Capturing an electron during a virtual transition via continuous measurement

We study a Triple Quantum Dot (TQD) setup with the Left dot (L) and the Right dot (R) attached to separate thermal baths, while the Central dot (C) is being continuously measured. L and R have the same energy while C is at a higher energy with the detuning being much higher than the hopping rate between L and C, or C and R. Therefore, C does not hybridize with the other two, leading to a small occupation. Nevertheless, direct tunneling between the outer dots is possible via virtual transitions involving C. The key question we would like to answer is whether C is occupied or not during a virtual transition when it is being explicitly monitored. We will look at the stochastic time evolution of the central dot occupation and the current through the TQD setup. We will investigate this problem in two different limits of continuous measurements: the stochastic quantum diffusion and the discrete quantum jumps.