  We study the hitherto un-addressed phenomenon of Quantum Hall Effect with a
magnetic and electric fields oscillating in time with resonant frequencies.
This phenomenon realizes an example of heterodyne device with the magnetic
field acting as a driving and is analyzed in detail in its classical and
quantum versions using Floquet theory. A bulk current flowing perpendicularly
to the applied electric field is found, with a frequency shifted by integer
multiples of the driving frequency. When the ratio of the cyclotron and driving
frequency takes special values, the electron's classical trajectory forms a
loop and the effective mass diverges, while in the quantum case we find an
analogue of the Landau quantization. Possible realization using metamaterial
plasmonics is discussed.
