time evolution of two level atom

[Arjit]

'm trying to plot the time evolution of two level atom by using mesolve but i was not able to get as I'm a beginner in the field , it would be very helpful if someone could help, 

i have taken random density matrix with unit trace and trying to see its evolution with time , of all the 4 states of a two two level system , 

taking Hamiltonian as [sigmaz() * omega /2] , take omega =1 and  every other constant in the simplest way possible to get the plot of all four states evolving in time .

im basically trying to plot all the four ode's given in equation 98 with respect to time.

please help!!