Quantum Zeno Effect and quantum decay

[Talisman]

Quantum Zeno Effect and quantum "decay"

Howdy,

My understanding of QM is mostly mathematical (I have a basic understanding of the Hamiltonian of something like the particle in the box, and the rest of what I know is from Quantum Information Science, with very little physics knowledge), so please go easy on me :)

In reading about the QZE on Wikipedia, they talk about "quantum decay." My understanding is that it should apply equally well to a simple system like a qubit whose state vector is slowly rotating around C^2 (not that I have any idea what the physical realization of such a system might be): successive measurements on it should collapse it to its initial eigenstate, if frequent enough.

So, what is quantum "decay," and why do they use it exclusively in QZE examples?

Thanks!
Talisman

 

[WesleyForest]

Hello,

Apologies in advance as I have, but cannot find the original QZE paper - which would probably help.
Anyway, the QZE is named in reference to Zeno's paradoxes (probably the dichotomy paradox).
The dichotomy paradox has that to travel half way somewhere you must first travel a quarter of the way, to travel a quarter of the way you must first travel and eighth of the way ... and so on. So in the end you will need to have done infinite parts of the journey - needing infinite time.
For the QZE a particle has been made that will decay with a certain probability. With that probability in mind we can measure the particle after time, T, and find it not decayed. After that measurement we do another measurement after time T/2 and it will still not have decayed. And so on with T/4, T/8 ...
So decay is analogous to the final destination.

And when we say "decay" we mean radioactive decay changing the particle into another - e.g. Alpha.

Hope that helped!
@WesleyForest

 

[Talisman]

Thanks Wesley. Let me try to rephrase my question. I bungled it last time.

Suppose we have a qubit whose state over time is given by:

Psi(t) = sin(t) |0> + cos(t) |1>

(Not that I have any idea if such a thing exists in reality). Then quick successive measurements will leave the particle in state |1>.

How does this look for radioactive decay (thanks for pointing out it was radioactive decay, btw)? I suppose I could think of |1> as un-decayed and |0> as decayed, and then the time evolution is simply the usual exponential decay function. I'm just trying to frame QZE for decay in a familiar way (like the qubit example).

[Actually, I just came upon this blog post which may explain it: http://carlbrannen.wordpress.com/2008/04/09/the-quantum-zeno-paradox-or-effect/]

[edit: btw, one thing that was confusing me was talk of the particle's state decaying. I wasn't sure if this was something different from its state evolving)

 

[Talisman]

A ha! It turns out that my "random" example describes the evolution of an electron's magnetic moment in a magnetic field (Larmor precession). Line up a bunch of Stern-Gerlach devices, and you get QZE.