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In spin qubit arrays the exchange coupling can be harnessed to implementtwo-qubit gates and to realize intermediate-range qubit connectivity along aspin bus. In this work, we propose a scheme to characterize the exchangecoupling between electrons in adjacent quantum dots. We investigatetheoretically the transmission of a microwave resonator coupled to a triplequantum dot (TQD) occupied by two electrons. We assume that the right quantumdot (QD) is always occupied by one electron while the second electron cantunnel between the left and center QD. If the two electrons are in adjacentdots they interact via the exchange coupling. By means of analyticalcalculations we show that the transmission profile of the resonator directlyreveals the value of the exchange coupling strength between two electrons. Fromperturbation theory up to second order we conclude that the exchange can stillbe identified in the presence of magnetic gradients. A valley splittingcomparable to the inter-dot tunnel coupling will lead to further modificationsof the cavity transmission dips that also depend on the valley phases.

Proposal for a cavity-induced measurement of the exchange coupling in quantum dots