Time dependent hamiltonian in a rotating frame approximation

I’ve got this code which uses a rotating frame approximation. I got it to work when the Hamiltonian was time independent, but now I’m trying to implement a time dependent Hamiltonian and nothing happens to the graph. I understand how to do this, but I’m not sure how it differs when using a rotating frame approximation.

h = 6.62607015e-34
b = 0.1786195317554453  #magnetic field
b_AC = 3.572390635108906e-05  #oscillating magnetic field
g = 2 #g-factor
u = 9.274E-24 #bohr magneton
w = g*u*b/h #omega 
w0 = 5e9  # omega0 is the rotating frame frequency

gamma_phi = 999000
gamma_minus = 1000

epsilon = g*u*b/h*(2*cmath.pi)
Delta = g*u*b_AC/h*(2*cmath.pi)

H0 = (w-w0)*epsilon/2 * sz #+ Delta/2*sy

def pulse(t0,t):
    return np.heaviside(t0,2e-9)

def H1_coeff(t,args):
    t0=args['t0']
    phi=args['phi']
    return Delta*pulse(t0,t)*np.sin((w-w0)*t+phi)

H = [H0,[sx,H1_coeff]]

times=np.linspace(0, 0.0001, 1000)

#our initial qubit state 
state0=(state_z_plus)/(np.sqrt(1))

[atmalik123]

Thank you for your feedback. I was able to get the results I wanted. Just to provide some closure, I’m sending a photo

[BoxiLi]

No, I’m using w-w0 just to show that the code works fine with my suggested changes in pulse(t0,t). It is just the numbers that are wrong.

First, please check the equation you are using again because (I guess) H0 should be (w-w0)/2 * sz and not the one you give in the code above. In your definition, w-w0 and epsilon is the same thing. The drive frequency (in sinus function) should match with H0.

Second, it not clear to me what you want to achieve with this. If the drive frequency matches the system frequency (both w-w0 here), H0 is exactly 0 in the rotating frame.