MODE-LOCKING IN QUANTUM-HALL-EFFECT POINT CONTACTS

We study the effect of an ac drive on the current-voltage (I-V) charac teristics of a tunnel junction between two fractional quantum Hall flu ids at filling nu(-1) an odd integer. Within the chiral Luttinger-liqu id model of edge states, the point-contact dynamics is described by a driven damped quantum mechanical pendulum. In a semiclassical limit wh ich ignores electron tunneling, this model exhibits mode locking, whic h-corresponds to current plateaus in the I-V curve at integer multiple s of I = e omega/2 pi, with omega the ac drive angular frequency. By a nalyzing the full quantum model at nonzero nu using perturbative and e xact methods, we study the effect of quantum fluctuation on the mode-l ocked plateaus. For nu=1, quantum fluctuations smear completely the pl ateaus, leaving no trace of the ac drive. For nu greater than or equal to 1/2 smeared plateaus remain in the I-V curve, but are not centered at the currents I=ne omega/2n. For nu<1/2 rounded plateaus centered a round the quantized current values are found. The possibility of using mode locking in fractional quantum-Hall-effect point contacts as a cu rrent-to-frequency standard is discussed.