Dynamics of coupled qubits interacting with an off-resonant cavity

We study a model for a pair of qubits that interact with a single off-resonant cavity mode and, in addition, exhibit a direct interqubit coupling. Possible realizations for such a system include coupled superconducting qubits in a line resonator as well as exciton states or electron spin states of quantum dots in a cavity. The emergent dynamical phenomena are strongly dependent on the relative energy scales of the interqubit coupling strength, the coupling strength between qubits and cavity mode, and the cavity mode detuning. We show that the cavity mode dispersion enables a measurement of the state of the coupled-qubit system in the perturbative regime. We discuss the effect of the direct interqubit interaction on a cavity-mediated two-qubit gate. Further, we show that for asymmetric coupling of the two qubits to the cavity, the direct interqubit coupling can be controlled optically via the ac Stark effect.