Theory of relaxation for spontaneous emission of Bloch oscillation radiation

Abstract

A theory for the spontaneous emission (SE) of radiation for a Bloch electron traversing a single energy miniband of a superlattice (SL) in a cavity while undergoing scattering is presented. The Bloch electron is accelerated under the influence of superimposed constant external and internal inhomogeneous electric fields while radiating into a microcavity. The constant external electric field strength is chosen so that the emitted radiation lies in the terahertz spectral range. The quantum dynamics for the inhomogeneous field correction is obtained from a Wigner–Weisskopf-like long-time, time-dependent perturbation theory analysis based on the instantaneous eigenstates of the electric field-dependent Bloch Hamiltonian. It is shown that SE for the cavity-enhanced Bloch electron probability amplitude becomes damped and frequency shifted due to the perturbing inhomogeneity. The developed general quantum approach is applied to the case of elastic electron scattering due to SL interface roughness (SLIR). In the analysis, the interface roughness effects are separated into contributions from independent planar and cross-correlated neighboring planar interfaces; it is estimated that the crosscorrelated contribution to the SE relaxation rate is relatively small compared to the independent planar contribution. When analyzing the total emission power, it is shown that the degradation effects from SLIR can be more than compensated for by the enhancements derived from microcavity-based confinement tuning.