Bloch gain in a quantum cascade laser

We present a microscopic model, based on a density matrix formalism, which unifies the apparently quite different gain mechanisms in intersubband transitions: the inversion gain of a quantum cascade laser and the Bloch gain in a periodic superlattice. The theory also provides an expression for the spontaneous emission in intersubband transitions, which accounts for the temperature-dependent asymmetry of measured luminescence spectra. While the luminescence profile is hardly altered, the peak gain position depends critically on the ratio of populations. Thus, the degree of population inversion is accessible by simultaneous observation of both signals. For these measurements, whispering gallery quantum cascade laser are particularly suitable as scattered laser light and luminescence are of comparable strength over a wide range of injected currents.