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

kelly0303
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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 Schrodinger 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!
 
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kelly0303 said:
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:
gentzen said:
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:
gentzen said:
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".
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!
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