Dispersive readout of valley splittings in cavity-coupled silicon quantum dots

The band structure of bulk silicon has a sixfold valley degeneracy. Strain in the Si/SiGe quantum well system partially lifts the valley degeneracy, but the materials factors that set the splitting of the two lowest lying valleys are still under intense investigation. Using cavity input-output theory, we propose a method for accurately determining the valley splitting in Si/SiGe double quantum dots embedded in a superconducting microwave resonator. We show that low lying valley states in the double quantum dot energy level spectrum lead to readily observable features in the cavity transmission. These features generate a "fingerprint" of the microscopic energy level structure of a semiconductor double quantum dot, providing useful information on valley splittings and intervalley coupling rates.