  One of the promising systems to realize quantum computation is a hybrid
system where a superconducting flux qubit plays a role of a quantum processor
and the NV center ensemble is used as a quantum memory. We have theoretically
and experimentally studied the effect of magnetic fields on this hybrid system,
and found that the lifetime of the vacuum Rabi oscillation is improved by
applying a few mT magnetic field to the NV center ensemble. Here, we construct
a theoretical model to reproduce the vacuum Rabi oscillations with/without
magnetic fields applied to the NV centers, and we determine the reason why
magnetic fields can affect the coherent properties of the NV center ensemble.
From our theoretical analysis, we quantitatively show that the magnetic fields
actually suppress the inhomogeneous broadening from the strain in the NV
centers.
