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We investigate a Josephson field-effect transistor in which the electron gas in an InAs quantum well serves as the weak link between superconducting Nb electrodes. We modulate the density Ns of electrons and the critical current Ic in the weak link by applying a voltage to an insulated gate. Measurements of the dependence of Ic on Ns are in good agreement with a model in which each occupied subband of the InAs quantum well makes an independent contribution to Ic. Inclusion of the nonparabolic band structure in InAs is crucial to this agreement.

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