Quantum and Tunnelling Capacitance in Charge and Spin Qubits

TL;DR

This paper provides a theoretical framework for analyzing the capacitance in charge and spin qubits within double quantum dots, highlighting how different capacitance components reveal qubit states and system parameters at high frequencies.

Contribution

It introduces a formalism to distinguish quantum and tunnelling capacitance contributions, enabling non-invasive qubit state characterization and parameter extraction.

Findings

Capacitance lineshape depends on qubit state and controllable variables.

The analysis allows extraction of relaxation times, tunnel coupling, and g-factor.

Provides a basis for high-sensitivity, dispersive qubit readout.

Abstract

We present a theoretical analysis of the capacitance of a double quantum dot in the charge and spin qubit configurations probed at high-frequencies. We find that in general the total capacitance of the system consists of two state-dependent terms: The quantum capacitance arising from adiabatic charge motion and the tunnelling capacitance that appears when repopulation occurs at a rate comparable or faster than the probing frequency. The analysis of the capacitance lineshape as a function of externally controllable variables offers a way to characterize the qubits' charge and spin state as well as relevant system parameters such as charge and spin relaxation times, tunnel coupling, electron temperature and electron g-factor. Overall, our analysis provides a formalism to understand dispersive qubit-resonator interactions which can be applied to high-sensitivity and non-invasive quantum-state readout.