Nonlinear Coherent States Research Articles

Generalized complex Hermite polynomials with associated nonlinear coherent states

Generalized complex Hermite polynomials with associated nonlinear coherent states

Amplification of squeezing and anti-bunching in the output beams from a degenerate parametric amplifier: linear and nonlinear coherent state approaches

Amplification of squeezing and anti-bunching in the output beams from a degenerate parametric amplifier: linear and nonlinear coherent state approaches

The Mth nonlinear coherent states

Since radiation field states are very important in the interaction with the various atomic structures, in this article we introduce a new type of quantum states, which we call ‘Mth nonlinear coherent states’. We define these states based on acting of the number operator M times nˆM on a nonlinear coherent state. By analyzing the photon distribution function and its overlap with the nonlinear coherent states, it becomes clear that these states are very similar to the corresponding nonlinear coherent states. We also investigate the nonclassical features of such states for different values of M, and it is determined that the occurrence of sub-Poissonian photon statistics, normal squeezing, and amplitude squared squeezing are considerable nonclassical properties of the Mth nonlinear coherent states. Also, examining the Husimi function shows a local behavior for the introduced states. Furthermore, by calculating the Wigner function, we find out that in some points of the phase space, the value of this function is negative which could be considered as a nonclassical feature for these states.

Properties of new even and odd nonlinear coherent states with different parameters

We construct a class of nonlinear coherent states (NLCSs) by introducing a more general nonlinear function and study their nonclassical properties, specifically the second-order correlation function [Formula: see text], Mandel parameter Q, squeezing, amplitude-squared squeezing and Wigner function of the optical field. The results indicate that the nonclassical properties of the new types of even and odd NLCSs crucially depend on the nonlinear functions. More concretely, we find that the new even NLCSs could exhibit the photon-bunching effect, whereas the new odd NLCSs could show the photon-antibunching effect. The degree of squeezing is also significantly affected by the parameter selection of these NLCSs. By employing various forms of nonlinear functions, it becomes possible to construct the NLCSs with diverse properties, thereby providing a theoretical foundation for the corresponding experimental investigations.

Teleportation of superposed nonlinear coherent states

In this paper, we study the teleportation of nonlinear coherent cat states assuming even and odd nonlinear quasi-Bell states as the channel. Odd nonlinear quasi-Bell states are shown to be maximally entangled independent of the coherent parameter and also nonlinear function but the entanglement of the even nonlinear coherent states depends on the parameters involved. Subsequently, the teleportation probability is evaluated for some nonlinear functions. Our research reveals that when even and odd nonlinear quasi-Bell states are assumed as the quantum channel, the probabilities for successful teleportation are oppositely varied by increasing coherent parameter. For the special case of nonlinear harmonious states, the teleportation probability is a decreasing (increasing) function of the coherent parameter if even (odd) nonlinear quasi-Bell state is used as the channel.

Nonclassicality of entangled Schrödinger cat states associated to generalized displaced Fock states

In this paper, we introduce some distinct classes of entangled cat states associated to generalized displaced Fock states. For this purpose, we use the formalism of nonlinear coherent states corresponding to nonlinear oscillator algebra which yields various kinds of f-deformed entangled states. We also take a particular class of Gilmore-Perelomov-type of SU(1, 1) and a class of SU(2) coherent states. We then obtain the amount of entanglement between subsystems of the quantum states of interest by applying the measure of concurrence. Furthermore, examining some of the most important criteria, such as Mandels Q parameter, quadrature squeezing and Vogels characteristic function, we study the nonclassicality of the introduced quantum states. The numerical results show remarkable values of entanglement, sub-Poissonian statistics of the field, and squeezing indicating that the introduced states can be regarded as possible candidates for nonclassical entangled states. Afterwards, we see that the Vogel function for quantum states of interests goes beyond the value of characteristic function of the ground state, which shows the nonclassicality of the introduced states.

Exploring quantum critical phenomena in a nonlinear Dicke model through algebraic deformation

In this work, we use a deformed version of the Heisenberg–Weyl algebra in the Dicke Model to incorporate a Kerr medium and nonlinear interaction between matter and radiation fields. The deformed algebra allows us to define two distinct nonlinear coherent states for the radiation field. These coherent states, along with the conventional Heisenberg–Weyl coherent states and their symmetry-adapted versions, are employed as trial variational states in the energy-surface minimisation method. The obtained results reveal that the Kerr medium introduces a delay in reaching the super-radiant region, with the delay becoming more pronounced as the nonlinear parameter increases. To evaluate the different approaches, we analyse the behaviour of the critical coupling, ground-state energy, entropy of entanglement between matter and radiation, and fidelity between the numerical solution and the symmetry-adapted solution. We find that one particular deformed coherent state outperforms the other trial states in approximating the ground state of the system, providing an accurate description of the critical behaviour in the proposed nonlinear model.

