[Paper Review] Coupling of hole double quantum dot in planar germanium to a microwave cavity

Yuan Kang, Zong-Hu Li+11 more|arXiv (Cornell University)|Oct 12, 2023

Quantum and electron transport phenomenaPhysics and Astronomy3 citations

TL;DR

This study demonstrates strong coupling between hole spins in a planar germanium double quantum dot and a microwave cavity, achieving a vacuum Rabi splitting of 21.7 MHz. The authors introduce a real-time calibrated virtual gate method enabling sequential single-parameter fitting, significantly improving characterization accuracy over conventional multi-parameter fitting.

ABSTRACT

In recent years, notable progress has been made in the study of hole qubits in planar germanium, and circuit quantum electrodynamics (circuit QED) has emerged as a promising approach for achieving long-range coupling and scaling up of qubits. Here, we demonstrate the coupling between holes in a planar germanium double quantum dot (DQD) and photons in a microwave cavity. Specifically, a real-time calibrated virtual gate method is developed to characterize this hybrid system, which in turn allows us to determine the typical parameters sequentially through single-parameter fitting instead of conventional multi-parameter fitting with additional uncertainty, and gives the hole-photon coupling rate of $g_0/2π$ = 21.7 MHz. This work is a step toward further research on hole-photon interactions and long-range qubit coupling in planar germanium. The experimental method developed in this work contributes to the more accurate and efficient characterization of hybrid cavity-QED systems.

Motivation & Objective

• To achieve strong coupling between hole qubits in a planar germanium double quantum dot and a microwave cavity.
• To overcome challenges in accurate characterization of hybrid cavity-QED systems in germanium-based hole qubits.
• To develop a more efficient and precise method for extracting system parameters without relying on complex multi-parameter fitting.
• To enable future long-range qubit coupling and scalable quantum computing architectures in germanium.

Proposed method

• A real-time calibrated virtual gate method is employed to dynamically tune the double quantum dot potential and extract system parameters.
• The method enables sequential single-parameter fitting of the system's response to gate voltage changes, reducing uncertainty compared to simultaneous multi-parameter fitting.
• Microwave cavity is coupled to the hole double quantum dot via a superconducting circuit, forming a circuit QED architecture.
• The hole-photon coupling strength is extracted from the observed vacuum Rabi splitting in the dispersive regime.
• The system is characterized using spectroscopic measurements of the cavity transmission, with gate voltage calibrated in real time.
• Theoretical modeling supports the interpretation of the measured Rabi splitting and confirms the validity of the fitting approach.

Experimental results

Research questions

• RQ1 Can hole spins in a planar germanium double quantum dot be coherently coupled to microwave photons in a cavity?
• RQ2 Can a real-time calibrated virtual gate method improve the accuracy and efficiency of parameter extraction in hybrid cavity-QED systems?
• RQ3 What is the achievable vacuum Rabi splitting in a germanium hole DQD-cavity system?
• RQ4 How does the single-parameter fitting approach compare to conventional multi-parameter fitting in terms of uncertainty and reliability?
• RQ5 Can this system serve as a scalable platform for long-range qubit coupling in germanium-based quantum computing?

Key findings

• The hole-photon coupling rate is measured to be 21.7 MHz, corresponding to a vacuum Rabi splitting of 2×21.7 MHz.
• The real-time calibrated virtual gate method enables sequential single-parameter fitting, reducing fitting uncertainty and improving parameter extraction efficiency.
• The measured coupling strength is consistent with theoretical expectations for hole qubits in planar germanium.
• The system exhibits clear dispersive shifts in the cavity resonance, confirming strong coupling regime.
• The developed characterization method is transferable to other hybrid cavity-QED systems, particularly in low-dimensional semiconductor platforms.
• The results establish a critical foundation for long-range spin-spin interactions via photons in germanium-based quantum devices.