Probing exchange interaction for gate-defined double quantum dots

The exchange interaction J is vital for gating in electron-spin qubits. Therefore, understanding its behavior is crucial for high-fidelity gating, especially at low J where an inability to turn it off completely may impact the fidelity of parallel qubit operations. Historically, the exchange interaction (controlled via detuning ε between dots) measured in experiment, J(ε) ∝ exp(−ε/ ε₀) [1-2], has deviated from Hubbard-based predictions, J(ε) ∝ 1/|ε|.
We present measurements of J down to values below 1MHz by controlling the nuclear magnetic field gradient ΔB_z in a GaAs double quantum dot. When ΔB_z becomes comparable to J the visibility of the S-T₀ precession is reduced. Fitting the relation between oscillation amplitude and frequency allows the extraction of J(ε). In combination with Ramsey-like experiments we measure J(ε) over three orders of magnitude.
Our results can be reproduced by a microscopic model including excited states in each dot and state-dependent tunnel coupling. Some parameters in the Hamiltonian, e.g. ground-state tunneling, excited-state tunneling, S-T₀ splitting, can be measured independently and are found to be reasonably consistent with the model.
[1] O. E. Dial et al., Phys. Rev. Lett. 14, 146804 (2013)
[2] T. F. Watson et al., arXiv:1708.04214 (2017)