Bargmann transform and statistical properties for nonlinear coherent states of the isotonic oscillator

Abstract We construct a new class of nonlinear coherent states for the isotonic oscillator by replacing the factorial of the coefficients z n / n ! ${z}^{n}/\sqrt{n!}$ of the canonical coherent states by the factorial x n γ ! = x 1 γ . x 2 γ … x n γ ${x}_{n}^{\gamma }!={x}_{1}^{\gamma }.{x}_{2}^{\gamma }\dots {x}_{n}^{\gamma }$ with x 0 γ = 0 ${x}_{0}^{\gamma }=0$ , where x n γ ${x}_{n}^{\gamma }$ is a sequence of positive numbers and γ is a positive real parameter. This also leads to the construction of a Bargmann-type integral transform which will allow us to find some integral transforms for orthogonal polynomials. The statistics of our coherent states will also be considered by the calculus of one called Mandel parameter. The squeezing phenomenon was also discussed.

Apodizer Design to Efficiently Couple Light into a Fiber Bragg Grating

We provide an optimal control framework for efficiently coupling light in a bare fiber into Bragg gratings with cubic nonlinearity. The light-grating interaction excites gap solitons, a type of localized nonlinear coherent state which propagates with a central frequency in the forbidden band gap, resulting in a dramatically slower group velocity. Due to the nature of the band gap, a substantial amount of light is back-reflected by the grating’s strong reflective properties. We optimize, via a projected gradient descent method, the transmission efficiency of previously designed nonuniform grating structures in order to couple more slow light into the grating. We further explore the space of possible grating designs, using genetic algorithms, along with a previously unexplored design parameter: the grating chirp. Through these methods, we find structures that couple a greater fraction of light into the grating with the added bonus of creating slower pulses.

Phase space nonclassicality and sub-Poissonianity of deformed photon-added nonlinear cat states: algebraic and group theoretical approach.

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.

Quantum coherence and entanglement of the system of a five-level atom in the presence of nonlinear fields

We investigate the atom-field system in the framework of harmonic oscillators based on deformed Heisenberg algebras. We explore the dynamic characteristics of the considered system under the effect of a nonlinear field. In particular, we consider the atomic population, atomic coherence, and atom-field entanglement for a system that comprises a single five-level atom interacting with a single-mode nonlinear field when the deformation effect is taken into account. We examine the time evolution of the quantum quantifiers in the presence of deformation when the initial state of the quantized field is defined to be a nonlinear coherent state (CS) or a superposition state.

Kernel method based on non-linear coherent states in quantum feature space

In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of the fact that the radial basis function is recovered when data is mapped to a complex Hilbert state represented by coherent states, non-linear coherent states can be considered as a natural generalisation of the associated kernels. In this paper, as an example of kernels based on non-linear coherent states, we propose kernel functions based on generalized hypergeometric functions, as orthogonal polynomial functions. The suggested kernel is implemented with the support vector machine (SVM) on two well known datasets (make_circles, and make_moons) and outperforms the baselines, even when the level of noise is high. In addition, we study the impact of the geometrical properties of the feature space, obtained by the non-linear coherent states, on the SVM classification task, by considering the Fubini–Study metric of the associated coherent states.

Nonlinear optical effects on the atom–field interaction based on the nonlinear coherent states approach

In this paper, to study the effects of a nonlinear medium on the atom–field interaction, we use the nonlinear coherent states approach. For this purpose, we choose the two-mode cross-Kerr as our nonlinear optical phenomena, and with the use of its algebra, we show that it can be considered as a deformed oscillator as well as a deformedsu(2)algebra. Then we construct the associated two-mode nonlinear coherent states and investigate their statistical properties. After that, as an example of applicability of the constructed coherent states, we investigate the nonlinear effects of the medium on the dynamics of atom–field interaction within the framework of the coherent states. By using the time-dependent Schrödinger equation, we study the effect of the nonlinear medium on the occupation probabilities of the atomic levels and consider the relation between the revival time of the atomic occupation probabilities and the nonlinear parameter of the medium. Then, to study the nonlinear effects on the dynamical properties of the cavity field, we consider the photon distribution, correlation function, Mandel parameters of the field, von Neumann entropy, and also the squeezing. Particularly, the nonlinearity of the media on the nonclassical properties of the two modes is clarified.

A Poisson-Gaussian Noise Limited Quantum Iterative Multi-User System With Non-Ideal Photon-Counting Receiver

Coherent state quantum communication is attracting extensive attention for its great value in terrestrial and satellite information networks. This paper proposes a new non-orthogonal quantum multi-user (MU) iterative detection scheme. At the receiving end, we develop a composite quantum receiver with multi-stage measurement instrument and soft iterative MU detector. Furthermore, based on a three-dimensional factor graph, a nonlinear Poisson-Gaussian noise limited coherent state iterative MU parallel interference cancellation (PIC) algorithm is derived. Our results demonstrate that this system can well support MU communication and achieve good performance. Quantitatively, for the 8 users scenario, the BER of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-6}$</tex-math></inline-formula> can be obtained when the photon number is 19. Further numerical results show that the system we designed exhibits superior robustness against imperfections (e.g., quantum mode mismatch and quantum thermal noise).

