# Measurements of capacitive coupling within a quadruple quantum dot array

## TL;DR

This study measures and models capacitive coupling in a quadruple quantum dot array in silicon, demonstrating tunability and providing a detailed parameter extraction method for quantum dot qubits.

## Contribution

It introduces a method to extract all parameters of a 4D Hamiltonian from 2D charge stability diagrams and models how capacitive coupling depends on device capacitances.

## Key findings

- Capacitive coupling energy measured at 20.9 GHz.
- Capacitive coupling tunable from 15 to 32 GHz.
- Model predictions agree with experimental measurements.

## Abstract

We present measurements of the capacitive coupling energy and the inter-dot capacitances in a linear quadruple quantum dot array in undoped Si/SiGe. With the device tuned to a regime of strong ($>$1 GHz) intra-double dot tunnel coupling, as is typical for double dot qubits, we measure a capacitive coupling energy of $20.9 \pm 0.3$ GHz. In this regime, we demonstrate a fitting procedure to extract all the parameters in the 4D Hamiltonian for two capacitively coupled charge qubits from a 2D slice through the quadruple dot charge stability diagram. We also investigate the tunability of the capacitive coupling energy, using inter-dot barrier gate voltages to tune the inter- and intra-double dot capacitances, and change the capacitive coupling energy of the double dots over a range of 15-32 GHz. We provide a model for the capacitive coupling energy based on the electrostatics of a network of charge nodes joined by capacitors, which shows how the coupling energy should depend on inter-double dot and intra-double dot capacitances in the network, and find that the expected trends agree well with the measurements of coupling energy.