Graduate How Are Rotations on the Bloch Sphere Implemented in Practice?

[kelly0303]

Hello! I am curious about how different rotations on the Bloch sphere are done in practice. For example, assuming we start in the lower energy state of the z-axis (call it |0>), a resonant rotation on the Bloch sphere by $\pi/2$ around the x-axis will take you to $\frac{|0>-i|1>}{\sqrt{2}}$ (where $|1>$ is the excited state in the z direction). If we do the same thing around the y-axis we end up with $\frac{|0>-|1>}{\sqrt{2}}$. This phase difference matters in practice in various scenarios (e.g. when doing a spin echo). But how do you change the rotation axis in practive? The field applied in the lab frame is $E\cos{(\omega t + \phi)}$. You can make $\omega$ resonant and $E$ such that you get a $\pi/2$ pulse for the right time, but if you solve the Schrödinger equation in the rotating wave approximation, the $\phi$ term actually cancels in the final formula, so I am not sure what other degrees of freedom one has in order to achieve this. Thank you!

 

[gentzen]

Hello! I am curious about how different rotations on the Bloch sphere are done in practice.

It is different for photons (polarization), and for particles with a magnetic moment (spin). I recently fell into that trap:

Well, I was thinking mostly in terms of optics and polarization. A more correct translation of that situation to an electron is that the spin states perpendicular to the direction of propagation are much easier to measure directly (by Stern-Gerlach type experiments) than the ones parallel to the direction of propagation.
[...]
My optics analogies were wrong, but the distinctions they suggested still remain somewhat true for electrons: Even so it seems easy to change the direction of propagation of a "particle" from y-direction to x-direction, it is only "theoretically easy" to do so without changing the spin in case the "particle" is not electrically neutral. But in that case, the Stern-Gerlach type experiment itself becomes difficult.

Let me be clear that my optical analogies had been more wrong than I was aware of. And because they were wrong, my post that you corrected was certainly confusing, both for experts and novices.

I am not sure how to exactly do it for particles with a magnetic moment. My guess is:

But maybe one could use Lamor precession to rotate the spin of the "particle" instead of the direction of propagation. At least it seems possible "theoretically".