Theory of the microwave spectroscopy of a phosphorus-donor charge qubit in silicon: Coherent control in the Si:P quantum-computer architecture

We present a theoretical analysis of a microwave spectroscopy experiment on a charge qubit defined by a ${\mathrm{P}}_{2}^{+}$ donor pair in silicon, for which we calculate Hamiltonian parameters using the effective-mass theory of shallow donors. The master equation of the driven system in a dissipative system is solved to predict experimental outcomes. We describe how to calculate physical parameters of the system from such experimental results, including the dephasing time, ${T}_{2}$, and the ratio of the resonant Rabi frequency to the relaxation rate. Finally we calculate probability distributions for experimentally relevant system parameters for a particular fabrication regime.