Magnetopolaron effects in light reflection and absorption of a three-level system in a QW

Abstract

The light absorption {\cal A} and reflection{\calR} coefficients for a three-level system in a quantum well (QW) in a strong magnetic field {\bf H}, directed perpendicularly to the QW's plane, have been calculated. The energy levels correspond to the ground state and to magnetopolaron energy levels \hbarω_{1(2)} with the inverse lifetimes γ_{r1(2)} and γ_{1(2)}. The inverse radiative lifetime of an EHP in a QW γ_{rξ}(\bf{\cal K}_{\perp})\not=0 only under condition {\cal K}_{\perp}\leω_ξn/c, where \hbarω_ξis the EHP energy. It has been shown that γ_{rξ}(\bf{\cal K}_{\perp}) is proportional to H. The values γ_{ra}(\bf{\cal K}_{\perp}) and γ_{rb}(\bf{\cal K}_{\perp}) for an excitation consisting of a hole and a usual magnetopolaron have been calculated. The index a(b) designates a magnetopolaron upper (lower) term. In the resonance at H_{res}=m_ecω_{LO}/|e|~~ γ_{ra}^{res}=γ_{rb}^{res}=γ_{rξ_0}^{res}/2, where the index ξ_0 corresponds to the EHP with n_e=n_h=1. The dependencies {\cal A}(H)$ and ${\cal R}(H) for various values of ω_l in the magnetophonon resonance vicinity have been obtained. The existence of "combined"and "weak" polarons has been predicted. The resonant value H_{res} for the combined polaron case depends on a QW's depth and width.