Questions to the quantum Zeno effect

Question

I have some questions regarding the quantum Zeno effect (QZE). It is known that this effect occurs, when a system interacts strongly to its environment (one says that there are done measurements extremely frequently). In the opposite case, if no interaction with environment takes place, the system may evolve coherent due to no environment interactions that can decohere quantum states.

Questions:

i) The conditions, where QZE applies, is a very small time uncertainty $\Delta t$, implying that the energy uncertainty $\Delta E$ is large in this case. That means that the system gets into a quantum state superposition of different energy states. Will there be a coherence (high energy uncertainty) despite very intense interaction with the environment? Will there be more quantum fluctuations in case of frequent interaction than in not so frequent interaction (the system behaves less classical)?

ii) Electron-positron pairs can be created for a very short time interval. Can QZE slow this process down so much that electron-positron-pairs live a lot longer than without frequent measurements?

iii) Frequent interactions will make a strong entanglement with the environment. Is it possible to transfer information from the environment to the system or back easier in the case of frequent measurements?

Answer 1

i-a) Interaction (strong and weak) with an environment generally add random phases to the state of the system. This is what is called decoherence. High energy uncertainty can exists in a system that is both evolving coherently and incoherently (with random phases due to interaction with the environment)

i-b) Large quantum fluctuations can exists both a system which is decoupled to an environment and one that is strongly coupled. A weakly coupled environment will in evolve mostly independent from the system. This evolution will appear random to the system and the coupling to the bath will induce statistical or thermal fluctuations. So in general an environment coupled such that there is the quantum zeno effect will have more thermal fluctuations in the weak coupling limit. The amount of quantum fluctuations in both cases will depend on your system.

ii) In general, yes, but a major issue will be measuring the positron with out annihilating it with a different electron. The best situation I could think of is, taking positronium, (an electron and positron orbiting each other) and continuously measure it's angular momentum. You could possibly do this by putting it in an magnetic field and tracking it's motion by continuously shining light on it. But how you shined and measured the light would determine how strongly coupled and you would have to worry about exciting/exciting it in the right way. But it could be possible to delay the decay of positronium by continuously measuring it in a similar way.

iii) In the quantum zeno effect, your essentially collapsing the system into one state. So your minimizing the entropy or the information required to represent that state. But once you turn on the interaction with the environment, it will be quite difficult to recover your original state regardless of the interaction strength. The reason being is that with a large enough environment, the system and the environment will evolve chaotically and the information about the initial state will be lost in the large size of the environment. If the environment is small enough or has some special properties you could see the original state reappear after long enough time. This is called collapse and revival and depends more on the nature of the bath then the strength of coupling.