On a General Formalism of Nonlinear Charge Coherent States, Their Quantum Statistics and Nonclassical Properties

Abstract

In this paper, we will present a general formalism for constructing the nonlinear charge coherent states which in special case lead to the standard charge coherent states. The su Q (1, 1) algebra as a nonlinear deformed algebra realization of the introduced states is established. In addition, the corresponding even and odd nonlinear charge coherent states have been also introduced. The formalism has the potentiality to be applied to systems either with known "nonlinearity function" f (n) or solvable quantum system with known "discrete non-degenerate spectrum" e n . As some physical appearances, a few known physical systems in the two mentioned categories have been considered. Finally, since the construction of nonclassical states is a central topic of quantum optics, nonclassical features and quantum statistical properties of the introduced states have been investigated by evaluating singleand two-mode squeezing, su(1, 1)-squeezing, Mandel parameter and antibunching effect (via g-correlation function) as well as some of their generalized forms we have introduced in the present paper.

A new class off-deformed charge coherent states and their nonclassical properties

“…In the present paper, our main aims may be expressed as follows: i) reobtaining the explicit form of |q, λ in two-mode Fock-space by using a rather different method other than the η| representation has been followed in [12], ii) generalizing ĝ operator (combination of bosonic annihilation and creation operators in (13)) to Ĝ operator (combination of f -deformed ladder operators) and obtaining the common eigenstates of Q and Ĝ have been called by us as "f -deformed charge coherent states" 2 and finally iii) investigating some of the nonclassical features and quantum statistical properties of the f -deformed charge coherent states associated with a few quantum systems with particular nonlinearity functions, in addition to the state |q, λ which is indeed a special case of our f -deformed charge coherent states with f (n) = 1. Obviously, our new type of f -deformed charge coherent states in the present paper is substantially different from the states in ( 9) have been introduced in [11].…”

“…Obviously, our new type of f -deformed charge coherent states in the present paper is substantially different from the states in (9) have been introduced in [11]. The paper is organized as follows.…”

“…We have selected this name to be distinguished from the previous nonlinear charge coherent states in[11], whereas it is clear that both classes of states are in fact nonlinear or f -deformed.…”

Entanglement dynamics and position-momentum entropic uncertainty relation of a Λ-type three-level atom interacting with a two-mode cavity field in the presence of nonlinearities

“…The left plots concern the absence of the intensity-dependent coupling, that is f i n i 1, and in the right plots the intensity-dependent coupling with f i n i n i p is considered. The physical interest in this nonlinearity function and its associated coherent state arises naturally from the Hamiltonian illustrating the interaction with intensity-dependent coupling between a two-level atom and a radiation field [29][30][31][32]. In Fig.…”

Entanglement analysis of a two-atom nonlinear Jaynes–Cummings model with nondegenerate two-photon transition, Kerr nonlinearity, and two-mode Stark shift

“…It is worthwhile mentioning that, the obtained formalism can be applied for any physical system with arbitrary nonlinearity function. In this paper, we use the nonlinearity function f (n) = √ n (associated with the atom-field coupling) where its associated coherent state is arisen naturally from the Hamiltonian illustrating the interaction with intensity-dependent coupling between a two-level atom and a radiation field [49,50,51]. Experimental verification of this function has been recently reported in [52].…”