In this paper, we study the non-Gaussian character in generalized coherent states in the framework of a noncommutative space by adding photons to deformed coherent states, which is called the photon-added nonlinear coherent states (PANCSs). We find that the non-Gaussianity of PANCSs is enhanced with the increase of the photon-added number and it increases monotonically with the amplitude of the coherent states. Interestingly, we obtain that the maximal value of non-Gaussianity measure occurs at a certain critical value of the coherent state amplitude, where this critical value is determined by the kind of the deformation. Using the Mandel’s parameter, we examine the statistical properties for the PANCSs and show that the Mandel’s parameter may take positive and negative values depending on the choice of the amplitude and deformation parameter, exhibiting sub-Poissonian distribution and super-Poissonian distribution.
In this paper, we study the non-Gaussian character in generalized coherent states in the framework of a noncommutative space by adding photons to deformed coherent states, which is called the photon-added nonlinear coherent states (PANCSs). We find that the non-Gaussianity of PANCSs is enhanced with the increase of the photon-added number and it increases monotonically with the amplitude of the coherent states. Interestingly, we obtain that the maximal value of non-Gaussianity measure occurs at a certain critical value of the coherent state amplitude, where this critical value is determined by the kind of the deformation. Using the Mandel’s parameter, we examine the statistical properties for the PANCSs and show that the Mandel’s parameter may take positive and negative values depending on the choice of the amplitude and deformation parameter, exhibiting sub-Poissonian distribution and super-Poissonian distribution.
In this Letter, we introduce four distinct classes of f-deformed photon-added nonlinear cat state. This would be achieved by recalling a nonlinear coherent states approach, as well as a particular class of Gilmore-Perelomov-type of SU(1,1) coherent state and a class of SU(2) coherent state. We then examine the role of photon addition and nonlinearity functions in the phase space structure and sub-Poissonianity of even, odd, and Yurke-Stoler nonlinear cat states. The effect of photon addition, which results in a π phase shift at the origin of the Wigner function toward negativity, interestingly enhances the nonclassicality by means of the Wigner function and Mandel parameter. Furthermore, owing to photon addition, we can observe a deformation in the Gaussian shape of the Wigner function, which may be found to be potentially useful in quantum noise reduction. Moreover, the deformation function shows a remarkable role in revealing the nonclassical behavior and can increase the depth and the domain of nonclassicality.
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 construct the photon-added coherent states of a noncommutative harmonic oscillator associated to a q-deformed oscillator algebra. Various nonclassical properties of the corresponding system are explored, first, by studying two different types of higher-order quadrature squeezing, namely, the Hillery type and the Hong-Mandel type, and second, by testing the sub-Poissonian nature of photon statistics in higher order with the help of the correlation function and the Mandel parameter. Also, we compare the behavior of different types of quadrature and photon number squeezing of our system with those of the ordinary harmonic oscillator by considering the same set of parameters.
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.
We construct deformed photon-added nonlinear coherent states (DPANCSs) by application of the deformed creation operator upon the nonlinear coherent states obtained as eigenstates of the deformed annihilation operator and by application of a deformed displacement operator upon the vacuum state. We evaluate some statistical properties like the Mandel parameter, Husimi, and Wigner functions for these states and analyze their differences; we give closed analytical expressions for them. We found a profound difference in the statistical properties of the DPANCSs obtained from the two abovementioned generalizations.
Abstract In this paper, we aim to introduce a new state called photon-subtracted-then-added squeezing-enhanced coherent state (PSASECS) by multiple photon subtraction and then addition to a squeezing-enhanced coherent state. We investigate the non-Gaussianity and nonclassicality of this new state in detail, including its Wigner function, sub-Poissonian statistics, Q -function, squeezing, and antibunching properties. The obtained results indicate that these non-Gaussian and nonclassical characteristics have been enhanced by appropriately changing between photon subtraction l and photon addition k . Additionally, the non-Gaussianity and nonclassicality of PSASECS are enhanced compared to cases involving only the addition or subtraction of photons. This demonstrates the importance of subtracting and then adding photons to the squeezing-enhanced coherent state, and introducing a significant state for application in quantum optics, particularly in mitigating phase noise fluctuations in quantum devices.