The authors demonstrate quadratic mixing of weak time harmonic electromagnetic fields applied to Superconducting Quantum Interference Filters, manufactured from high-$T_{mathrm{c}}$ grain boundary Josephson junctions and operated in active microcooler. The authors use the parabolic shape of the dip in the dc-voltage output around B=0 to mix emph{quadratically} two external rf-signals, at frequencies $f_{mathrm{1}}$ and $f_{mathrm{2}}$ well below the Josephson frequency $f_{mathrm{J}}$, and detect the corresponding mixing signal at $| {f_{1}-f_{2}}| $. Quadratic mixing takes also place when the SQIF is operated without magnetic shield. The experimental results are well described by a simple analytical model based on the adiabatic approximation.
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