Optical and magneto-optical absorption in parabolic quantum wells

We show that an n-doped parabolic quantum well absorbs far infrared radiation at the bare harmonic-oscillator frequency ${\mathrm{\omega }}_0$ independently of the electron-electron interaction and the number of electrons in the well. In the presence of a magnetic field tilted with respect to the plane of the quantum well, we find that the cyclotron resonance becomes coupled to this ${\omega }_0$ frequency mode. The absorption then occurs at two frequencies, which are again independent of the electron-electron interaction and the fractional filling of the well.