On precession of entangled spins in a strong laser field
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ELEMENTARY PARTICLES AND FIELDS Theory
On Precession of Entangled Spins in a Strong Laser Field* M. Eliashvili1)** , V. Gerdt2)*** , and A. Khvedelidze1), 2)**** Received October 14, 2008
Abstract—A dynamics of the entanglement under an environmental influence is modelled by a bound state composed of two heavy particles interacting with a strong laser. Adopting the semiclassical attitude, a trajectory of the bound state’s center-of-mass is found from the Newton equations solved beyond the dipole approximation and taking into account the magnetic field effect. At the same time the dynamics of constituent spins under the laser coupling is studied quantum mechanically solving the nonrelativistic von Neumann equation with the effective Hamiltonian determined by the bound state’s classical trajectory. Based on the solution, the effects of an intense linearly polarized monochromatic plane wave on the precession of entangled spins are discussed for a specific kind of mixed initial states including a family of maximally entangled Werner states. PACS numbers: 42.50.Ct, 03.65.Ud, 03.67.Bg, 34.80.Qb DOI: 10.1134/S1063778809050068
1. INTRODUCTION This article addresses the question how a highintensity laser interacting with a charged composite system affects the evolution of its entangled subsystems (for the definition and properties of the entanglement see, e.g., recent books [1–3]). To understand the dynamics of entanglement under a laser coupling a simple model is formulated. A laser beam is modelled by a strong linearly polarized monochromatic electromagnetic plane wave and a composite system is represented by a bound state consisting of two heavy spin-1/2 particles. The behavior of a nonrelativistic charged particle driven by a low intensity laser is completely determined by the electric component of electromagnetic field with no mention at all of its magnetic component. The electric-field dominance together with the dipole approximation provides a consistent solution to the equation of motion for a particle classical trajectory and allows to determine the dynamics of spin degrees of freedom [4]. However, as an intensity of radiation is growing up, an accelerating-particle velocity can attain the relativistic values [5, 6]. As a result the dipole approximation becomes inconsistent and the magnetic part of the Heaviside–Lorentz force is not ∗
The text was submitted by the authors in English. A. Razmadze Mathematical Institute, Tbilisi, Georgia. 2) Joint Institute for Nuclear Research, Dubna, Russia. ** E-mail: [email protected] *** E-mail: [email protected] **** E-mail: [email protected] 1)
negligible any more. This, in turn, makes an influence on a particle spin evolution unavoidable. In the present article, based on the recent results [7], we make a step forward to the relativistic description and consider a particle motion beyond the dipole approximation and taking into account the magnetic-field effect. We neglect the influence of a particle spin on the classical orbit and consider the spin evolution quantum mechanically as precession i
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