Algebraic and group treatments to nonlinear displaced number states and their nonclassicality features

Abstract

Recently, nonlinear displaced number states (NDNSs) have been \emph{manually} introduced, in which the deformation function $f(n)$ has been artificially added to the well-known displaced number states (DNSs). In this paper, after expressing enough physical motivation of our procedure, four distinct classes of NDNSs are presented by applying algebraic and group treatments. To achieve this purpose, by considering the DNSs and recalling the nonlinear coherent states formalism, the NDNSs are logically defined through an algebraic consideration. In addition, by using a particular class of Gilmore-Perelomov-type of $SU(1,1)$ and a class of $SU(2)$ coherent states, the NDNSs are introduced via group theoretical approach. Then, in order to examine the nonclassical behaviour of these states, sub-Poissonian statistics by evaluating Mandel parameter and Wigner quasi-probability distribution function associated with the obtained NDNSs are discussed, in detail.

10 pages

References in corpus (15)

• Reconstruction of non-classical cavity field states with snapshots of their decoherence
• The Construction of Some Important Classes of Generalized Coherent states: The Nonlinear Coherent States Method
• Tripartite entanglement dynamics and entropic squeezing of a three-level atom interacting with a bimodal cavity field
• Entanglement, quantum statistics and squeezing of two $\Xi$-type three-level atoms interacting nonlinearly with a single-mode field
• Dynamics of entanglement of a three-level atom in motion interacting with two coupled modes including parametric down conversion
• Entropy squeezing and atomic inversion in the $k$-photon Jaynes-Cummings model in the presence of Stark shift and Kerr medium: full nonlinear approach
• 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
• Number-phase entropic squeezing and nonclassical properties of a three-level atom interacting with a two-mode field: Intensity-dependent coupling, deformed Kerr medium and detuning effects
• 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
• Number-phase entropic uncertainty relations and Wigner functions for solvable quantum systems with discrete spectra
• On the non-classicality features of new classes of nonlinear coherent states
• New nonlinear coherent states associated to inverse bosonic and $f$-deformed ladder operators
• Gazeau$-$Klauder squeezed states associated with solvable quantum systems
• Nonlinear Quantum Optical Springs and Their Nonclassical Properties
• Quantum statistical properties of some new classes of intelligent states associated with special quantum systems