  We study electron transport through double quantum dots (DQD) coupled to a
cavity with a single photon mode. The DQD is connected to two electron
reservoirs, and the total system is under an external perpendicular magnetic
field. The DQD system exhibits a complex multi-level energy spectrum. By
varying the photon energy, several anti-crossings between photon dressed
electron states of the DQD-cavity system are found at low strength of the
magnetic field. The anti-crossings are identified as multiple Rabi resonances
arising from the photon exchange between these states. As the results, a dip in
the current is seen caused by the multiple Rabi resonances. By increasing the
strength of the external magnetic field, a dislocation of the current dip to a
lower photon energy is found and the current dip can be diminished. The
interplay of the strength of the magnetic field and the geometry of the states
the DQD system can weaken the multiple Rabi resonances in which the exchange of
photon between the anti-crossings is decreased. We can therefore confirm that
the electron transport behavior in the DQD-cavity system can be controlled by
manipulating the external magnetic field and the photon cavity parameters.
