One-Photon Scattering by an Atomic Chain in One- and Two-Mode Resonators

Abstract

A chain of N identical two-level atoms coupled with the electromagnetic field, prepared via a single-photon Fock state, is investigated. It is found that, if the interaction between atoms is negligible, than the obtained dynamic equations for the probability amplitudes allow, in a certain sense, an interpretation of the dynamics of states in the classical fashion in terms of a superposition of oscillatory modes of the system under study. The derived equations reveal how a space configuration of the system of atoms affects the dynamics of the atomic states, particularly the "decay" rates of separate atoms and the system as the whole. K e y w o r d s: one-photon scattering, atomic system, Fock state, Schrödinger equation.

One-photon scattering by an atomic chain in a two-mode resonator: cyclic conditions

“…As it was supposed in the derivative of the differential equations with the damping items such like (12) (see the details in the work [11], the available volume V for the system of atoms and field defines the ‘available’ modes for the electromagnetic field. The value of volume V can determine one of the inequalities D < Ω 2 and D > Ω 2 ($D<{\Omega }_2^{\prime }$ and $D>{\Omega }_2^{\prime }$), therefore defining the character of the system relaxation.…”

“…Therefore, substituting Equation 4 into 3 and differentiating one more time, after applying the Weisskopf-Wigner approximation (details in [ 11 ]), we can derive the following system of evolution equations:…”

“…In the present paper, a system (chain) of N identical two-level non-interacting atoms, prepared ‘via a single-photon Fock state’ in the one- or two-mode resonator, is investigated. The main goal of the paper is to obtain the information about the state of electromagnetic field and atomic system (chain) in a Weisskopf-Wigner approximation (see [ 10 ] chapter 6, page 206 and some comments in [ 11 ]). The calculations of the state amplitudes of the atomic system are made for several approximations in resonator (cavity) characteristics and for several types of space configurations of the atoms in the chain.…”

“…Let us first provide below some general theoretical premises. More detailed derivations of the corresponding mathematical model can be found in [ 11 ].…”

The conservative system ofNatoms coupled with one photon

“…In practice, the thermalization can be combined with coherent effects, as in the case of ''superradiance'' [3,[9][10][11][12], that can in turn be destroyed by the Doppler broadening of the atomic (electronic) resonant frequencies (see analysis in [13]). Some comments on a certain approximation are also provided in [14]. We neglect here any kind of thermal motion and discover a system with ''fixed'' atomic positions.…”