Driving term in Hamiltonian
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Najme*
Apr 19, 2018, 1:06:48 PM4/19/18
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Hi every one,
I'm trying to solve a master equation for a Hamiltonian which has a deriving term like this:"1j*hbar*E*(a.dag()-a)".
But when I'm adding this term to the Hamiltonian, with the E>=300 kc,("kc=0.1 omega_c" is the decay rate of the cavity mode and "omega_c=1" is the normal mode frequency of the cavity),the Bosonic Algebra for the photonic operator "a" doesn't satisfy any more.
Is there any way to fix this problem?
Regards,
Najme
I'm trying to solve a master equation for a Hamiltonian which has a deriving term like this:"1j*hbar*E*(a.dag()-a)".
But when I'm adding this term to the Hamiltonian, with the E>=300 kc,("kc=0.1 omega_c" is the decay rate of the cavity mode and "omega_c=1" is the normal mode frequency of the cavity),the Bosonic Algebra for the photonic operator "a" doesn't satisfy any more.
Is there any way to fix this problem?
Regards,
Najme
Alex Pitchford
Apr 19, 2018, 1:26:42 PM4/19/18
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Can you post a code snippet and any actual error you received please.
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Najme Ettehadi
Apr 19, 2018, 2:11:33 PM4/19/18
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I,m starting with a simple J-C Hamiltonian and add a driving term to it:
from qutip import *
import numpy as np
import matplotlib.pyplot as plt
#-----------times----------------------
N=10;
times = np.linspace(0.0, 20.0, 100)
#-----initial state---------------
psi0 = tensor(ket2dm(fock(2, 0)), thermal_dm(N, 5));
#-----------Operators---------------
a = tensor(qeye(2),destroy(N));
sm =tensor(destroy(2),qeye(N));
#-----------parameter's values---------------
kc=0.1;
etta=1*300*kc;
#-----------Algebra--------------------------
coma=a*a.dag()- a.dag()* a;
comz=sm*sm.dag()+sm.dag()*sm;
#-----------System's Dynamics----------------
opt=Options(nsteps=1000)
H = 2 * np.pi * a.dag() * a + 2 * np.pi * sm.dag() * sm + 2 * np.pi * 0.25 * (sm*a.dag() + sm.dag()*a)+ 1j*etta*(a.dag()-a);
data = mesolve(H, psi0, times, [np.sqrt(0.1)*a], [coma,comz,a.dag()*a, sm.dag()*sm],options=opt)
#----------Plot----------------
plt.figure()
plt.plot(times, data.expect[0], times, data.expect[1],times, data.expect[2],times, data.expect[3])
plt.title('Master equation time evolution')
plt.xlabel('Time')
plt.ylabel('Expectation values')
plt.legend(("Boson Algebra","Fermion Algebra","cavity photon number", "atom excitation probability"))
plt.show()
As can be seen the bosonic commutation relation converges to zero instead of 1(blue curve).from qutip import *
import numpy as np
import matplotlib.pyplot as plt
#-----------times----------------------
N=10;
times = np.linspace(0.0, 20.0, 100)
#-----initial state---------------
psi0 = tensor(ket2dm(fock(2, 0)), thermal_dm(N, 5));
#-----------Operators---------------
a = tensor(qeye(2),destroy(N));
sm =tensor(destroy(2),qeye(N));
#-----------parameter's values---------------
kc=0.1;
etta=1*300*kc;
#-----------Algebra--------------------------
coma=a*a.dag()- a.dag()* a;
comz=sm*sm.dag()+sm.dag()*sm;
#-----------System's Dynamics----------------
opt=Options(nsteps=1000)
H = 2 * np.pi * a.dag() * a + 2 * np.pi * sm.dag() * sm + 2 * np.pi * 0.25 * (sm*a.dag() + sm.dag()*a)+ 1j*etta*(a.dag()-a);
data = mesolve(H, psi0, times, [np.sqrt(0.1)*a], [coma,comz,a.dag()*a, sm.dag()*sm],options=opt)
#----------Plot----------------
plt.figure()
plt.plot(times, data.expect[0], times, data.expect[1],times, data.expect[2],times, data.expect[3])
plt.title('Master equation time evolution')
plt.xlabel('Time')
plt.ylabel('Expectation values')
plt.legend(("Boson Algebra","Fermion Algebra","cavity photon number", "atom excitation probability"))
plt.show()
Paul Nation
Apr 19, 2018, 2:22:46 PM4/19/18
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Your probably driving the system too strong. Either increase your Hilbert space size, or increase the damping rate.
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Najme Ettehadi
Apr 19, 2018, 2:37:08 PM4/19/18
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I'll try it. thanks a lot.
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