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Journal of Experimental and Theoretical Physics Letters

Entanglement in a two-boson coupled system

Alexei Vladimirovich Chizhov

Published Mar 1, 2007• 1 citation
Publisher

Abstract

A model for two nondegenerate cavity fields coupled through a reservoir is considered. Such a model can be employed for the study of Raman scattering in which the Stokes and anti-Stokes fields indirectly interact via a bath of phonon. An analysis for appearance of quantum entanglement between the fields and evaluation of the entanglement measure depending on initial states of the fields and on a state of the phonon reservoir is given.

DOI
10.1134/s0021364007010201

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A model for two nondegenerate cavity fields coupled through a reservoir is considered. Such a model can be employed for the study of Raman scattering in which the Stokes and anti-Stokes fields indirectly interact via a bath of phonon. An analysis for appearance of quantum entanglement between the fields and evaluation of the entanglement measure depending on initial states of the fields and on a state of the phonon reservoir is given.
A quantum-mechanical model of Raman scattering from a phonon bath is formulated. A master equation is derived for the density operator of the light fields alone. This model correctly describes the stochastic coupling of Stokes and anti-Stokes radiation through the phonon bath. Since quantum fluctuations are included, this treatment contains the spontaneous and stimulated Raman effects in one self-consistent formalism. The photon statistics of the light fields are obtained by the solution of a Fokker-Planck equation.
The quantum theory of Stokes--anti-Stokes processes in a degenerate system in a cavity is developed. The Raman transition is pumped by a coherent field. Effects of many atoms, cavity losses, and thermal photons are included in the theory. An exact solution for the model is obtained. An explicit expression for the reduced density matrix of the cavity field is given. The spectrum of the cavity field is obtained and is interpreted in terms of the eigenstates of the effective Hamiltonian describing Stokes--anti-Stokes processes. The spectrum develops sidebands due to strong Raman coupling.
We present an alternative cavity QED model with three nondegenerate quantized field modes. The atom-field interaction is a cavity analog of Raman scattering, and the three field modes can be associated with pump, Stokes, and anti-Stokes frequencies. Unlike systems based on the Jaynes-Cummings model, this one has two independent channels connecting the two active atomic levels, leading to the possibility of quantum interferences. Despite its complexity, the model has eigenstates and eigenvalues that can be found exactly and fully analytically in finite terms. The most interesting eigenstates have a ``chain'' character unknown in previous cavity QED models. Both Fock-state and coherent-state solutions are presented for a number of quantities, including complex three-mode variables. Heisenberg operator solutions are demonstrated in a few cases, and an example of fourth-order quantum interferences due to the coupled channels is worked out in full.
We consider a cavity model in which the dynamics of photons and phonon modes, as well as their interaction with a boson reservoir, are taken into account. The second- and fourth-order quantum coherence functions are evaluated and examined under various conditions of coupling coefficients, phases, and noise. For the case when the laser–anti-Stokes coupling is larger than the laser–Stokes coupling, the quantum correlations between field operators are identified in the form of sum and ordinary squeezing. The reservoir can be noisy without severely degrading the sum squeezing.