The analytical solution of the problem of two two-level atoms with degenerate two-photon transitions interacting with a single-mode radiation field in the presence of a parametric amplifier term is presented. The purity of the atomic state has been used to measure the degree of entanglement between the atom and the field. The temporal evolution of variance and entropy squeezing as well as atomic inversion for the single-atom case are studied. It has been shown that maximum squeezing for the variance and entropy squeezing occurs when the ratio between the amplifier coupling λ3 and the field frequency ω equals 0.26. Increasing the value of the ratio λ3/ω further leads to the vanishing of squeezing from the system. It is also noted that the existence of the coupling parameter results in the system never reaching the pure state except at the points of revival times. The Q function has been also considered to give more information in the phase space about the system. These aspects are sensitive to changes in the amplifier parameter.
The analytical solution of the problem of two two-level atoms with degenerate two-photon transitions interacting with a single-mode radiation field in the presence of a parametric amplifier term is presented. The purity of the atomic state has been used to measure the degree of entanglement between the atom and the field. The temporal evolution of variance and entropy squeezing as well as atomic inversion for the single-atom case are studied. It has been shown that maximum squeezing for the variance and entropy squeezing occurs when the ratio between the amplifier coupling λ3 and the field frequency ω equals 0.26. Increasing the value of the ratio λ3/ω further leads to the vanishing of squeezing from the system. It is also noted that the existence of the coupling parameter results in the system never reaching the pure state except at the points of revival times. The Q function has been also considered to give more information in the phase space about the system. These aspects are sensitive to changes in the amplifier parameter.
The problem of two two-level atoms in interaction with a nondegenerate parametric amplifier is considered. The analytical solution of the wavefunction is obtained and used to derive the density matrix operator. The temporal evolution of the atomic inversion, the degree of entanglement, as well as the variance and entropy squeezing are discussed. In our analysis, we assumed that the atomic systems are in the excited states and the fields in the squeezed-pair coherent state. It has been shown that the coupling parameter, λ3 (the coupling between the two fields), gets more effective for the case in which the q-parameter is not equal to zero. Also for a strong coupling parameter λ3 the superstructure phenomenon can be observed. In the meantime, as we increase the value of the coupling parameter, the entanglement between the atoms and the fields gets stronger. Also it has been shown that in the presence of the parametric amplifier term, the system never reaches the pure state except during revival periods.
In this paper, the interaction between a Λ-type three-level atom and a two-mode cavity field is discussed. The detuning parameters and cross-Kerr nonlinearity are taken into account, and it is assumed that the atom–field coupling and Kerr medium are f-deformed. Even though the system seems complicated, the analytical form of the state vector of the entire system for the considered model is exactly obtained. The time evolution of nonclassical properties, such as quantum entanglement and position–momentum entropic uncertainty relation (entropy squeezing) of the field are investigated. In each case, the influences of the detuning parameters, generalized Kerr medium, and intensity-dependent coupling on the latter nonclassicality signs are analyzed in detail.
In this paper, we study the interaction between a two-level atom and three types of interaction of three quantized modes of a quantized field, namely: two parametric amplifiers and a frequency converter. The SU(1, 1) algebra is used to represent the combination of the interacting modes. A canonical transformation is used to cast the Hamiltonian into a tangible form. The solution of the Schrodinger equation for the wave function is given analytically. Using this solution we discuss numerically the atomic inversion, the degree of entanglement through the linear entropy and the variance entropy for chosen values of the detuning and coupling parameters. It is shown that the atomic inversion can be controlled through the rotation angle α and the atomic angle θ as well as the Bargmann index k. The degree of entanglement is affected by both α and θ in addition to the ratio ϵ. Variance squeezing is sensitive to changes in the atomic and the phase angles besides the parameter k. For entropy squeezing, the effective parameters are α, θ and k.
In this paper, we study the interaction between a Λ-type three-level atom and two quantized electromagnetic fields which are simultaneously injected in a bichromatic cavity surrounded by a Kerr medium in the presence of the field-field interaction (parametric down conversion) and detuning parameters. By applying a canonical transformation, the introduced model is reduced to a well-known form of the generalized Jaynes-Cummings model. Under particular initial conditions which may be prepared for the atom and the field, the time evolution of state vector of the entire system is analytically evaluated. Then, the dynamics of atom is studied through the evolution of the atomic population inversion. In addition, two different measures of entanglement between the tripartite system (three entities make the system: two field modes and one atom) i.e., von Neumann and linear entropy are investigated. Also, two kinds of entropic uncertainty relations, from which entropy squeezing can be obtained, are discussed. In each case, the influences of the detuning parameters and Kerr medium on the above nonclassicality features are analyzed via numerical results, in detail. It is illustrated that the amount of the above-mentioned physical phenomena can be tuned by choosing the evolved parameters, appropriately.
We consider a single Rydberg atom having two degenerate levels interacting with the radiation field in a single-mode ideal cavity. The transition between the levels is carried out by a Λ-type degenerate two-photon process via a third level far away from single-photon resonance. At the start of interaction, the atom is considered to be in a coherent superposition of its two levels and the field in a coherent state. We study the dynamics of the atomic as well as the field states. The squeezing in the quadratures of atomic states can reach up to 100%. The cavity field evolves to a statistical mixture of two coherent fields with the phase difference between them decided by the interaction time. Analysis of entropies of the atom and the field shows that the two systems are dis-entangled periodically in certain cases.
In this paper, we analyzed squeezing in the information entropy, quantum state fidelity, and qubit-qubit entanglement in a time-dependent system. The proposed model consists of two qubits that interact with a two-mode electromagnetic field under the dissipation effect. An analytical solution is calculated by considering the constants for the equations of motion. The effect of the general form of the time-dependent for qubit-field coupling and the dissipation term on the temporal behavior of the qubit-qubit entanglement, quantum state fidelity, entropy, and variance squeezing are examined. It is shown that the intervals of entanglement caused more squeezing for the case of considering the time-dependent parameters. Additionally, the entanglement between the qubits became more substantial for the case of time dependence. Fidelity and negativity rapidly reached the minimum values by increasing the effect of the dissipation parameter. Moreover, the amount of variance squeezing and the amplitude of the oscillations decreased considerably when the time dependence increased, but the fluctuations increased substantially. We show the relation between entropy and variance squeezing in the presence and absence of the dissipation parameter during the interaction period. This result enables new parameters to control the degree of entanglement and squeezing, especially in quantum communication.