Effect of stark shift on three-level atom interacting with a correlated two-mode of non-linear coherent state

In this manuscript, we study a new non-linear system which represents a ?-type five level atom interacting with a quantized four-mode electromagnetic field. A non-linear Stark shift is introduced, through the elimination of intermediate levels (two and four) using the adiabatic elimination technique. By using the Schrodinger equation we obtain the analytic solution this model. Some statistical aspects through the effective Hamiltonian are presented such as the collapses-revivals phenomenon, degree of purity, concurrence, and the squeezing phenomenon with respect to study the effect of Stark shift parameters on these statistical aspects. For small values of the Stark shift parameter, the collapse times increase and the atomic inversion symmetry axis shifts upward, while the entanglement decreases significantly. It has been noted that the system is affected by the Stark shift parameter.

Certain results on generating functions related to the associated Meixner-Pollaczek polynomials

In the present paper we first derive a new form of a generating function for the c-associated Meixner-Pollaczek polynomials. This generating function is of particular importance since its several reducible cases yield special cases of interest which also include an elegant extension of the main generating function of Ahbli and Mouayn [Integral Transform Spec Funct. 2018;28:352–366] that stems from an application of nonlinear coherent states with anti-holomorphic coefficients in applied physics. We further establish a new generating function for the associated Meixner polynomials and obtain a bilinear series relation which transforms a series involving the product of the c-associated Meixner-Pollaczek polynomials and Meixner-Pollaczek polynomials in terms of a series involving Lagrange polynomials. Several corollaries and special cases of the main results are also mentioned.

Non-linear ladder operators and coherent states for the 2:1 oscillator

The 2:1 two-dimensional anisotropic quantum harmonic oscillator is considered and new sets of states are defined by means of normal-ordering non-linear operators through the use of non-commutative binomial theorems as well as solving recurrence relations. The states generated are good candidates for the natural generalisation of the coherent states of the two-dimensional isotropic oscillator. The two-dimensional non-linear generalised ladder operators lead to several chains of states which are connected in a non trivial way. The uncertainty relations of the defining chain of states are calculated and it is found that they admit a resolution of the identity and the spatial distribution of the wavefunction produces Lissajous figures in correspondence with the classical 2:1 oscillator.

Entanglement Generation and Nonclassical Properties of Nonlinear Coherent States Created By Repeating the Photon Addition and Subtraction

We introduce a new kind of quantum states generated by repeated actions of the creation and annihilation operators on the standard nonlinear coherent states. We discuss the Klauder minimum set of conditions, which is necessary to obtain the coherent states. As an application, we consider the new quantum states to generate high amounts of entanglement, employing a beam splitter device. To detect the entanglement, we provide the conditions for obtaining the maximum-entangled and separable states, using the linear entropy as a quantifier of correlations. Therefore, we propose the possibility to obtain highly-entangled states and control the entanglement. Finally, we examine the quantum statistics of the new coherent states through the Mandel parameter and demonstrate how this quantity influences variations in the entanglement in terms of main physical parameters. The results obtained may open new prospectives in different problems of quantum information processing.

Dynamics of nonclassical properties of a SU(3) system interacting with two open parametric amplifier modes

We introduce an analytical description of an open bimodal cavity containing a Λ -type three-level atom. We explore the effect of the atom–cavity nonlinear interaction, the cavity dissipation, and the initial coherent intensity on the dynamics of the nonclassical correlations for a cavity prepared initially in a superposition of nonlinear coherent states. The nonlinear interaction generates a regular entanglement between the subsystems, and populates the energy atomic states. We show that the collapse phenomenon is a good indicator of the generated quantum coherence. The growth of the entropy is used to explore the generated entanglement (if the dissipation is absent) and mixedness (in the presence of the dissipation). It is found that the generation and the robustness of the quantum synchronization and the correlations between the subsystems are very sensitive to the dissipation, the superposition, and the coherent intensity of the initial Barut–Girardello coherent states.

A new generalization of nonlinear coherent states for the pseudoharmonic oscillator

We construct two-parameters family of nonlinear coherent states by replacing the factorial in coefficients $$z^n/\sqrt{n!}$$ of the canonical coherent states by a specific generalized factorial $$x_n^{\gamma ,\sigma }!$$ where parameters $$\gamma $$ and $$\sigma $$ satisfy some conditions for which the normalization condition and the resolution of identity are verified. The obtained family is a generalization of the Barut–Girardello coherent states and those of the philophase states. In the particular case of parameters $$\gamma $$ and $$\sigma $$ , we attache these states to the pseudoharmonic oscillator depending on two parameters $$\alpha ,\beta > 0$$ . The obtained nonlinear coherent states are superposition of eigenstates of this oscillator. The associated Bargmann-type transform is defined and we derive some results.