It is my understanding so far that in this kind of experiments like the one measuring the 4π (i.e. 720° Dirac Belt trick) rotation characteristic of 1/2 spin fermions like neutrons, two neutron beams are polarized via S-G apparatus to the same quantum spin number. The two separated polarized beams are initially in phase meaning identical in every aspect. Continuing, one of the two beams is then brought out of phase from the other by forcing it to continuous Larmor precession while the other beam is not forced to precess. The two beams are then combined together in superposition and a interference signal is obtained.
I understand that because in the one beam the neutrons are wobbling all the time (Larmor precession) most of the time the beams are never in phase and don't have all four quantum numbers identical and therefore the Pauli's exclusion principle is not violated. Therefore, most of the time a steady noise interference output signal is produced of the two neutron beams combined.
However, as these experiments show for every 4π of Larmor rotation period, the two beams get momentarily in phase and a maxima in the signal output is generated due constructive interference:
My question here is, at the points where the maxima in the interference signal are observed as shown above, meaning the two beams are monetarily in phase, do these events not violate the Pauli's exclusion principle?
The best explanation I could find so far in the literature to resolve my confusion is that mathematically this means the wavefunctions of the two combined fermions must be antisymmetric (antiparallel spin) which leads to the probability amplitude of the interference wavefunction going to a zero maxima if the two fermionic particle beams are in the same phase.
Thus according to the above interpretation IMO the signal output will be like this:
But then how can be the two beams be in phase and at the same time having a destructive interference? And most importantly, if the two neutron beams combined end up having anti parallel spin because the Pauli's exclusion principle, how then can these experiments measure the 720° rotation Dirac Belt trick characteristic of these fermions (i.e. neutrons)?
Would that not totally mess up the experiment?
I'm confused, please help.
A step by step procedure description of such an experiment example to measure the 4π phase characteristic of the neutron would be most beneficial for a general audience to understand how this measurement is carried out and therefore why the Pauli's exclusion principle is not violated in this experiment.