## State representation in Spinach

Topics related to Spinach package
faq_user
Posts: 49
Joined: Tue Jul 13, 2021 8:33 am

### State representation in Spinach

I have a question about the state representation in spinach.

First, let me start by thanking you, it is a great tool. We are using it for simulating an experiment that we are implementing and it is incredibly helpful.

We are using sphten-liouv basis for a 3-spin system. The state is an array with 64 elements. According to the documentation, these should be the coefficients of the product of the Pauli operators. But I am trying to figure out the order of the operators. For instance, is the second element the coefficient for I * I * X or X * I * I or something else?

Your help and time are much appreciated.
kuprov
Posts: 125
Joined: Mon Mar 29, 2021 4:26 pm

### Re: State representation in Spinach

They are not quite Pauli operators, they are combinations called Irreducible Spherical Tensors. This is because spins higher than ½ also have operators like Sx^2, and then the most straightforward classification is by spherical symmetry.

Basis set indexing is described in Section 2.1 of the enclosed paper; a more technical description is here:

http://spindynamics.org/wiki/index.php? ... e_indexing

The indices of Eq (3) in that paper are stored in spin_system.bas.basis as a sparse array – use full() command to display it as a matrix.

To see which operators contribute to a particular state, use this:

http://spindynamics.org/wiki/index.php? ... tateinfo.m

there is also a function that projects this irreducible spherical tensor basis back into the Zeeman basis – like it would be if the density matrix was assembled from Pauli matrices by the textbook and then stretched, see

http://spindynamics.org/wiki/index.php? ... n2zeeman.m

025_kuprov_2011.pdf