The Construction of Some Important Classes of Generalized Coherent states: The Nonlinear Coherent States Method

Abstract

Considering some important classes of generalized coherent states known in literature, we demonstrated that all of them can be created via conventional fashion, i.e. the "lowering operator eigen-state" and the "displacement operator" techniques using the {\it "nonlinear coherent states"} approach. As a result we obtained a {\it "unified method"} to construct a large class of coherent states which already have been introduced by different prescriptions.

17pages, The section 7 in last version is revised, Some references are added

References in corpus (12)

• f-Oscillators and Nonlinear Coherent States
• Temporally stable coherent states for infinite well and Pöschl-Teller potentials
• New nonlinear coherent states and some of their nonclassical properties
• Photon-added coherent states as nonlinear coherent states
• Representations of Coherent States in Non-orthogonal Bases
• Experimental limit on the blue shift of the frequency of light implied by a q-nonlinearity
• Coherent-State Approach to Two-dimensional Electron Magnetism
• Generalized Intelligent States for Nonlinear Oscillators
• Representations of Coherent and Squeezed States in a $f$-deformed Fock Space
• Photon-added coherent states for exactly solvable Hamiltonians
• Coherent and generalized intelligent states for infinite square well potential and nonlinear oscillators
• Coherent States for Discrete Spectrum Dynamics

Cited by in corpus (32)

• Coherent states for Hamiltonians generated by supersymmetry
• Deformed photon-added nonlinear coherent states and their nonclassical properties
• Entanglement, quantum statistics and squeezing of two $\Xi$-type three-level atoms interacting nonlinearly with a single-mode field
• Tripartite entanglement dynamics and entropic squeezing of a three-level atom interacting with a bimodal cavity field
• The Construction of the Dual Family of Gazeau-Klauder Coherent States via Temporally Stable Nonlinear Coherent States
• Quantum entanglement and position-momentum entropic squeezing of a moving Lambda-type three-level atom interacting with a single-mode quantized field with intensity-dependent coupling
• Dynamics of entropy and nonclassicality features of the interaction between a $♢$-type four-level atom and a single-mode field in the presence of intensity-dependent coupling and Kerr nonlinearity
• Photon added nonlinear coherent states for a one mode field in a Kerr medium
• Superposition of two nonlinear coherent states $\frac{\pi }{2}$ out of phase and their nonclassical properties
• Generalized $su(1,1)$ coherent states for pseudo harmonic oscillator and their nonclassical properties
• Quantum phase properties associated to solvable quantum systems using the nonlinear coherent states approach
• On the quantum information entropies and squeezing associated with the eigenstates of isotonic oscillator
• On the non-classicality features of new classes of nonlinear coherent states
• A theoretical scheme for generation of Gazeau-Klauder coherent states via intensity-dependent degenerate Raman interaction
• New nonlinear coherent states associated to inverse bosonic and $f$-deformed ladder operators
• Gazeau$-$Klauder squeezed states associated with solvable quantum systems
• Coherent and squeezed states: introductory review of basic notions, properties and generalizations
• Ladder operators and coherent states for the trigonometric Pöschl-Teller potential
• Nonlinear Quantum Optical Springs and Their Nonclassical Properties
• Superpositions of the dual family of nonlinear coherent states and their non-classical properties
• Generalized $su(2)$ coherent states for the Landau levels and their nonclassical properties
• On a general formalism of nonlinear charge coherent states, their quantum statistics and nonclassical properties
• Quantum statistical properties of some new classes of intelligent states associated with special quantum systems
• Phase space picture of Morse-like coherent states based upon the Wigner function
• Nonclassical properties of coherent states and excited coherent states for continuous spectra
• Algebraic and group treatments to nonlinear displaced number states and their nonclassicality features
• Nonlinear optical effects on the atom-field interaction based on the nonlinear coherent states approach
• A report on the nonlinear squeezed states and their non-classical properties of a generalized isotonic oscillator
• Deformed Boson Algebras and ${\mathcal{W}}_{\alpha ,\beta ,\nu }$-Coherent States: A New Quantum Framework
• Complexifier Versus Factorization and Deformation Methods For Generation of Coherent States of a 1D NLHO: I. Mathematical Construction
• Nonlinear Coherent States of the Fokas-Lagerstrom Potential
• A set of nonlinear coherent states for the pseudoharmonic oscillator