A theory for the spontaneous emission of radiation for a Bloch electron in a single superlattice (SL) energy band under the influence of an external, spatially homogeneous, classical ac electric field is presented. The classical external ac electric field is described in the vector-potential gauge. The quantum radiation field is described by the free-space quantized electromagnetic field in the Coulomb gauge. Utilizing the instantaneous eigenstates of the Bloch Hamiltonian as the basis states, the Bloch electron dynamics is described to all orders in the classical ac electric field. It is shown that the spontaneous emission occurs with frequencies equal to integral multiples of the classical ac electric field frequency; this is due to the imposition of temporal periodic motion of the Bloch electrons in the SL miniband from the external periodic ac field. From appropriately derived selection rules for photon frequency and wave-vector transitions, the total spontaneous-emission probability (TSEP) is derived to first-order perturbation theory in the quantized radiation field. A general expression is obtained for the TSEP in terms of arbitrary SL miniband parameters; further, the TSEP is analyzed in detail based on the band model for the nearest-neighbor tight-binding approximation, and results show multiharmonic behavior and ac electric field tuning properties. In the nearest-neighbor tight-binding approximation, specific results for single Bloch electron manifest distinct plateaulike step structure in the analysis of normalized TSEP as a function of the ratio ${\omega }_0/\omega$, where ${\omega }_0$ is the characteristic frequency, proportional to the ac electric field amplitude, and $\omega$ is the ac electric field frequency; the plateau centers of gravity are found to be defined by the Stark delocalization condition established in ac-field transport. Further, the influence of a microcavity waveguide is established and shows enhancement as well as harmonic tuning of the TSEP due to coupling to the microcavity modal environment. Finally, the one-electron TSEP is extended, within the independent electron approximation, so as to include fractional band filling along with a constant-temperature-dependent and electron-density-dependent analysis; from this analysis, TSEP numerical estimates are projected at terahertz external field frequencies for a half-filled GaAs/AlGaAs SL miniband at zero temperature.

• Received 18 August 2009

DOI:https://doi.org/10.1103/PhysRevB.80.165328