The Zeno effect and relaxation rates in a triple quantum dot system

We study the quantum Zeno effect (QZE) and relaxation rates in a three quantum dot system with a mesoscopic detector near one of the three dots. The evolution of three dot states is analyzed under different conditions. For small energy differences, we find that quantum anti-Zeno effect (QAZE) occurs because measurements cannot localize the electron in the initial dot state at arbitrary voltage or temperature, but accelerate quantum transition of the electron. For large energy gaps, dot states remain the initial values, namely, Zeno effect occurs. With increasing voltage or temperature, the relaxation rates which are related to quantum transition between eigenstates increase. Furthermore, it is demonstrated that they are not absolutely dependent on the eigen energy and the difference of eigen energy. The voltage and temperature play a similar role on the relaxation rates, but a different role on occupation probabilities. In addition, it is proved that the voltage induces relaxation at zero temperature. Moreover, we demonstrate that the change rates of occupation probabilities under eigenstate and dot state are related to the energy differences. In both dot-state and eigenstate representations, the first derivatives of occupation probabilities versus voltage change obviously when the voltage is matched with the difference of eigen energy (We use the unit system of e = kB = ℏ = 1), but the first derivatives of occupation probabilities versus temperature change obviously when the temperature is matched with the difference of dot-state energy. Especially, for large energy gaps, the first derivatives of occupation probabilities versus voltage change rapidly when the voltage is matched with the difference of dot-state energy. The temperatures, at which the first derivatives of occupation probabilities versus temperature change rapidly, are independent of the differences of both dot-state and eigen energy. Graphical abstract