We show how the switching-on of an electron transport through a system of two parallel quantum dots embedded in a short quantum wire in a photon cavity can trigger coupled Rabi and collective electron-photon oscillations. We select the initial state of the system to be an eigenstate of the closed system containing two Coulomb interacting electrons with possibly few photons of a single cavity mode. The many-level quantum dots are described by a continuous potential. The Coulomb interaction and the para- and dia-magnetic electron-photon interactions are treated by exact diagonalization in a truncated Fock-space. To identify the collective modes the results are compared for an open and a closed system with respect to the coupling to external electron reservoirs, or leads. We demonstrate that the vacuum Rabi oscillations can be seen in transport quantities as the current in and out of the system.
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