Real-time detection of single electron tunneling through a T-shaped double quantum dot is simulated, based on a Monte Carlo scheme. The double dot is embedded in a dissipative environment and the presence of electrons on the double dot is detected with a nearby quantum point contact. We demonstrate directly the bunching behavior in electron transport, which leads eventually to a super-Poissonian noise. Particularly, in the context of full counting statistics, we investigate the essential difference between the dephasing mechanisms induced by the quantum point contact detection and the coupling to the external phonon bath. A number of intriguing noise features associated with various transport mechanisms are revealed.
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