  We propose a frequency-mixed effect of Terahertz (THz) and Gigahertz (GHz)
electromagnetic waves in the cryogenic system of electrons floating on liquid
helium surface. The THz wave is near-resonant with the transition frequency
between the lowest two levels of surface state electrons. The GHz wave does not
excite the transitions but generates a GHz-varying Stark effect with the
symmetry-breaking eigenstates of electrons on liquid helium. We show an
effective coupling between the inputting THz and GHz waves, which appears at
the critical point that the detuning between electrons and THz wave is equal to
the frequency of GHz wave. By this coupling, the THz and GHz waves
cooperatively excite electrons and generate the low-frequency ac currents along
the perpendicular direction of liquid helium surface to be experimentally
detected by the image-charge approach [Phys. Rev. Lett. 123, 086801 (2019)].
This offers an alternative approach for THz detections.
