Understanding the Quantum Zeno Effect (QZE)

[James MC]

Hi there, I'm trying to understand the Quantum Zeno Effect (QZE) but am coming across some difficulties.

A common experiment used to illustrate the effect uses polarization directions of photons (http://arxiv.org/abs/1211.3498). The photons are either "vertical" or "horizontal", but one can "rotate" their polarisation direction (e.g. "by 15 degrees"). Here, one sends vertical photons down a path of six rotators (so you eventually get a 90 degree turn and hence state transition), before the photon is measured by a polarizer, which absorbs horizontal photons, transmits vertical. Now the goal is to inhibit transition from vertical to horizontal. One does this simply by measuring the polarisation after each rotator interaction (with another polarizer). The polarizer after the first rotator will re-transmit the photon down the path (with some probability?), and apparently it can be shown that if one increases the number of stages, decreasing "rotation angle" at each stage, probability of transmission to final detector increases. If there were an infinite number of stages rotation is completely inhibited yielding QZE.

If the photons can only be "vertical" or "horizontal", then how can one rotate them just by 15 degrees? What exactly do the rotators do to the photons? Do they put them into a superposition of being vertical (with high amplitude) and being horizontal (with low amp)? Then I could see how continuous measurement (collapse) would inhibit state transition. But then why call such superpositions "rotations"?

Please help! :)

 

[mfb]

If the photons can only be "vertical" or "horizontal", then how can one rotate them just by 15 degrees?

The photons can only be measured as vertical or horizontal in a vertical (or horizontal) polarizer. They can have a different orientation, and you can measure a different orientation, but that is not done here.

Do they put them into a superposition of being vertical (with high amplitude) and being horizontal (with low amp)?

Yes, that is an alternative description of a photon rotated by 15 degrees. The two components have a specific phase relation, leading to those 15 degrees.

 

[James MC]

Thanks, I now see how QZE works in this case: rotators cause photon to enter into superposition of (high amp) vertical and (low amp) horizontal; the quicker the subsequent polarisation measurement, the lower the probability of collapse into horizontal state; taking the limit horizontal collapse becomes impossible --> QZE.

I was confused as to why this superposing is called "rotating". But I think I get it now: when the rotator's "rotate by 15 degrees" they only superpose the photons in the orientation of the polarizer's used in the experiment; but such "rotated" photons will actually be in eigenstates of vertial/horizontal for a polarizer that is rotated by 15 degrees? Then it would be analogous to spin, where particle is only spin-up or spin-down in some direction, and in that case, superposed given a different direction.

 

[mfb]

I was confused as to why this superposing is called "rotating". But I think I get it now: when the rotator's "rotate by 15 degrees" they only superpose the photons in the orientation of the polarizer's used in the experiment; but such "rotated" photons will actually be in eigenstates of vertial/horizontal for a polarizer that is rotated by 15 degrees? Then it would be analogous to spin, where particle is only spin-up or spin-down in some direction, and in that case, superposed given a different direction.

Exactly.