In this paper, two distinct classes of generalized deformed Kerr states are introduced by considering the standard and deformed Kerr mediums, when the initial field state that enters the Kerr medium has been prepared in the well-known nonlinear coherent state. Indeed, the conversion of the third-order susceptibility of the (standard) Kerr medium to its deformed counterpart via an intensity-dependent function K ( n ) is performed. Interestingly, the obtained generalized states are still of f -deformed type, with a special form of the nonlinearity function. Some physical realizations of the proposed approach are presented. Finally, the nonclassicality features, the quantum phase properties and the autocorrelation function of the introduced states are studied numerically.
In this paper, two distinct classes of generalized deformed Kerr states are introduced by considering the standard and deformed Kerr mediums, when the initial field state that enters the Kerr medium has been prepared in the well-known nonlinear coherent state. Indeed, the conversion of the third-order susceptibility of the (standard) Kerr medium to its deformed counterpart via an intensity-dependent function K ( n ) is performed. Interestingly, the obtained generalized states are still of f -deformed type, with a special form of the nonlinearity function. Some physical realizations of the proposed approach are presented. Finally, the nonclassicality features, the quantum phase properties and the autocorrelation function of the introduced states are studied numerically.
In this paper, based on the nonlinear coherent states formalism and using the Hamiltonian for a single mode field in a Kerr medium, the deformed photon-added nonlinear coherent states with negative m corresponding to the nonharmonic oscillators are constructed. In addition, some of the nonclassical properties associated with these states such as the Mandel parameter, quadrature squeezing and second-order correlation function are investigated. It is found that the deformed photon-added nonlinear coherent states with negative m for the one-mode field in a Kerr medium are nonclassical states.
We construct a distinct class of nonlinear displaced Kerr states by application of the displacement operator upon a state which is prepared by sending the well-known photon-added coherent state through a normal Kerr medium. A sketch for the experimental setup for preparing the state is suggested. We evaluate some statistical properties such as the photon number distribution, Mandel’s Q parameter, Husimi-Q and Wigner functions, and quadrature squeezing for the nonlinear displaced Kerr state and then analyze the nonclassicality in terms of these standard parameters. We reduce the infinite-level problem to a truncated discrete two-level system by using a low Kerr parameter approximation and then convert the generated nonclassicality into bipartite entanglement between the two modes of an output state of a linear optical device.
Abstract In this paper, by making use of the nonlinear coherent states approach, the generalized photon added and subtracted f ‐deformed displaced Fock states are introduced. In other words, a natural link between photon added and subtracted displaced Fock states and nonlinear coherent states associated with nonlinear oscillator algebra is obtained. It is found that various kinds of nonclassical states can be generated by adopting appropriately controlling parameters in both linear and nonlinear regimes. Moreover, examining some of the most nonclassical properties such as Mandel's Q parameter, different types of squeezing, namely, quadrature, amplitude–squared and phase entropic squeezing, and Vogel's characteristic function, the nonclassicality features of the considered quantum states of interest are studied. Furthermore, to obtain the degree of quantum coherence, the relative entropy of coherence is investigated. Indeed, the nonclassicality aspects of the states obtained have been numerically studied to understand the roles of deformation functions, photons added and subtracted, and photon number occupied in the Fock state on physical properties. It is demonstrated that the depth and the domain of the nonclassicality features of the system can properly be controlled by selecting the suitable parameters.
In this paper, we will try to present a general formalism for the construction of deformed photon-added nonlinear coherent states (DPANCSs) |α, f , m ⟩, which in a special case lead to the well-known photon-added coherent state (PACS) |α, m ⟩. Some algebraic structures of the introduced DPANCSs are studied and particularly the resolution of the identity, as the most important property of generalized coherent states, is investigated. Meanwhile, it will be demonstrated that the introduced states can also be classified in the f -deformed coherent states, with a special nonlinearity function. Next, we will show that these states can be produced through a simple theoretical scheme. A discussion on the DPANCSs with negative values of m , i.e. |α, f , − m ⟩, is then presented. Our approach has the potentiality to be used for the construction of a variety of new classes of DPANCSs, corresponding to any nonlinear oscillator with known nonlinearity function, as well as arbitrary solvable quantum system with known discrete, non-degenerate spectrum. Finally, after applying the formalism to a particular physical system known as the Pöschl–Teller (P-T) potential and the nonlinear coherent states corresponding to a specific nonlinearity function , some of the non-classical properties, such as the Mandel parameter, second-order correlation function, in addition to first- and second-order squeezing of the corresponding states, will be investigated numerically.
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 also been 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 nondegenerate spectrum" en. 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 single- and 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.
Two-mode charge (pair) coherent states have been introduced previously by using the 〈η| representation. In this paper, we reobtain these states by a rather different method. Then, using the nonlinear coherent state approach and based on a simple manner by which the representation of two-mode charge coherent states is introduced, we generalize the bosonic creation and annihilation operators to the f -deformed ladder operators and construct a new class of f -deformed charge coherent states. Unlike the (linear) pair coherent states, our presented structure has the potential to generate a large class of pair coherent states with various nonclassicality signs and physical properties which are of interest. For this purpose, we use a few well-known nonlinearity functions associated with particular quantum systems as some physical appearances of our presented formalism. After introducing the explicit form of the above correlated states in the two-mode Fock space, several nonclassicality features of the corresponding states (as well as the two-mode linear charge coherent states) are numerically investigated by calculating quadrature squeezing, the Mandel parameter, the second-order correlation function, the second-order correlation function between the two modes and the Cauchy–Schwartz inequality. Also, the oscillatory behaviour of the photon count and the quasi-probability (Husimi) function of the associated states will be discussed. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.