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We study the interaction of two entangled two-energy-level atoms interacts with a single-mode and two-photon cavity field. The atom state is detected after exiting the cavity, and it is found that the nonclassical properties of the field states depend strongly on the entanglement degree between the two atoms. Meanwhile it is shown that squeezing of field and photon antibunching can be greatly enhanced via selective atomic measurements.

This work investigates the time-dependent squeezed and extruded flow of viscous incompressible and electrically conducting fluid between two convective parallel plates under an impressed transversely applied magnetic field. The governing nonlinear partial differential equations are reduced to dimensionless form using some selected dimensionless parameters and solved numerically in Matlab. A detail analysis illustrating the influence of various governing parameters like extrusion, squeezing, Eckert, Hartmann number, dimensionless time and Biot number on fluid velocity, normal fluid velocity, temperature, rate of heat transfer and local coefficient of skin friction are highlighted and discussed. The results reveal that rate of heat transfer and coefficient of local skin friction can be optimized by increasing/decreasing the squeezing parameter. Also, the result also reveal that increasing the extrusion parameter and the Hartmann number reduces the rate of heat transfer and enhances the coefficient of local skin efriction.

In this paper, we study the one-parameter $\kappa$-generalized oscillator algebra ${{𝒜}}_{\kappa }$ (which includes the case of the standard Weyl–Heisenberg algebra). This algebra admits representations of finite-dimensional for negative values of the parameter $\kappa$. We construct the associated Perelomov like coherent states. We discuss their statistical properties. In particular, we derive the expressions of the Mandel parameter and Husimi function and we discuss the squeezing of the ${{𝒜}}_{\kappa }$ coherent states.

The properties of the displaced Fock states (DFS's) superpositions are reviewed. The interaction of these states with a two-level atom in cavity with the presence of additional Kerr medium is studied. Exact general matrix elements of the time-dependent operators of a Jaynes-Cummings model (JCM), in the presence of a Kerr medium, with these states are derived. The atomic inversion and photon number distribution are discussed. The quantum entropy and the entanglement of the atom-field are investigated. The exact results are employed to perform a careful investigation of the temporal evolution of the entropy. The connection between the field entropy and the collapses and revivals of the atomic inversion has been established. The general conclusions reached are illustrated by numerical results.

We study amplitude-squared squeezing in interaction of coherent light with a nonlinear Kerr medium modelled as an anharmonic oscillator with interaction Hamiltonian H = ½ λ a⁺²a², where λ is proportional to χ⁽³⁾ of the nonlinear medium and a is annihilation operator for the interacting field. We find the squeezing parameter S ( τ, r) in terms of a dimensionless interaction time τ = λ t and Kerr parameter r, which is product of, τ and the average number of photons and obtain almost complete amplitude-squared squeezing (i.e., S ≈ 0) for very small interaction time and very large intensity of the interacting light. We optimize squeezing parameter S ( τ, r) by an analytic estimation assuming high intensity of the interacting light and realistic values of Kerr nonlinearity following J.Bajer et al. [Czech. J. Phy. 52, 1313 (2002)] and obtain a scaling law for optimal amplitude-squared squeezing with minimum value S_min, at r = r_min for a given τ. The validity of the scaling law is checked numerically and analytically in the region of realistic values of Kerr nonlinearity and intensity of the interacting light.

By using the magnetic entangled state 〈λ| representation and the squeezing transform we derive Feynman propagator for a charged particle in a quantum dot in the presence of a uniform magnetic field. It is the neat expression of the squeezing operator in 〈λ| representation that provides the concise way and the brevity. The partition function of this sytem is thus obtained.

Squeezing and amplitude-squared squeezing for two two-level nonidentical atoms in lossless cavity has been investigated assuming the field to be initially in the coherent state. The time-dependent squeezing parameters have been calculated. The influence of the relative difference of two coupling constants on the squeezing parameters has been analyzed.

In the present paper, we consider the interaction of a single mode radiation initially in a coherent state with an assembly of two two-level atoms in some different states using the Hamiltonian, H = ω(a⁺a + S_z)+g(a S₊ + a⁺ S_-) in the natural units, where a⁺ and a are the creation and annihilation operators for radiation, S_z, S_± are the collective Dicke operators, g is the coupling constant, ω is the energy of the photons and energy difference between the two atomic levels. We solve it exactly. We study ordinary squeezing and amplitude-squared squeezing of radiation for the general operators, and Y_θ=1/2(a²e^-iθ+a⁺²e^iθ), when atoms are fully excited, super-radiant or in the ground state. We get a large ordinary squeezing (nearly 88% squeezing) for the super-radiant atomic state, at a time, which is 0.451 of the first revival time, and this should be easily observable. We also get a large amplitude-squared squeezing (nearly 20%) at the time, which is about 0.033 of the first revival time. Variation of variances near their minima with coupling time gt, square root of mean photon number |α| and phase are also discussed.

In this paper, we have constructed even and odd superpositions of supercoherent states, similar to the standard even and odd coherent states of the harmonic oscillator. Then, their nonclassical properties, that is, squeezing and entanglement have been studied. We have observed that even supercoherent states show squeezing behavior for some values of parameters involved, while odd supercoherent states do not show squeezing at all. Also sub-Poissonian statistics have been observed for some ranges of the parameters in both states. We have also shown that these states may be considered as logical qubits which reduce to the Bell states at a limit, with concurrence equal to 1.

