  We apply magnetic fields of up to 7 T to an indium arsenide (InAs) quantum
dot (QD) strongly coupled to a photonic crystal cavity. The field lifts the
degeneracy of QD exciton spin states, and tune their emission energy by a
combination of diamagnetic and Zeeman energy shifts. We use magnetic field
tuning to shift the energies of the two spin states to be selectively on
resonance with the cavity. Strong coupling between the cavity and both spin
states is observed. Magnetic field tuning enables energy shifts as large as
0.83 meV without significant degradation of the QD-cavity coupling strength.
