In this paper, we study a spin-1 system’s coherent states in the context of the f-deformed suf(2) algebra. This algebraic framework is used to generate intelligent coherent spin states, and the accompanying uncertainty relations are studied to analyze their quantum features. Nonlinear effects related to absorption saturation and dispersion phenomena are shown by calculating the coherent states of the entire spin system up to third order approximation. The resulting asymptotic formulas show that the excitation frequency and spin state transition processes have a significant influence on the nonlinear behavior. Additionally, we demonstrate that the suggested states have squeezing characteristics typical of intelligent states and meet minimum uncertainty relations. Additionally included are the impact of relaxation effects, material-dependent factors, and higher-order corrections on the nonlinear dynamics. These findings could lead to new advances in quantum information processing, nonlinear quantum systems, and quantum optics.
In this paper, we study a spin-1 system’s coherent states in the context of the f-deformed suf(2) algebra. This algebraic framework is used to generate intelligent coherent spin states, and the accompanying uncertainty relations are studied to analyze their quantum features. Nonlinear effects related to absorption saturation and dispersion phenomena are shown by calculating the coherent states of the entire spin system up to third order approximation. The resulting asymptotic formulas show that the excitation frequency and spin state transition processes have a significant influence on the nonlinear behavior. Additionally, we demonstrate that the suggested states have squeezing characteristics typical of intelligent states and meet minimum uncertainty relations. Additionally included are the impact of relaxation effects, material-dependent factors, and higher-order corrections on the nonlinear dynamics. These findings could lead to new advances in quantum information processing, nonlinear quantum systems, and quantum optics.
We consider the formation of entangled quantum states for an atomic Bose condensate interacting with an external electromagnetic field in a single-particle state under conditions of change in various regimes for exchange interaction processes. These states of the Bose system have high phase coherence and are accompanied by the generation of squeezed states of a new type in terms of the parameters defined by a combination of transition operators for the condensate atoms and external-field photons with an appropriate polynomial deformation of the algebra SU (2). We show that localized quantum structures corresponding to stable elementary excitations of the atoms and the field in the condensate can be formed in principle. We also analyze the purely quantum effects of collapse and revival for the level populations of the Bose condensate and the change in atomic statistics as well as determine the conditions for the formation of superstructure of these unsteady states for the Bose system.
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 deformed su(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.
Coherent and squeezed photon states have attracted a lot attetion in long time ago, since these states can generate in laboratory. These states are satisfying in minimum uncertainty relation. In recently, states have generates with electrons by Bose-Einstein condensations and particles oscillations. Also,this states are satisfying in minimum uncertainty relation, with this difference that parameters in this states are the first and second moments of soin operators instead of position and momentum operators.The similarity phenomenon about squeezing photon is exist for spin with that distance. The source of spin squeezing in multi-qubit states is entanglement. One applecations of spin squeezing is to detect quantum entanglement which plays a key role in both the foundations of quantum physics and quantum computation processing. In recent years, spin squeezing stsate parameters have close relation with entanglement measure, concurrence, that we can characterize entanglement for a class of many-body spin- states. In reality, spin squeezing parameters are witnesse for many bode entanglement. In this paper; we study relation betweenspin squeezed states and entanglement. Then; we stuy the squeezing spin for -mode and -mode entangled coherent states.
Quantum harmonic oscillators model a wide variety of phenomena ranging from electromagnetic fields to vibrations of atoms in molecules. Their excitations can be represented by bosons such as photons, single particles of light, or phonons, the quanta of vibrational energy. Linear interactions that only create and annihilate single bosons can generate coherent states of light or motion. Introducing nth-order nonlinear interactions, that instead involve n bosons, leads to increasingly complex quantum behaviour. For example, second-order interactions enable squeezing, used to enhance the precision of measurements beyond classical limits, while higher-order interactions create non-Gaussian states essential for continuous-variable quantum computation. However, generating nonlinear interactions is challenging, typically requiring higher-order derivatives of the driving field or specialized hardware. Hybrid systems, where linear interactions couple an oscillator to an additional spin, offer a solution and are readily available across many platforms. Here, using the spin of a single trapped ion coupled to its motion, we employ two linear interactions to demonstrate up to fourth-order bosonic interactions; we focus on generalised squeezing interactions and demonstrate squeezing, trisqueezing, and quadsqueezing. We characterise these interactions, including their spin dependence, and reconstruct the Wigner function of the resulting states. We also discuss the scaling of the interaction strength, where we drive the quadsqueezing interaction more than 100 times faster than using conventional techniques. Our method presents no fundamental limit in the interaction order n and applies to any platform supporting spin-dependent linear interactions. Strong higher-order nonlinear interactions unlock the study of fundamental quantum optics, quantum simulation, and computation in a hitherto unexplored regime.
The spin evolution equation of an isotropic, quantum ferromagnetic Heisenberg chain is analyzed in the continuum approximation using spin-coherent states. The advantages of this approach are discussed. Magnetic solitary-wave solutions are found, and the expectation values of the energy, momentum, and angular momentum corresponding to these solutions are determined. The energy-momentum dispersion relation for the nonlinear excitations is derived. The semiclassical spectrum is shown to arise when quantum effects are neglected by using a random-phase approximation to calculate certain expectation values. On including the quantum effects, it is found that the spectrum comprises two branches: a lower-energy branch of spin-wave-like, small-amplitude solitary waves with small quantum corrections, and a higher branch of particlelike large-amplitude solitary waves subject to significant quantum corrections for small S values. A heuristic discussion of the stability of these excitations is presented. A physical interpretation of the dispersion relation obtained is given.
In this paper, after a brief review of the single-mode excited entangled coherent states, two new classes of continuous-variable entangled pure states, namely, single-mode nonlinear excited entangled coherent states, have been produced by using the f -deformed creation operator instead of . In order to establish the nonclassicality of the states, some of the physical properties of the corresponding entangled states, such as entanglement degree, photon statistics, second-order correlation function and quadrature squeezing have been studied in detail by choosing a particular f -deformation function. In addition, the influence of photon excitations on the properties of our introduced states has been analyzed and the results compared with those of a single-mode excited entangled coherent state. In continuation, a theoretical scheme for their generation based on the interaction of a two-level atom with a quantized cavity field has been proposed.