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Okay, so last time we went over some of the general features and attractions of the Indy

Center as having a coherent spin.

And we also went over some of the level structures, particularly the ground state, the fact that

there's a ground state spin and a fixed state spin.

So all we know so far is that we have a ground state spin on the three degenerate levels

in the spin driven.

We know the excited state, the six degenerate levels.

Or what we know so far is the six degenerate levels, so we can have a spin triplet and

a probable spin of three times six.

And in fact, they're not degenerate, so we'll look at that quickly today.

And also, importantly, in the beginning, today we're going to look at the susceptibility

of the Indy's energy levels to where it's getting stuck in the dynamic of the strain

in the electric field and get some idea of the numbers.

So last time I wrote down, thinking of the ground state, I'm not talking about the ground

state in the spin, that orbital spin, spin triplet in the ground state.

So I'm not going to go into that.

I'm going to go over these terms.

So this element here is the only part of this Hamiltonian that is intrinsic to the diamond.

So the absence of any applied external fields, magnetic fields, this would be our magnetic

field.

This pi is, I'll define in a second, but that's a combination of electric fields and strain.

So in the absence of any applied electric magnetic and strain fields, all we have in

our home in Hamiltonian, so no field, is z, ds, s, z squared.

So if we look at what that does, here s, z is the Pali spin operator for spin one, because

it's a spin operator in the ground state.

And this is what's often called the zero field splitting, if one can think, that what this

does is it gives us one thing between the zero spin projection and the triplet, and

the plus and minus one, which I did that right.

So plus and minus one squared are the same, but zero squared is different.

So it gives us splitting of d, ds.

And physically, this comes, this ground state, ground state field splitting comes from spin

to spin interactions between your two objects.

And one thing, I think that previously, we're not going to go through that, actually one

has to be a lot of the root for your arguments, but we'll go through that as well.

But short stories, when you ask somebody field, in principle, what your ground state energy

manifold looks like.

And so this is sort of nice to begin with, because you already have a splitting for a

field, normally when you have a spin, maybe just an atomic spin, like an atom, a spin,

you have to apply that in a field in order to get a split.

So the fact that we already have a splitting between these two states is nice.

OK.

So this is the intrinsic part.

And all the rest are extrinsic.

So let's first do the magnetic field of the reaction, because that's the simplest.

So b, and then apply the magnetic field gamma to our magnetic ratio on gamma s, which is

the spin operator for our triplet.

And this is basically just a Zeeman split.