We study the quantization of the supercurrent and conductance of asuperconducting quantum point contact (SQPC) in a superconductor-twodimensional electrongas-superconductor (S-2DEG-S) Josephson junction with asplit gate. The supercurrent and the conductance values change stepwise as afunction of the gate voltage. We observe the onset of the first transport modecontributing both to the supercurrent and the conductance of the SQPC.Furthermore the steps in the supercurrent and the conductance appear at thesame gate voltage values. This shows, that each transport mode in the SQPCcontributes both to the normal state conductance and to the supercurrent.
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