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Physica A Statistical Mechanics and its Applications

The coherent generation of the photon pairs by a stream of excited atoms passing through the cavity

N. A. Enaki, Viorel Ciornea

Published May 11, 2004• 9 citations
Publisher

Abstract

The problem of the coherent generation of the entanglement photon pairs by an ensemble of the two-level atoms passing through the cavity is studied. The dependence of the generation rate of the photon pairs as a function of the coherent states of the atomic stream is established. Considering that the flying time of the atoms passing through the cavity is less than decay time, a new method of the elimination of atomic variables from the system is proposed. The master equation for multimode cavity electromagnetic field is obtained. Using the Fokker–Planck equations, the steady state solution of this master equation is studied. The quantum properties of the multimode electromagnetic field are analyzed, using the non-diagonal P representation for su (1,1) symmetry.

DOI
10.1016/j.physa.2004.04.038

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The two-photon generator of coherent light formed from entangled photon pairs is proposed. Considering the multi-mode field of micro-cavity in the processes of generation of photon pairs the two-photon resonator losses are proposed. The master equation for cavity biphotons is obtained from quantum treatment of problem. The analytical and numerical stationary solutions for master equation are presented. Also is found that the lasing of light is started from vacuum fluctuations of cavity field. The comparison of proposed model with other two-photon laser models is discussed.
QUANTUM CONTROL AND GENERATION OF QUANTUM ENTANGLEMENT In this thesis, the generation of entanglement is studied in a controlled environment. The model system of interest includes a cavity field interacting with a pair of atoms. The cavity field is heavily damped and it is pumped in order to maintain a steady state field population. Thus, we can eliminate the cavity field adiabatically and obtain the master equation describing only the qubits evolution in time. At first, this system is analyzed in the steady state, without making any measurement on the photons leaking through the cavity walls. In this way, the ideal physical parameter set for maximum entanglement in this model is investigated. In the second step, we assume a direct measurement on the leaking cavity photons, and observe the evolution of entanglement in a quantum trajectories approach. We simulate quantum trajectories approach by applying Monte Carlo method. The amount of entanglement is obtained as a function of time and number of photon detections.
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In this paper we investigated the entanglement dynamics of a pair of two-level atoms passing through a vacuum or thermal cavity one after another. We assumed that two atoms were initially prepared in separable coherent or entangled states. Using the exact solution of the density matrix evolution equation we calculated the time dependence of negativity for models with one-and two-photon interaction between atoms and the cavity field. For the two-photon model we took into account the dynamical Stark shift. We have found that the degree of atom-atom entanglement can be controlled by the Stark shift and cavity mean photon numbers.
A new method of elimination of squeezed field operators in nonlinear interaction with atomic subsystem is proposed. This method can be used for the opposite laser situation, in which the operators of an external coherent atomic source are eliminated from the density matrix equation. New types of master equations, belonging to su(1, 1) and su(2) symmetries are obtained. The solution of this equation is obtained using the generalized non-diagonal P and Q representations for su(1, 1) and su(2) symmetries. These master equations and their solutions can be used for further studies on the behavior of atomic polarization or quantum properties of the cavity field.
Quantum statistical properties of interacting optical fields in Kerr nonlinear couplers may be regarded as one of the most fundamental problems yet to be solved in quantum optics. As an analytical solution to this system is not always possible, a semi-analytic or direct numerical solution must be employed in order to obtain a more complete description of their evolution. This study investigates the quantum properties of four-mode couplers composed of two and four Kerr nonlinear waveguides, both with and without cavity set up via phase space representation. In these systems, the electromagnetic fields are described by their Hamiltonians, while the time-evolution of the systems are described by the Von-Neumann equation. Following standard techniques, the master equations for the density matrices of the systems are obtained and further converted to the corresponding classical Fokker- Planck equations using both positive P and Wigner representations. The corresponding set of Langevin Stochastic equations is then obtained from the Fokker-Planck equations by means of Ito rules. Finally, the systems are integrated numerically and averaged over many trajectories to get the relevant information. The effects of self-action nonlinearity, cross-action coupling and the initial energy of the coherent light on the evolution of the field quadrature variances are investigated. Furthermore, the influences of multimode interaction on the dynamics of the squeezed states are discussed. In this research, we show that the system may produce squeezed states in both quadrature variances for all calculated parameters. The multimode two channel model can provide better squeezing in contrast to the conventional device. The amplitude oscillation of maximal squeezing may be amplified by manipulation of the initial state of the coherent light in the first mode, and the range may be extended through multimode interaction. When the model is contained in a cavity, the system is able to generate better amplitude oscillations and squeezing range with leaf-revival-collapse-like behaviour; with the whole oscillation able to evolute below the standard quantum limit Regular photon transition and self trapping effects of the interacting modes in the four channels model are simulated, and squeezing is predicted for various initial intensities of the coherent field and nonlinear coupling parameter g. The cavity setup caused the system to undergo fluctuation amplification and the potential for different types of squeezing to be generated is observed. Depending on how we choose the interaction parameter values, the system may generate better squeezing in comparison to the cavity-less model.