[Unitary Hack][quera] Z2 phase prep explanation and Rydberg density heat map plot

[qmanning4]

I've added some explanation for defining the Rabi amplitude and detuning values. I've limited the explanation of the new detuning values as necessary for maintaining a characteristic blockade radius of $a < R_b < 2a$ for the Z2 phase. Perhaps it was also empirically found that defining a detuning value of 16.33 MHz maximizes Z2 state probability? Requiring $a = R_b / \sqrt{2}$ suggests we should set the lattice constant to about 5.57 micrometers which is not the case in our program. I'm unsure of the band structure for this problem, but perhaps we can validly throw away the blockade-violated states for this configuration even though our lattice constant is a bit large?

[Roger-luo]

@johnzl-777 has this been reviewed or not?

[johnzl-777]

@Roger-luo @weinbe58 and I took a look and it looks good!

To answer @qmanning4 's questions: It's quite likely the value was empirically found, one of the approaches to developing adiabatic protocols is to put the largest Rabi amplitude possible and then tweak the detuning value to achieve some optimal result (:

As for your second question I'm not entirely sure but it could be that this approach to the adiabatic protocol in particular allows for such behavior. Let me ask an expert here at QuEra and get back to you

[qmanning4]

@johnzl-777 Thanks very much for your response. Makes sense! I'd be interested to see what the band structure looks like.