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

Due to the quantum nature of current flow in single-electron devices, new physical phenomena can manifest when probed at finite frequencies. Here, we present a semi-classical small-signal model approach to replace complex single-electron devices by linear parametric circuit components that could be readily used in analogue circuit simulators. Our approach is based on weakly-driven quantum two-level systems and here we use it to calculate the finite-frequency impedance of a single-electron double quantum dot (DQD). We find that the total impedance is composed by three elements that were previously considered separately: a dissipative term, corresponding to the Sisyphus resistance, and two dispersive terms, comprised of the quantum and tunneling capacitance. Finally, we combine the parametric terms to understand the interaction of the DQD with a slow classical electrical oscillator which finds applications in non-resonant state readout of quantum bits and parametric amplification.