From the photon-added one-photon nonlinear coherent states a†m|α, 〉, we introduce a new type of nonlinear coherent states with negative values of m. The nonlinear coherent states corresponding to the positive and negative values of m are shown to be the result of nonunitarily deforming the number states |m〉 and |0〉, respectively. As an example, we study the sub-Poissonian statistics and squeezing effects of the photon-added geometric states with negative values of m in detail. Finally, we investigate the photon-added two-photon nonlinear coherent states and find that they are still the two-photon nonlinear coherent states with certain nonlinear functions. PACS Nos.: 42.50Dv, 03.65Fd
From the photon-added one-photon nonlinear coherent states a†m|α, 〉, we introduce a new type of nonlinear coherent states with negative values of m. The nonlinear coherent states corresponding to the positive and negative values of m are shown to be the result of nonunitarily deforming the number states |m〉 and |0〉, respectively. As an example, we study the sub-Poissonian statistics and squeezing effects of the photon-added geometric states with negative values of m in detail. Finally, we investigate the photon-added two-photon nonlinear coherent states and find that they are still the two-photon nonlinear coherent states with certain nonlinear functions. PACS Nos.: 42.50Dv, 03.65Fd
The photon-added nonlinear coherent states, defined as adaggerm∣alpha,f> up to a normalization constant, are still nonlinear coherent states with the nonlinear function f(N−m)[1−m/(N+1)]. Here is the nonlinear coherent state with the nonlinear function f(N), N is the number operator, adagger is the boson creation operator and m is a non-negative integer. We introduce a new type of nonlinear coherent states with the nonlinear function f(N+m)[1+m/(N+1)] obtained from the photon-added nonlinear coherent states with negative values of m. The nonlinear coherent states corresponding to the positive and negative values of m are shown to be the result of nonunitarily deforming the number states ∣m> and ∣0>, respectively. As an example, we study the sub-Poissonian statistics and squeezing effects of the photon-added geometric states with negative values of m in detail.
The states | , m , defined as up to a normalization constant and where m is a non-negative integer, are shown to be the eigenstates of where is a nonlinear function of the number operator . The explicit form of is constructed. The eigenstates of this operator for negative values of m are introduced. The properties of these states are discussed and compared with those of the state | , m . The eigenstates corresponding to the positive and negative values of m are shown to be the result of nonunitarily deforming the number states | m and |0 respectively.
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.
We show that the photon-added squeezed vacuum a m S ( z )|0 and the photon-added squeezed one-photon state a m S ( z )|1 , where m is a non-negative integer, may be regarded as even and odd nonlinear coherent states, respectively. To achieve this, we derive an operator-valued function f ( N , m ) of the number operator N = a a such that a m S ( z )| i ( i = 0,1) are eigenstates of f ( N , m ) a 2 . Based on this, and using the unified method developed by Shanta et al , we find that a m S ( z )| i can be equivalently expressed in exponential forms. The eigenstates of f ( N ,- m ) a 2 are also constructed and their nonclassical features are studied in detail.
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.
In this paper, after a brief review on the entangled squeezed states, we produce a new class of the continuous-variable-type entangled states, namely, deformed photon-added entangled squeezed states. These states are obtained via the iterated action of the f -deformed creation operator A = f ( n ) a † on the entangled squeezed states. In the continuation, by studying the criteria such as the degree of entanglement, quantum polarization as well as sub-Poissonian photon statistics, the two-mode correlation function, one-mode and two-mode squeezing, we investigate the nonclassical behaviors of the introduced states in detail by choosing a particular f -deformation function. It is revealed that the above-mentioned physical properties can be affected and so may be tuned by justifying the excitation number, after choosing a nonlinearity function. Finally, to generate the introduced states, we propose a theoretical scheme using the nonlinear Jaynes–Cummings model.