Dynamical charge susceptibility in nonequilibrium double quantum dots

TL;DR

This paper provides a theoretical analysis of the dynamical charge susceptibility in nonequilibrium double quantum dots, revealing key features of charge response and implications for spin qubit applications.

Contribution

It derives an analytical expression for the charge susceptibility in nonequilibrium double quantum dots and explores its implications for quantum RC circuits and spin qubit systems.

Findings

Identification of two maxima lines in charge susceptibility as a function of dot levels.

Derivation of capacitance and charge relaxation resistance in quantum RC circuits.

Qualitative agreement with experimental observations in spin qubit systems.

Abstract

Double quantum dots are one of the promising two-state quantum systems for realizing qubits. In the quest of successfully manipulating and reading information in qubit systems, it is of prime interest to control the charge response of the system to a gate voltage, as filled in by the dynamical charge susceptibility. We theoretically study this quantity for a nonequilibrium double quantum dot by using the functional integral approach and derive its general analytical expression. One highlights the existence of two lines of maxima as a function of the dot level energies, each of them being split under the action of a bias voltage. In the low frequency limit, we derive the capacitance and the charge relaxation resistance of the equivalent quantum RC-circuit with a notable difference in the range of variation for $R$ depending on whether the system is connected in series or in parallel. By incorporating an additional triplet state in order to describe the situation of a double quantum dot with spin, we obtain results for the resonator phase response which are in qualitative agreement with recent experimental observations in spin qubit systems. These results show the wealth of information brought by the knowledge of dynamical charge susceptibility in double quantum dots with potential applications for spin qubits.