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Due to the quantum nature of current flow in single-electron devices, newphysical phenomena can manifest when probed at finite frequencies. Here, wepresent a semi-classical small-signal model approach to replace complexsingle-electron devices by linear parametric circuit components that could bereadily used in analogue circuit simulators. Our approach is based onweakly-driven quantum two-level systems and here we use it to calculate thefinite-frequency impedance of a single-electron double quantum dot (DQD). Wefind that the total impedance is composed by three elements that werepreviously considered separately: a dissipative term, corresponding to theSisyphus resistance, and two dispersive terms, comprised of the quantum andtunneling capacitance. Finally, we combine the parametric terms to understandthe interaction of the DQD with a slow classical electrical oscillator whichfinds applications in non-resonant state readout of quantum bits and parametricamplification.

Small-signal equivalent circuit for double quantum dots at low-frequencies