Strange behaviour in a pumped cavity

[M Cotrufo]

Hi all,

I'm making a very simple script in which a cavity is pumped by an external source which is alternatingly on and off every 1 ns. I use the following code.

#Pump function which is alternatively on and off every 1 ns

def Pump(t,args): 

    if(np.mod(floor(t),2)==0):

        return 0;

    else:

        return 1

        

        

T=20 # Time range used, in ns

sizeT=10000 #Number of bins in which the time in range is divided. If this is not big enough, you get an error

tlist =np.linspace(0,T,sizeT) #These are the true times        

        

        

Kappa = 10 #Cavity losses

Na = 15;

psi0 = tensor(basis(Na,0)) 

a  = tensor(destroy(Na))

H1 = a.dag() + a

H = [[H1,Pump]]

c_op_list = []

c_op_list.append(sqrt(Kappa) * a)

output = mesolve(H, psi0, tlist,c_op_list, [],args=[])

N_c = expect(a.dag() * a,output.states)

#%% PLOT

Pumplist = np.zeros(len(tlist))

i=0

for t in tlist:

    Pumplist[i] = Pump(t,[])

    i=i+1

    

plt.rc('text', usetex=False)

plt.rc('font', family='arial',size=20)

fig, axes = plt.subplots(1, 1, figsize=(10,6))

ax = plt.subplot(111)

plt.plot(tlist,Pumplist/max(Pumplist), label="Pump")

plt.plot(tlist, N_c/max(N_c), label="Cavity")

ax.legend(loc='upper center', prop={'size':18},bbox_to_anchor=(0.5, -0.3),fancybox=True, shadow=True, ncol=5)

plt.xlabel('Time (ns)')

plt.ylabel('External Pulse')

plt.show()

I plot both the pump and the cavity population, both normalized to their respective maximum. Here is what I get:

As you see, it looks like the pump does not do anything to the cavity population for the first 13 ns, and only after that it start behaving correctly. I also tried changing the time T, and this behaviour changes: sometimes it seems that the pump has no influence at all, other times it starts to have an effect earlier than 13ns. 

Do you have any idea why I have this behaviour? Can you try reproducing this script on your computer?

[M Cotrufo]

Oh, I just realized that in this very recent post https://groups.google.com/forum/#!topic/qutip/T7KY6fG35fw they have the same problem

[M Cotrufo]

As suggested by Kevin in this other conversation ( https://groups.google.com/forum/#!topic/qutip/T7KY6fG35fw ), the problem can be solved by changing the max_step parameter of the Odeoptions. In particular, by modfiying the script above with 

opts = Odeoptions(max_step=0.01)

output = mesolve(H, psi0, tlist,c_op_list, [],args=[], options=opts)

Now all the pulses of the pump are correctly seen by the cavity.