B How does sideband detection work in a Penning trap?

[joegibs]

http://depts.washington.edu/uwptms/research.html
I'm having a hard time understanding how the sideband detection works. They say that they use an rf drive to observe the particle in the trap. But what is an rf drive and how does it observe the particle? Also, when this rf drive is put into the penning trap, does the particle's positional wave function collapse, or is it still uncertain?

 

[Nugatory]

http://depts.washington.edu/uwptms/research.html
I'm having a hard time understanding how the sideband detection works. They say that they use an rf drive to observe the particle in the trap. But what is an rf drive and how does it observe the particle?

"RF" is an acronym for "radio frequency", and an RF drive is just about any electronic device that oscillates at and radiates at these frequencies. We can learn a fair amount about a charged particle in a Penning trap or other potential well by observing whether it resonates when exposed to ("driven by") such radiation. "Sideband detection" is described in the paper that was linked in one of your earlier threads. It is a clever technique for ensuring that the weak signal from thh oscillation of the driven particle is not overwhelmed by the much stronger signal from the RF driver itself.

Also, when this rf drive is put into the penning trap, does the particle's positional wave function collapse, or is it still uncertain?

I have no idea what you mean by a "positional" wave function - it's the same wave function no matter what basis you write it in.

However, this and some of your other questions leave me thinking that you still misunderstand how position measurements work. The position operator has a continuous spectrum so its eigenfunctions are not physically realizable (from a formal mathematical perspective, they don't exist at all; we have to introduce the concept of the "rigged Hilbert space" to save the formalism). Thus, there is no such thing as a position measurement that collapses the wave function down to a definite position because there are no physically realizable states of definite position. After the measurement the position still isn't definite, we're just more likely to find the particle in a smaller region of space next time we look than before we measured; the wave function is more sharply peaked than it was before. Putting the particle in a Penning trap narrows the region of space in which the particle might be found, but no matter how small the trap is we still don't have a definite position.

 

[PeterDonis]

Putting the particle in a Penning trap narrows the region of space in which the particle might be found

To clarify one point: this happens when the particle initially goes into the trap, but as I understand it, once it's in the trap there is no additional narrowing of the region of space where the particle is; i.e., things like sideband detection do not affect the "spread" of the wave function in position space once the particle is confined in the trap.