# How to measure a mapped phase

1. Jan 8, 2014

### Verdict

I had a question regarding some text in a paper that I was reading. It had to do with ramsey interferometry, where they initialized a particle in spin up (lets say up along the z axis on the bloch sphere), after which they applied a pi/2 pulse to rotate it 90 degrees around the x-axis, they wait a time tau. Now, the applied RF pulses are off resonant, so in the rotating frame of the RF, the particle precesses around the z-axis in a superposition in the x-y plane. It does so with a frequency equal to the difference of the Rabi frequency of the particle and the frequency of the RF pulse, so the superposition picks up a phase related to this Rabi frequency times tau, which the experiment wanted to determine. (The rabi frequency).

The experiment then goes on to say they apply yet another pi/2 pulse to rotate by 90 degrees around the x axis, after which the accumulated phase is mapped onto the population of the spin up and down states. The paper then says that this phase can be measured.

My question is quite literally, how can this phase be measured? there is no mention of it in the paper, and I simply do not know how this is done. I'd be very grateful if someone would be able to explain to me how they measure this phase.

The paper is http://www.nature.com/nnano/journal/v7/n2/full/nnano.2011.225.html and the section I am talking about is in the methods section, in case it is not clear what I am describing.

Last edited by a moderator: May 6, 2017
2. Jan 8, 2014

### Cthugha

Don't they just measure the population of the spin up and down states? Have you had a look at the supplementary information? They discuss some more details there.

3. Jan 8, 2014

### Verdict

Hmm, I did indeed not read that one yet. If I understand correctly, what they do is before the sequence of pulses they measure the fluorescence, and then they do this again afterwards, repeat this many many times and from this they deduce the relative population of spin up and spin down, which again tells them what the phase is?

I apologize for my simple questions, I am very new to the subject and I am simply trying to get an intuitive overview for myself, which has not been trivial thus far.

4. Jan 9, 2014

### naima

I did not read the paper but i think that the solution is as usual in the formula:
P(v->u) = cos² (phi) where phi is the phase of the unitary vectors u and v.