Collective cyclotron resonance of an inhomogeneous electron gas

We report low-temperature far-infrared magneto-optical measurements on a remotely doped, asymmetric, wide parabolic ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum well with two curvatures. The collective cyclotron-resonance spectrum of the system, measured with an in-plane magnetic field, is found to depend on the electron areal density ${\mathit{N}}_{\mathit{s}}$. At sufficiently high ${\mathit{N}}_{\mathit{s}}$, so that the effective layer thickness is much larger than the magnetic length, two plasma frequencies associated with the two curvatures are observed, showing that the system behaves as a classical, inhomogeneous, three-dimensional electron plasma. At low ${\mathit{N}}_{\mathit{s}}$, only one resonance is observed, corresponding to the lowest optical transition between the quantized levels in the nearly empty well.