  We investigate magnetic-field influenced time-dependent transport of Coulomb
interacting electrons through a two-dimensional quantum ring in an
electromagnetic cavity under non-equilibrium conditions described by a
time-convolutionless non-Markovian master equation formalism. We take into
account the full electromagnetic interaction of electrons and cavity photons
without resorting to the rotating wave approximation or reduction to two
levels. A bias voltage is applied to semi-infinite leads along the x-axis,
which are connected to the quantum ring. The magnetic field is tunable to
manipulate the time-dependent electron transport coupled to a photon field with
either x- or y-polarization. We find that the lead-system-lead current is
strongly suppressed by the y-polarized photon field at magnetic field with two
flux quanta due to a degeneracy of the many-body energy spectrum of the mostly
occupied states. Furthermore, the current can be significantly enhanced by the
y-polarized field at magnetic field with half integer flux quanta.
