialgebras and their Poisson-Lie groups
• (Super)integrability from coalgebra symmetry: formalism and applications
• Generalized uncertainty relations and coherent and squeezed states
• Exact Solutions for the General Nonstationary Oscillator with a Singular Perturbation
• A Jordanian quantum two-photon/Schrodinger algebra
• Quantum Dynamics of Non-Degenerate Parametric Amplification
• Generation of single-mode SU(1,1) intelligent states and an analytic approach to their quantum statistical properties
• On the squeezed states for n observables
• Quasienergy operators and generalized squeezed states for systems of trapped ions
• Nonclassical properties and quantum resources of hierarchical photonic superposition states
• Macroscopicity of quantum superpositions on a one-parameter unitary path in Hilbert space
• Barut-Girardello coherent states for u(p,q) and sp(N,R) and their macroscopic superpositions
• N-dimensional integrability from two-photon coalgebra symmetry
• Quantum two-photon algebra from non-standard U_z(sl(2,R)) and a discrete time Schrödinger equation
• On a commutative ring structure in quantum mechanics