The conductance of a ballistic point contact linking two reservoirs at thermal equilibrium is quantized in multiples of the conductance quantum 2*e*^{2}/*h*. The origin of this phenomenon is the quantization of the transverse momentum in the narrow constriction. Intriguingly, the conductance of the contact remains finite even though no scattering is assumed at the constriction. This raises the question as to what happens if we replace the reservoirs with superconductors. This question was answered by Beenakker and van Houten a few years after the discovery of the conductance quantization [1]. They theoretically analyzed a superconducting quantum point contact (SQPC) made of a smooth and impurity-free superconducting constriction, and showed that superconducting Josephson current flows up to *eΔ*/*ħ* (*Δ*: superconducting gap) per quantized mode. Even more than 20 years after the theoretical prediction, there have been only a limited number of reports on its experimental verification [2]. In this work, we study a semiconductor/superconductor hybrid QPC that exhibits staircase variation of the Josephson critical current *I*_{c} with respect to the number of quantized mode *n*, which provides a compelling evidence of the quantization of *I*_{c} [3].

The hybrid QPC consists of a QPC formed in a high-In-content In_{0.75}Ga_{0.25}As two-dimensional electron gas (2DEG) and two Nb electrodes in the vicinity of the QPC [Fig. 1]. Josephson coupling is attained via Andreev reflection of Bogoliubov quasiparticles confined in the 2DEG. The transport properties of the quasiparticles, and hence the Josephson junction characteristics, can be controlled by means of the external electric field from a gate electrode. Figure 2 shows the gate voltage *V*_{g} dependence of *I*_{c} measured at 20 mK. *I*_{c} shows a clear stepwise variation as *n* changes with *V*_{g}, demonstrating a Josephson coupling through the quantized mode. The experimental value of *I*_{c} per mode is 10.3 nA, which is one order of magnitude smaller than the theoretical value of 125 nA. This discrepancy is accounted for by the presence of a proximity layer having smaller *Δ* at the InGaAs/Nb interface. The suppressed stepheights for *n* = 1 and 2 are caused by the finite temperature effect. From those observations, we experimentally prove the quantization of Josephson current and demonstrate a single-channel SQPC for the first time.

This work was supported by KAKENHI.