How to index matrices inside a loop?

Hey all,

I'm trying to index a matrix on witch it's elements vary inside a loop. The code aims to evaluate the time evolution operator in a 2-level quantum system, therefore I need to be able to identify the matrix in a specific time interation, i.e., I need to know the matrix values at U(1), U(20000) and so on. I apologize if it's a simple matter, I'm a self-taught MATLAB user and haven't found any awnsers using the search engine. Thanks in advance!

Here is the code

%% Quantum Control

format long
clear all
clc

%% Variables

        for ft = -20000:.1:20000 % Time
       
        alpha = 0.001; % Transition parameter
        
        beta = 0.001; % Transition parameter
        
        ai = 0.2; % Initial population |1>
        
        ai2 = 0.8; % Initial population |2>
        
        af = 1; % Final population |1>
        
        w0 = 0.02; % w0 = (E2 - E1)/h
        
        mi = 6; % dipole operator
        
        phii = pi/24; % initial relative phase
        
        phif = pi/4; % final relative phase
        
        E1 = 1.98; % eigen-energy 1

        E2 = 2; % eigen-energy 2

        H = [0 1;1 0]; % Interation hamiltonian

        H0 = [E1 0;0 E2]; % hamiltonian

%% Control function
    
        g = 1./(1+exp(-alpha.*ft));
           
        f = ai*(1-g)+af*g;
         
        p = 1./(1+exp(-beta.*ft));
        
        h = phii*(1-p)+phif*p;
        
%% Electric field 
        
        E = alpha.*(af-ai).*exp(alpha.*ft).*sin(w0.*ft+h)./(mi.*(1+exp(alpha.*ft)).*sqrt((1-ai+(1-af).*exp(alpha.*ft)).*(ai+af.*exp(alpha.*ft))))+2.*beta.*(phif-phii).*exp(beta.*ft).*sqrt(f.*(1-f)).*cos(w0.*ft+h)/(mi.*(1-2.*f).*(1+exp(beta.*ft).^2));
    
%% Time evolution operator

        [V, D]=eig(H);
        
        Z = expm(H0);

        Z1 = expm(D);
        
        U = exp(-1i*ft/2)*Z*exp(1i*mi*E*ft)*V*Z1*inv(V)*exp(-1i*ft/2)*Z
        
        end
    
%% End

Answer 1

[infinity]

Hello,

You can change your code a bit like this

%% Quantum Control
format long
clear all
clc
%% Variables
time = -20000:.1:20000; % Time
n = length(time);
U = zeros(1,n);
        for i = 1:n % Time
        ft = time(i);    
       
        alpha = 0.001; % Transition parameter
        
        beta = 0.001; % Transition parameter
        
        ai = 0.2; % Initial population |1>
        
        ai2 = 0.8; % Initial population |2>
        
        af = 1; % Final population |1>
        
        w0 = 0.02; % w0 = (E2 - E1)/h
        
        mi = 6; % dipole operator
        
        phii = pi/24; % initial relative phase
        
        phif = pi/4; % final relative phase
        
        E1 = 1.98; % eigen-energy 1
        E2 = 2; % eigen-energy 2
        H = [0 1;1 0]; % Interation hamiltonian
        H0 = [E1 0;0 E2]; % hamiltonian
%% Control function
    
        g = 1./(1+exp(-alpha.*ft));
           
        f = ai*(1-g)+af*g;
         
        p = 1./(1+exp(-beta.*ft));
        
        h = phii*(1-p)+phif*p;
        
%% Electric field 
        
        E = alpha.*(af-ai).*exp(alpha.*ft).*sin(w0.*ft+h)./(mi.*(1+exp(alpha.*ft)).*sqrt((1-ai+(1-af).*exp(alpha.*ft)).*(ai+af.*exp(alpha.*ft))))+2.*beta.*(phif-phii).*exp(beta.*ft).*sqrt(f.*(1-f)).*cos(w0.*ft+h)/(mi.*(1-2.*f).*(1+exp(beta.*ft).^2));
    
%% Time evolution operator
        [V, D]=eig(H);
        
        Z = expm(H0);
        Z1 = expm(D);
        
        U(i) = exp(-1i*ft/2)*Z*exp(1i*mi*E*ft)*V*Z1*inv(V)*exp(-1i*ft/2)*Z
        
        end
    
%% End 

Now, U will be a vector.

[guilherme stahlberg]

Hello there! Thanks for the help, but when I try to run the code I keep getting this error:

"In an assignment A(:) = B, the number of elements in A and B must be the same.

Error in d_morph (line 89)

U(i)=exp(-1i*ft/2)*Z*exp(1i*mi*E*ft)*V*Z1*inv(V)*exp(-1i*ft/2)*Z;"

Any ideais why? Thanks again.

[infinity]

Hello,

The problem is that "exp(-1i*ft/2)*Z*exp(1i*mi*E*ft)*V*Z1*inv(V)*exp(-1i*ft/2)*Z"

is a matrix of 2x2. Therefore, we need to change the type of U to cell and store the result to this.

What you can do is to change

U = zeros(1,n); 

become

U = cell(1,n);

and

U(i) = exp(-1i*ft/2)*Z*exp(1i*mi*E*ft)*V*Z1*inv(V)*exp(-1i*ft/2)*Z

become

U{i} = exp(-1i*ft/2)*Z*exp(1i*mi*E*ft)*V*Z1*inv(V)*exp(-1i*ft/2)*Z;

[guilherme stahlberg]

It solved! Thanks a lot, good sir!