The shift in phase response of the reflected signal, as shown in Fig. 2B, is ascribed to the addition of a quantum capacitance (CQ) to the LC circuit (2225) when holes can tunnel between the two atoms, given byEmbedded Image(3)where ΔαTG is the difference in capacitive coupling from the top gate to each acceptor (found to be 0.14 eV/V in the transport measurements), q is the electron charge, ε is the energy detuning between the two acceptors, and t is the tunnel coupling between the (1,1) and (2,0) S states. All other tunnel couplings between the (1,1) and (2,0) states are considered to be much smaller and therefore not contributing to a change in the detected reflected signal. The total phase shift (Δϕ) was determined by the difference in occupation, given by the Boltzmann distribution, of the lower and upper branches of the heavy hole singlet state (35)Embedded Image(4)where ES− and ES+ are the energies of the bonding and antibonding singlet states, respectively, and Ei describes the energies of all the involved states. Using Eqs. 3 and 4, the magnetic field dependence of the phase shift caused by the interacceptor tunneling was calculated, as shown in Fig. 2C. We note that, although the crossing of the Q state and the S state has some influence on the Boltzmann distribution of the S states, this influence is not distinguishable in the measurement. However, for completeness, we displayed the BSQ crossing point in Fig. 2C, as found in the relaxation hotspot measurement, together with an estimated g factor of the Q state.

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