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Exchange interaction in gate-defined quantum dots beyond the Hubbard model

Willmes, Alexander, Bethke, Patrick, Shehata, Mohamed Mohamed El Kordy, Simion, George E, Wolfe, Michael A., Botzem, Tim, McNeil, Robert, Ritzmann, Julian, Arne Ludwig, Andreas Dirk Wieck

Published Nov 26, 2025• 1 citation
Publisher
DOI
10.5281/zenodo.17722981

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A quantitative description of the exchange interaction in quantum dots is relevant for modeling gate operations of spin qubits. By measuring the amplitude and frequency of exchange-driven qubit state oscillations, we measure the detuning dependence of the exchange coupling in a GaAs double quantum dot over three orders of magnitude. Both 1D and 3D full configuration interaction simulations can replicate the observed behavior. Extending a Hubbard model by including excited states increases the range of detuning where it provides a good fit, thus elucidating the underlying physics.
We present a theory for understanding the exchange interaction between electron spins in neighboring quantum dots, either by changing the detuning of the two quantum dots or independently tuning the tunneling barrier between quantum dots. The Hubbard model and a more realistic confining-potential model are used to investigate how the tilting and barrier control affect the effective exchange coupling and thus the gate fidelity in both the detuning and symmetric regimes. We show that the exchange coupling is less sensitive to the charge noise through tunnel barrier control (while allowing for exchange coupling operations on a sweet spot where the exchange interaction has zero derivative with respect to the detuning). Both GaAs and Si quantum dots are considered, and we compare our results with experimental data showing qualitative agreements. Our results answer the open question of why barrier gates are preferable to tilt gates for exchange-based gate operations.
Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases.Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains.In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted.Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers.To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required.Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array.We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met.Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian.Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlettriplet measurements on each nearest-neighbor pair and the correlations therein.The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.