Interplay of Electric Dipole Spin Resonance and Multilevel Landau-Zener Interference in p-Type Silicon Quantum Dots

Abstract: In this work, we examine microwave responses of the Pauli spin blockade (PSB) leakage current through a p-type silicon double quantum dot. We observe more than the expected two resonance lines with the main resonance line exhibits both positive and negative peaks as a function of the magnetic field, corresponding to enhancement and suppression of the PSB leakage current, respectively. We attribute the observed spectra to the interplay between two spin rotation mechanisms: spin-orbit-mediated electric dipole spin resonance (EDSR) and multilevel Landau-Zener (MLLZ) interference, both of which are present in electrically driven devices with strong spin-orbit coupling (and enhanced in the vicinity of orbital level crossings). A numerical simulation taking into account both mechanisms show agreement with the experimental results. While these unconventional spectral behaviours can be readily suppressed away from the orbital level crossing or in devices with weak spin-orbit coupling, our study showcases the potential complexity of spin-rotating mechanisms for electrically driven spin qubits.

• The paper demonstrates that EDSR and MLLZ interference jointly shape complex resonance spectra in p-type silicon double quantum dots, validated through experimental and simulation work.
• It employs microwave spectroscopy and a Lindblad master equation framework to analyze spin transitions influenced by spin-orbit coupling and detuning effects.
• The findings highlight practical trade-offs in device engineering for optimal spin qubit control, emphasizing the impact of interference on qubit fidelity.

Interplay of EDSR and MLLZ Interference in p-Type Silicon Double Quantum Dots

Experimental Framework and Observations

This study investigates spin dynamics in p-type silicon double quantum dots (DQDs), utilizing electrically driven Pauli spin blockade (PSB) transport spectroscopy to reveal the underlying mechanisms for spin manipulation in systems with strong spin-orbit coupling (SOC). The experimental architecture consists of lithographically defined DQDs fabricated on silicon-on-insulator substrates, employing a polysilicon top gate to establish a two-dimensional hole gas and enable fine-tuned electrical control of spin qubits.

Microwave-frequency spectroscopy targeting the PSB leakage current exhibits marked deviations from typical resonances attributed solely to electric dipole spin resonance (EDSR). Specifically, at low interdot detuning, the spectrum reveals three resonance lines; the principal resonance demonstrates an asymmetric peak-and-dip structure, contrary to the canonical pair of symmetric peaks. In contrast, at high detuning, only a single peak resonance is detected. These observations cannot be ascribed to either SOC-driven EDSR or multilevel Landau-Zener (MLLZ) interference in isolation and indicate a regime where both mechanisms simultaneously modulate spin transitions.

Theoretical Interpretation: EDSR–MLLZ Coupling

The experimental anomalies are addressed through simulations incorporating both EDSR and MLLZ dynamics within a Lindblad master equation framework for DQD charge and spin states. The system Hamiltonian includes Zeeman splitting (with extracted $g$-factors: $g_R = 1.18$, $g_L = 0.895$), complex tunnel couplings ($t_x, t_y, t_z, t_c$), and time-dependent driving terms accounting for both effective magnetic fields (EDSR) and detuning oscillations (MLLZ).

EDSR in this p-type silicon architecture arises from SOC, which facilitates all-electrical spin rotations via an AC electric field, leveraging the SOC-induced mixing of spin and orbital degrees of freedom. MLLZ interference emerges as the AC field modulates interdot detuning, generating transitions between two spin states via a mediating third level, with the effect amplified near zero detuning due to enhanced anticrossings.

Numerical simulations reproduce the following strong empirical features:

• Multiple resonance lines at low detuning, with a central line exhibiting a nontrivial asymmetric peak-dip signature, and additional dip lines, consistent with the joint action of both mechanisms.
• Suppression of MLLZ features at large detuning, yielding a single peak resonance, indicative of dominant EDSR behavior in this regime.

Fits with models omitting either EDSR or MLLZ fail to capture the observed spectral line asymmetry and multiplicity, confirming the necessity of including both processes.

Mechanistic Analysis and Line-Shape Origin

In low-detuning conditions, the simulated transitions correspond to:

• An EDSR-induced peak (spin rotation primarily in the right dot)
• MLLZ dips (including left-dot spin transitions and dark Bell-state generation via two-photon processes near average Zeeman splitting)

The asymmetric peak-dip line shape at the main resonance arises from the constructive and destructive quantum interference between EDSR and MLLZ pathways. Simulations demonstrate that the relative dominance of these processes depends sensitively on the detuning and the amplitude of the driving fields. The effective suppression of MLLZ phenomena outside the anticrossing regime underscores the detuning dependence of interference effects.

Some discrepancies remain between experimental and simulated line widths and slopes, potentially attributable to contributions from nonideal auxiliary states (e.g., dark Bell states, parasitic dots, or excited hole states) not included in the minimal four-state system model. The paper discusses the possibility of dark Bell states as alternative origins for the sharp dip features but finds their contribution insufficient to fully explain the spectra in the absence of combined EDSR and MLLZ coupling.

Implications for Spin Qubit Control and Future Directions

The results underscore the importance of accounting for the interplay between EDSR and MLLZ interference in future strategies for electrically driven spin manipulation. The presence of nontrivial spectral features, particularly in the vicinity of zero detuning, implies that coherent control protocols leveraging pure EDSR may become unwieldy or unreliable under conditions where MLLZ processes are non-negligible. This is especially pertinent for multi-qubit gate implementations, such as two-qubit controlled-rotation gates, which often operate near energy-level anticrossings.

The study suggests that refined device engineering—either by detuning operation points away from anticrossings or by mitigating SOC strength—can suppress unwanted MLLZ features, but this may come at the cost of reduced EDSR efficiency. Optimizing spin-qubit fidelity and scaling in silicon platforms will require comprehensive understanding and control of both mechanisms.

Subsequent research should focus on quantitatively resolving the contributions of higher-excited and parasitic states, developing robust error models for quantum control sequences subject to EDSR–MLLZ interplay, and exploring the impact in more complex architectures and material systems.

Conclusion

This work demonstrates that the microwave response of PSB leakage current in p-type silicon DQDs is governed by the coexistence and interplay of SOC-mediated EDSR and MLLZ interference, both of which are electrically driven phenomena enhanced near orbital level crossings. The combined experimental and numerical results challenge simple interpretations of resonance spectra and call for a reevaluation of control schemes for silicon spin qubits in regimes of strong SOC. The insights provided herein will inform the design and operation of next-generation silicon quantum processors, emphasizing the crucial role of complex quantum interference effects in scalable qubit architectures.

Reference: "Interplay of Electric Dipole Spin Resonance and Multilevel Landau-Zener Interference in p-Type Silicon Quantum Dots" (2603.29164)