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 semiclassical small-signal model approach to replace complex single-electron devices by parametric circuit components that could be readily used in analog circuit simulators. Our approach is based on weakly driven quantum two-level systems, and here, we use it to calculate the low frequency impedance of a single-electron double quantum dot (DQD). We find that the total impedance is composed of three elements that were previously considered separately: a dissipative term, corresponding to the Sisyphus resistance, and two dispersive terms, composed 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 nonresonant state readout of quantum bits and parametric amplification.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 semiclassical small-signal model approach to replace complex single-electron devices by parametric circuit components that could be readily used in analog circuit simulators. Our approach is based on weakly driven quantum two-level systems, and here, we use it to calculate the low frequency impedance of a single-electron double quantum dot (DQD). We find that the total impedance is composed of three elements that were previously considered separately: a dissipative term, corresponding to the Sisyphus resistance, and two dispersive terms, composed 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 nonresonant state readout of quantum bits and parametric amplification.