Proposal for a cavity-mediated measurement of the exchange interaction in a triple quantum dot

In spin qubit arrays the exchange coupling can be harnessed to implement two-qubit gates and to realize intermediate-range qubit connectivity along a spin bus. In this work, we propose a scheme to characterize the exchange coupling between electrons in adjacent quantum dots. We investigate theoretically the transmission of a microwave resonator coupled to a triple quantum dot occupied by two electrons. We assume that the right quantum dot (QD) is always occupied by one electron while the second electron can tunnel between the left and center QD. If the two electrons are in adjacent dots they interact via the exchange coupling. By means of exact analytical expressions we show that the transmission profile of the resonator directly reveals the value of the exchange coupling strength between two electrons. From perturbation theory up to second order we conclude that the exchange can still be identified in the presence of magnetic gradients. In case of a lifted valley degeneracy prior knowledge about the valley splitting and valley phase differences is important to correctly identify the transmission dips and thus the exchange coupling.