ANDREEV REFLECTION AND THE JOSEPHSON EFFECT IN A QUANTUM POINT CONTACT - AN ANALOGY WITH PHASE-CONJUGATING RESONATORS

We discuss the analogy between the axial mode spectrum of an optical resonator with one or two phase-conjugating mirrors, and the quasiparticle excitation spectrum of an NS or SNS junction (N = normal metal, S = superconductor). As a first application, we consider Andreev reflection at an NS interface for the case that the injector of the current is a quantum point contact. We point out that when the point contact is close to pinch-off quantum interference effects will arise in the current-voltage characteristic, and discuss the relation to the well-known geometrical resonances occurring when a wide tunnel barrier is used as an injector. As a second application, we show that the quantized conductance of a point contact has its counterpart in the stationary Josephson effect: The critical current of a superconducting quantum point contact, short compared to the coherence length, is demonstrated to increase stepwise as a function of its width or Fermi energy, with a universal step height e-DELTA-o/hBAR