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 $g^{(2)}(0)$, 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.

The mathematical and physical properties of the states which are generated by excitations on the coherent state of a harmonic oscillator in a finite-dimensional Hilbert space are studied. It is shown that the state exhibits squeezing in one of the quadratures of the field and sub-Poissonian photon statistics.

In this article, the problem of a double Ξ-type four-level atom interacting with a single-mode cavity field is considered. The considered model describes several distinct configurations of a four-level atom. Also, this model includes the detuning parameters of the atom-field system. We obtain the constants of motion and the wavefunction is derived when the atom is initially prepared in the upper state. We used this model for computing a number of the field aspects for the considered system. As an illustration, the model is used for studying the time evolution of the Mandel Q-parameter, amplitude-squared squeezing phenomenon and Q-function when the input field is considered in a coherent state. The results show that these phenomena are affected by the presence of detuning parameters.

The atomic system on which we focus is a single four-level atom interacting with two-mode cavity fields. We obtain the wavefunction when the atom is initially in an excited state. The result presented in this context is employed to discuss the collapses–revivals phenomenon, the photon statistics and frequency sum squeezing phenomenon. The influence of the detuning on these phenomena are investigated for two four-level atomic systems. We found that the presence of the detuning leads to an increase of the collapse time while the amount of squeezing decreases. Also, the photon statistics is affected by the existence of the detuning parameters where the anti-bunching effect appears.

We investigate theoretically the generation of squeezed states in spontaneous and stimulated five-wave mixing process. It has been found that squeezing occurs in field amplitude, amplitude-squared, amplitude-cubed and fourth-order amplitude states of the fundamental mode in the process. It is found to be dependent on coupling parameter g and phase values of the field amplitude of the fundamental mode. The process involves the absorption of two pump photons each having frequency ω₁, emission of two probe photons of same frequency ω₂ and a signal photon of frequency ω₃. It is shown that squeezing is greater in a stimulated interaction than the corresponding squeezing in the spontaneous process. It is found that the degree of squeezing depends on the photon number in the first and higher orders. We study the statistical behaviour of quantum field in the fundamental mode. It has been found that the field shows sub-Poissonian behavior in this mode.

The generation and evolution of entanglement and squeezing for the two-mode fields are discussed in a cascade three-level atomic system. Two photons of a strong external pump field induce atomic coherence between the top and bottom levels. The dynamics of this system in the presence of cavity losses is studied. It is shown that entanglement and squeezing between the two modes increase initially, then decrease and eventually disappear. The periods of them are extended with the increasing of the pump field intensity. The effects of the cavity losses on squeezing and entanglement are also discussed.

In this paper, a model describing the interaction of a five-level (⁸⁵Rb) atom with one-mode cavity field including Kerr nonlinearity is discussed. Analytical solution for this model is presented when the atom is initially prepared in its upper state. The obtained results are then employed to examine the dynamical behavior of atomic inversion, field statistics and field squeezing when the input field is initially considered in a coherent state. It is found that the atom-field properties are influenced by the changing of the coupling constants, the detuning parameters and the Kerr medium.

Squeezing in four wave mixing process was studied recently using perturbation method by Giri and Gupta [D. K. Giri and P. S. Gupta, J. Opt. B: Quantum Semiclass. Opt.6 (2004) 91.] We reexamine this using a coherent intense pump mode and with a much better approximation which results in validity of our results for much larger interaction times. We find that for the range of phase where these authors obtained squeezing, only a small squeezing is obtained for a brief period but larger squeezing at large times is obtained in the other range of phase. We also obtain larger amplitude squared squeezing.

We study the interaction between a single mode electromagnetic field and a three-level $\Lambda$-type atom in the presence of a classical homogenous gravitational field when the atom is prepared initially in the momentum eigenstate. The model includes the detuning parameters and the classical homogenous gravitational field. The wave function is calculated by using the Schrödinger equation for a coherent electromagnetic field and an atom is in its excited state. The influence of the detuning parameter and the classical homogenous gravitational field on the temporal behavior of the mean photon number, the normalized second-order correlation function and the normal squeezing is analyzed. The results show that the presence of these parameters has an important effect on these phenomena. The conclusion is reached and some features are given.

In this paper, some properties through the moving four-level $N$-type atom interacting with a two-mode radiation field are presented. We study this system in the presence of the nonlinearity. The exact solution of this model is given by using the Schrödinger equation when the atom and the field are initially in an excited state and a squeezed state, respectively. We employed the results to perform a careful investigation of the temporal evolution of the cross-correlation function, the momentum increment, the difference mean photon numbers and the normal squeezing. The influence of the Kerr and the cross-Kerr medium parameters on these aspects is examined. It is found that the atom-field properties are affected by the changing of these parameters.

Second generation ground-based gravitational wave detectors, scheduled to be operating by the middle of this decade, will be limited in sensitivity over much of their detection range by optical quantum noise. As they will be operating at power levels close to the tolerance of the optical components, significant further improvement in sensitivity will require the use of quantum optical techniques such as the injection of squeezed states. In this paper we briefly review squeezing and plans for its implementation into advanced gravitational wave detectors.