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Journal of Physics B Atomic Molecular and Optical Physics

Uncertainty relation and information entropy of a time-dependent bimodal two-level system

Mahmoud Abdel‐Aty, M. Sebawe Abdalla, A.‐S. F. Obada

Published Nov 11, 2002• 47 citations
Publisher

Abstract

In this paper we consider a nonlinear interaction between a two-level atom and two modes of the electromagnetic field within a cavity. As the instantaneous position of the particle inside the cavity depends on both velocity and acceleration, we have assumed the coupling parameter to be explicitly time dependent. We have obtained the dynamical operators by solving the Heisenberg equations of motion and then constructed the density operator. The Heisenberg uncertainty relation is used to examine the entropy squeezing for this system. We have studied the effects of the phase, velocity and acceleration on entropy squeezing and atomic inversion. In addition the possibility of Bell-state production is discussed.

DOI
10.1088/0953-4075/35/23/302

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In this paper we consider a nonlinear interaction between a two-level atom and two modes of the electromagnetic field within a cavity. As the instantaneous position of the particle inside the cavity depends on both velocity and acceleration, we have assumed the coupling parameter to be explicitly time dependent. We have obtained the dynamical operators by solving the Heisenberg equations of motion and then constructed the density operator. The Heisenberg uncertainty relation is used to examine the entropy squeezing for this system. We have studied the effects of the phase, velocity and acceleration on entropy squeezing and atomic inversion. In addition the possibility of Bell-state production is discussed.
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 terms of a new Hamiltonian we introduce a modified Jaynes–Cummings model to represent the interaction between a two-level atom and two electromagnetic fields injected simultaneously within a perfect cavity. The field–field interaction is assumed to be in the frequency converter form. Exact expressions of the dynamical operators is given by solving the equations of the motion in the Heisenberg picture. The entropy squeezing is examined in the framework of Shannon information entropy. Using the entropic uncertainty relation, one can be able to show that there is a new kind of quantum squeezing in the entropy.
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.
From a quantum information point of view we study the entropy squeezing of a two-level atom interacting with two modes with intensity-dependent coupling. The Hamiltonian we consider consists of all acceptable forms of nonlinearities. A definition of squeezing is presented for this system, based on information theory. The utility of the definition is illustrated by examining squeezing in the information entropy of a two-level atom in the presence of a nonlinear medium. We examine the influence of the nonlinear interaction, the atomic coherence and the detuning parameter on the properties of the entropy and squeezing of the atomic variables. It is shown that features of the quantum entropy are influenced significantly by the kinds of intensity-dependent atom-field coupling and the nonlinearities of the two-mode fields.
In this paper, we study the interaction between a ΛΛΛ-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.
A model of a two-coupled two-level atom under the action of an external magnetic field is introduced. The system is assumed to be isotropic and the coupling between the atoms is taken to be explicitly time dependent. Direct solution for the equations of motion in the Heisenberg picture is used to obtain the explicit expression for the dynamical operators when we assumed the coupling parameter is constant. In the meantime we have employed the rotating wave approximation for the case in which the coupling parameter is time dependent. The variance and entropy squeezing for both cases are discussed. It has been shown that the variance squeezing and entropy squeezing are sensitive to any change in the atomic states, so that there is no variance squeezing reported for the case in which one or both the atoms are in the pure states (e.g., lower or excited states). Further, the phenomenon of squeezing is also affected by the value of the coupling parameter, where we have noted that for a strong coupling parameter the squeezing is pronounced for a long period of time.