Quantum Dot Spin Control Improved by Disentangling Orbital and Spin Effects

Researchers are increasingly focused on valence-band hole spins as promising candidates for quantum computing, but strong spin-orbit coupling complicates control of the g-factor, a critical parameter for qubit manipulation. Sommer, Seidler, and Schupp, alongside Paredes, Hendrickx, Massai et al., have now disentangled the orbital and confinement contributions to the g-factor in germanium/silicon-germanium hole quantum dots. Their investigation, utilising excitation and addition spectra, clarifies existing discrepancies in g-factor measurements obtained from different orbital states and hole numbers. Significantly, the team demonstrates a 15% gate-tunability of these g-factors, paving the way for all-electric qubit control and advancing the potential of hole spins in scalable quantum technologies.

Electrical Tuning of Spin-Orbit Interactions in Germanium Quantum Dots

Researchers have achieved a significant advance in controlling spin qubits within germanium quantum dots, demonstrating a 15% tunability of key qubit parameters using only electrical signals. This work addresses a critical challenge in quantum computing, the precise control of qubit behaviour, by disentangling the complex interplay between spin and orbital properties of holes within the semiconductor material.

The study focuses on the out-of-plane g-factor, a parameter that dictates how strongly a qubit responds to magnetic fields, and reveals how it is influenced by both spin and orbital contributions. By employing both excitation and addition spectroscopy, scientists have clarified discrepancies in previously measured g-factor values, accounting for variations arising from different orbital states and hole numbers.

The research centres on germanium/silicon-germanium heterostructures, materials known for their suitability in creating hole quantum dots with low effective mass, simplifying gate design. Investigations into the g-factor were conducted using excitation spectra, which isolate the pure Zeeman effect, the splitting of energy levels in a magnetic field, from orbital influences, despite the strong spin-orbit coupling inherent in valence-band hole systems.

This distinction is crucial for accurately determining the g-factor and understanding its behaviour. Furthermore, the team successfully demonstrated that these g-factors can be modified by as much as 15% through gate voltage adjustments, opening avenues for all-electric qubit manipulation. This level of gate-induced tunability is particularly noteworthy, as it bypasses the need for external magnetic fields, simplifying qubit control and reducing system complexity.

Measurements were performed on two nominally identical double quantum dot devices to ensure the reproducibility of the findings, both fabricated from the same germanium wafer. By meticulously mapping the energy spectrum of individual hole states using Coulomb blockade addition spectroscopy and pulsed excited-state spectroscopy, the researchers were able to separate the contributions of orbital and confinement effects to the g-factor. The resulting data provides a detailed understanding of how these parameters interact, paving the way for more robust and scalable quantum devices.

Double quantum dot device fabrication and spectroscopic characterisation

A planar germanium/silicon-germanium heterostructure incorporating a gate-defined quantum dot served as the foundation for this research. Two nominally identical double quantum dot (DQD) devices, fabricated from the same wafer in separate fabrication runs, were utilised to ensure reproducibility of the experimental findings.

Each device featured two quantum dots positioned beneath plunger gates, P1 and P2, with interdot coupling controlled by a barrier gate, B12. A proximal quantum dot charge sensor detected charge transitions by measuring the differential current between source and drain. To reconstruct the energy spectrum of each quantum dot, Coulomb blockade addition spectroscopy (CBAS) and pulsed excited-state spectroscopy (PESS) were performed.

CBAS measurements were conducted on device 1 as a function of an out-of-plane magnetic field, B⊥, applied perpendicular to the quantum well plane. The plunger gate voltage, VP1, was swept while maintaining fixed values of B⊥, and the derivative of the detector current with respect to VP1 was plotted to identify charge transitions.

These peak positions, delineated by coloured lines, indicated the charge states between them. The occupancy of the first quantum dot was systematically tuned from zero to eight holes while the second quantum dot remained fully depleted. By comparing CBAS and PESS within the same dot, researchers separated the pure Zeeman contribution from orbital effects, clarifying discrepancies between the two methods.

Furthermore, the study explored gate-induced modifications of the g-factor by tuning the confinement potential with virtual gate voltages, VP1 and VP2, demonstrating a tunability level of 15% relevant for all-electric qubit manipulation. This precise control over the g-factor is essential for reliable qubit operation.

Germanium quantum dot g-factors determined by photoluminescence excitation spectroscopy

Excitation and addition spectra of germanium dots reveal out-of-plane g-factors and gate-tunability crucial for spin qubit control. Measurements of the pure spin g-factor, derived from excitation spectra, demonstrate values of approximately 0.48 for both the N = 0 ↔ 1 and N = 1 ↔ 2 regions. These values were obtained by analysing Zeeman splitting of energy levels, yielding a g↑o1−↓o1 and gT0−T− of 0.48 within experimental error.

Comparison with charge-based absorption spectroscopy (CBAS) reveals significant differences in g-factor determination, with CBAS yielding larger values. Specifically, the CBAS g-factor exhibits a discrepancy, while PESS measurements maintain consistency between the two hole number configurations. Analysis of orbital contributions to the g-factors indicates that changes in orbital wave function can contribute up to 10% to the apparent Zeeman splitting.

The energy difference between the first excited and ground orbital states remains approximately constant up to 0.5 Tesla, after which it begins to increase. This suggests that orbital effects systematically deviate from linear fits of the data, influencing the accuracy of g-factor extraction. Furthermore, the study establishes a gate-tunability of g-factors at the level of 15%, demonstrating the potential for all-electric qubit manipulation.

The research details orbital splittings of 2.56 meV for the N = 0 ↔ 1 transition and 1.07 meV for the N = 1 ↔ 2 transition at zero applied magnetic field. These values decrease with increasing hole number due to increased screening of the confinement potential. PESS measurements, combined with CBAS analysis, allow for the extraction of both pure spin and orbital-influenced g-factors, providing a comprehensive understanding of the magnetic properties of these quantum dots. Voltage tuning experiments demonstrate the ability to manipulate the g-factor, paving the way for advanced qubit control schemes.

Distinguishing Orbital and Zeeman Contributions to g-factor in Hole-type Germanium Quantum Dots

Researchers have developed a method to accurately determine the Zeeman g-factor in hole-type germanium quantum dots, separating it from orbital contributions caused by strong spin-orbit coupling. This distinction addresses inconsistencies in g-factor values previously obtained using different measurement techniques, orbital states, and varying numbers of holes within the quantum dot.

Investigations utilising excitation and addition spectra revealed that orbital effects can account for up to 10% of the bare Zeeman splitting within a magnetic field range of 0 to 1 Tesla. Furthermore, the study demonstrates gate-induced tunability of these g-factors, achieving a 15% variation by spatially shifting the quantum dot states.

This tunability suggests a potential pathway for all-electric manipulation of qubit states. The authors acknowledge that accurate g-factor characterisation in hole quantum dots is complex, influenced by factors such as confinement potential changes, screening effects, and electron correlation. Comparisons of g-factor values reported by different research groups require careful consideration of these influences. Future work may focus on exploiting the observed gate-tunability to realise practical all-electric qubit control schemes and further refine the understanding of many-body effects within these quantum dots.