Abstract
In the investigation of the transfer function (field sensitivity) of a weak link ultra-low capacity RF-SQUID, there is a problem which concerns the response of the quantum nonlinear oscillator formed by the geometrical inductance of the superconducting ring, the Josephson inductance and the weak link capacity, to the external magnetic flux. In order to account for the influence of the small quantum charge fluctuation on the Josephson potential, a phenomenological approach is proposed, which leads to a phase shift consisting of two additives. The first additive is a constant depending on the weak link parameters, and the second is linear in the external magnetic flux. The influence of the quantum fluctuation is effectively reduced to increasing the period of the current-phase relation for the RF-SQUID in the external magnetic flux, which leads to a reduction of the response of such a quantum SQUID in comparison with the usual RF SQUID.
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