Parametric resonance in the ultracold Rydberg plasma under the influence of an acoustic wave

Abstract

The article considers weakly ionized ultracold Rydberg plasma under the influence of an acoustic wave of the terahertz range. The effect of an acoustic wave on Langmuir oscillations of Rydberg plasma is described using a hydrodynamic approach. The mechanism of the influence of an acoustic wave on Langmuir oscillations in such plasma, which consists in the scattering of electrons by neutral atoms oscillating in a high-frequency acoustic field, is considered. The unitary Kramers—Henneberger transformation in the Schrцdinger equation is used to calculate the cross section for the scattering of electrons by atoms performing high-frequency oscillations in the field of a terahertz acoustic wave. On this basis, a deep analogy is shown between the problem of scattering of an electron in the field of an external electromagnetic wave by a stationary atom and the problem of scattering of an electron by an atom vibrating in an external acoustic field. Numerical calculations demonstrate the oscillatory character of the cross section for the scattering of an electron by a Rydberg atom vibrating in a high-frequency acoustic field. Within the framework of the chosen hydrodynamic model, in view of the time dependence of the cross section for scattering of electrons by plasma atoms, the change in the electron density in such a system is described by the Mathieu equation, well known in mathematical physics. On the basis of this equation, the fundamental possibility of the appearance of parametric resonance, in the form of the buildup of Langmuir oscillations, in such a system is shown theoretically. The conditions for the appearance of resonance in Rydberg plasma initiated by a high-frequency acoustic wave are indicated.