Effect of Measurement on the Decay Rate of a Quantum System

We investigated the electron tunneling out of a quantum dot in the presence of continuous monitoring by a detector. It is shown that the Schrödinger equation for the whole system can be reduced to new Bloch-type rate equations describing the time development of the detector and the measured system at once. Using these equations we find that the continuous measurement of the unstable system does not affect its exponential decay, $\exp (-\Gamma t)$, contrary to expectations based on the quantum Zeno effect. However, the width of the energy distribution of the tunneling electron is no longer $\Gamma$, but increases due to the decoherence, generated by the detector.