  We explore a possibility of measuring deviation from the exponential decay
law in pure quantum systems. The power law behavior at late times of decay time
profile is predicted in quantum mechanics, and has been experimentally
attempted to detect, but with failures except a claim in an open system. It is
found that electron tunneling from resonance state confined in man-made atoms,
quantum dots, has a good chance of detecting the deviation and testing
theoretical predictions. How initial unstable state is prepared influences
greatly the time profile of decay law, and this can be used to set the onset
time of the power law at earlier times. Comparison with similar process of
nuclear alpha decay to discover the deviation is discussed, to explain why
there exists a difficulty in this case.
