Mode locking in quantum-Hall-effect point contacts.

We study the effect of an ac drive on the current-voltage (I-V) characteristics of a tunnel junction between two fractional quantum Hall fluids at filling n an odd integer. Within the chiral Luttinger-liquid model of edge states, the point-contact dynamics is described by a driven damped quantum mechanical pendulum. In a semiclassical limit which ignores electron tunneling, this model exhibits mode locking, which corresponds to current plateaus in the I-V curve at integer multiples of I5ev/2p , with v the ac drive angular frequency. By analyzing the full quantum model at nonzero n using perturbative and exact methods, we study the effect of quantum fluctuation on the mode-locked plateaus. For n51, quantum fluctuations smear completely the plateaus, leaving no trace of the ac drive. For n> 1 2 smeared plateaus remain in the I-V curve, but are not centered at the currents I5nev/2p . For n, 1 2 rounded plateaus centered around the quantized current values are found. The possibility of using mode locking in fractional quantum-Hall-effect point contacts as a current-tofrequency standard is discussed. @S0163-1829~96!06040-7#