## Extending spinach to other physical implementation

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yunwei
Posts: 7
Joined: Wed Aug 11, 2021 5:39 am

### Extending spinach to other physical implementation

I am thinking if Spinach can be used to construct any kind of Hamiltonian.

For example, H=w_c*a_dag*a+w_q*sigmaz+g(a+a_dag)*(sigmax), which is cavity coupling to a 2-level system.
And H=wc*b_dag*b+a*(b_dag*b-1)*b_dag*b, which is anharmonic oscillator.

I want to apply the optimal model to the system H shown above, but I am not sure if I can do some tricks and construct such H in Spinach.
kuprov
Posts: 123
Joined: Mon Mar 29, 2021 4:26 pm

### Re: Extending spinach to other physical implementation

Hmmm, an interesting idea. So long as the excitation ladder is truncated at some point, a harmonic oscillator would be isomorphic mathematically to a spin...

I would suggest using pauli.m function to get creation and annihilation operators, and then trying to build the rest of the mathematics out of those. Much of Spinach functionality relies on the spin_system object existing, but in principle we could try adding a possibility of some of the particles inthe spin system being harmonic oscillators instead.

Do you have a simple five-line example of your harmonic oscillator calculation? I can take a look and see if we can extend the kernel to handle that.
yunwei
Posts: 7
Joined: Wed Aug 11, 2021 5:39 am

### Re: Extending spinach to other physical implementation

It would be fine, I just see the instruction to define the spin system.

I have another question, can I define interaction like S_z1+S_z2+S_x1*S_x2?
kuprov
Posts: 123
Joined: Mon Mar 29, 2021 4:26 pm

### Re: Extending spinach to other physical implementation

Well, that's a pretty standard Hamiltonian - of course you can. Either specify an interaction matrix with zeros in the right places, or build your own operator.
yunwei
Posts: 7
Joined: Wed Aug 11, 2021 5:39 am

### Re: Extending spinach to other physical implementation

function program()
function [b_dag,b]=cavity(h_dim)
b_dag=[1:h_dim-1];
b_dag=sqrt(diag(b_dag,-1));
b=[1:h_dim-1];
b=sqrt(b);
b=diag(b,1);
end
[b_dag,b]=cavity(10);
w_c=3.9*2*pi;%frequency of cavity
H0=w_c*b_dag*b;
end

These are lines to get the matrix of harmonic oscillator, which is also called cavity in quantum optics.
Could you please give me an example to construct such a Hamiltonian? Thanks!
kuprov
Posts: 123
Joined: Mon Mar 29, 2021 4:26 pm

### Re: Extending spinach to other physical implementation

Would this function suffice?

https://spindynamics.org/wiki/index.php ... cillator.m

If not, then call this:

https://spindynamics.org/wiki/index.php?title=Pauli.m

and use the raising and lowering operators that it returns as creation and annihilation operators of a truncated Harmonic oscillator.