Influence of measurement on the lifetime and the linewidth of unstable systems - art. no. 032102

We investigate the quantum Zeno effect in the case of electron tunneling ou t of a quantum dot in the presence of continuous monitoring by a detector. It is shown that the Schrodinger equation for the-whole system can be reduc ed to Bloch-type rate equations describing the combined time development of the detector and the measured system. Using these equations we find that c ontinuous measurement of the unstable system does not affect its exponentia l decay to a reservoir with a constant density of states. The width of the energy distribution of the tunneling electron, however, is not equal to the inverse lifetime-it increases due to the decoherence generated by the dete ctor. We extend the analysis to the case of a reservoir described by an ene rgy-dependent density of states, and we show that continuous measurement of such quantum systems affects both the exponential decay rate and the energ y distribution, The decay does not always slow down, but might be accelerat ed The energy distribution of the tunneling electron may reveal the lines i nvisible before the measurement.