title: One-photon scattering by an atomic chain in a two-mode resonator: cyclic conditions.
abstract: In this work, a chain of N identical two-level atoms coupled with a quantized electromagnetic field, initially prepared via a single-photon Fock state, is investigated. The N-particle state amplitude of the system is calculated for several space configurations of the atoms in the Weisskopf-Wigner approximation. It was shown that the space configuration of an atomic chain, the total number of atoms, and even the available volume for the field modes define the behavior of the system state amplitude with time. Applying the condition of 'cyclic bonds', presented in this work, to the elaborated theory allows to describe the system time evolution, practically, for any space configuration.
authors.affiliation: Department of Radiophysics, Kyiv Taras Shevchenko National University, Acad. Glushkova Avenue 4-g, Kyiv 03022, Ukraine.
authors.forename: Andrii S
authors.initials: AS
authors.lastname: Sizhuk
authors.affiliation: Department of Radiophysics, Kyiv Taras Shevchenko National University, Acad. Glushkova Avenue 4-g, Kyiv 03022, Ukraine ; Department of Physics, Kyiv Taras Shevchenko National University, Acad. Glushkova Avenue 2, Kyiv 03022, Ukraine.
authors.forename: Stanislav M
authors.initials: SM
authors.lastname: Yezhov
keywords: Atoms; Fock state; Weisskopf-Wigner approximation