In [1]:
%matplotlib inline
import matplotlib.pyplot as plt
In [2]:
import numpy as np
from qutip import *
from IPython.display import display
In [15]:
def solve(H, psi0, c_ops, a_ops, e_ops):
result_me = mesolve(H, psi0, times, c_ops, e_ops)
result_brme = brmesolve(H, psi0, times, a_ops, e_ops)
fig, ax = plot_expectation_values([result_me, result_brme])
display(fig)
plt.close(fig)
R, ekets = bloch_redfield_tensor(H, a_ops)
print("="* 20 + " Bloch-Redfield tensor: ")
display(R)
L = liouvillian(H, c_ops)
print("="* 20 + " Lindblad liouvilllian: ")
display(L)
print("="* 20 + " Bloch-Redfield steadystate dm")
R_rhoss_eb = steadystate(R)
R_rhoss = R_rhoss_eb.transform(ekets, True)
display(R_rhoss)
print("="* 20 + " Lindblad steadystate dm")
L_rhoss = steadystate(L)
display(L_rhoss)
print("="* 20 + " Steadystate expectation values")
print("R_ob: ", [expect(e, R_rhoss) for e in e_ops])
print("R_eb: ", [expect(e.transform(ekets), R_rhoss_eb) for e in e_ops])
print("L : ", [expect(e, L_rhoss) for e in e_ops])
print("="* 20 + " Dynamics final states")
print("R: ", [e[-1].real for e in result_brme.expect])
print("L: ", [e[-1] for e in result_me.expect])
In [16]:
delta = 0.0 * 2 * np.pi
epsilon = 0.5 * 2 * np.pi
gamma = 0.25
times = np.linspace(0, 50, 100)
In [17]:
H = delta/2 * sigmay() + epsilon/2 * sigmaz()
psi0 = (2 * basis(2, 0) + basis(2, 1)).unit()
c_ops = [np.sqrt(gamma) * sigmam()]
a_ops = [[sigmax(),lambda w : gamma * (w >= 0)]]
e_ops = [sigmax(), sigmay(), sigmaz()]
In [18]:
solve(H, psi0, c_ops, a_ops, e_ops)
==================== Bloch-Redfield tensor:
Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & 0.250\\0.0 & (-0.125-3.142j) & 0.0 & 0.0\\0.0 & 0.0 & (-0.125+3.142j) & 0.0\\0.0 & 0.0 & 0.0 & -0.250\\\end{array}\right)\end{equation*}
==================== Lindblad liouvilllian:
Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}-0.250 & 0.0 & 0.0 & 0.0\\0.0 & (-0.125+3.142j) & 0.0 & 0.0\\0.0 & 0.0 & (-0.125-3.142j) & 0.0\\0.250 & 0.0 & 0.0 & 0.0\\\end{array}\right)\end{equation*}
==================== Bloch-Redfield steadystate dm
Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\begin{equation*}\left(\begin{array}{*{11}c}0.0 & 0.0\\0.0 & 1.0\\\end{array}\right)\end{equation*}
==================== Lindblad steadystate dm
Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\begin{equation*}\left(\begin{array}{*{11}c}0.0 & 0.0\\0.0 & 1.0\\\end{array}\right)\end{equation*}
==================== Steadystate expectation values
R_ob: [0.0, 0.0, -1.0]
R_eb: [0.0, 0.0, -1.0]
L : [0.0, 0.0, -1.0]
==================== Dynamics final states
R: [0.0015427968283087687, 2.506068854864511e-07, -0.999994037354897]
L: [0.001542796828343541, 2.5060686974779289e-07, -0.99999403735489634]
In [25]:
N = 10
w0 = 1.0 * 2 * np.pi
g = 0.05 * w0
kappa = 0.15
times = np.linspace(0, 50, 1000)
In [26]:
a = destroy(N)
H = w0 * a.dag() * a + g * (a + a.dag())
psi0 = ket2dm((basis(N, 4) + basis(N, 2) + basis(N,0)).unit())
a_ops = [[a + a.dag(),lambda w : kappa * (w >= 0)]]
e_ops = [a.dag() * a, a + a.dag()]
In [27]:
c_ops = [np.sqrt(kappa) * a]
In [28]:
solve(H, psi0, c_ops, a_ops, e_ops)
==================== Bloch-Redfield tensor:
Quantum object: dims = [[[10], [10]], [[10], [10]]], shape = (100, 100), type = super, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 1.926\times10^{-25}\\0.0 & (-0.075-6.283j) & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & (-0.150-12.566j) & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & (-0.225-18.850j) & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & (-0.300-25.133j) & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & (-1.090+25.288j) & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & (-1.165+19.005j) & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & (-1.240+12.722j) & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & (-1.312+6.437j) & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & -1.286\\\end{array}\right)\end{equation*}
==================== Lindblad liouvilllian:
Quantum object: dims = [[[10], [10]], [[10], [10]]], shape = (100, 100), type = super, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}0.0 & -0.314j & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\-0.314j & (-0.075-6.283j) & -0.444j & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & -0.444j & (-0.150-12.566j) & -0.544j & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & -0.544j & (-0.225-18.850j) & -0.628j & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & -0.628j & (-0.300-25.133j) & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & (-1.050+25.133j) & -0.770j & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & -0.770j & (-1.125+18.850j) & -0.831j & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & -0.831j & (-1.200+12.566j) & -0.889j & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & -0.889j & (-1.275+6.283j) & -0.942j\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & -0.942j & -1.350\\\end{array}\right)\end{equation*}
==================== Bloch-Redfield steadystate dm
Quantum object: dims = [[10], [10]], shape = (10, 10), type = oper, isherm = True\begin{equation*}\left(\begin{array}{*{11}c}0.998 & -0.050 & 0.002 & -5.090\times10^{-05} & 1.273\times10^{-06} & -2.846\times10^{-08} & 5.809\times10^{-10} & -1.098\times10^{-11} & 0.0 & 0.0\\-0.050 & 0.002 & -8.817\times10^{-05} & 2.545\times10^{-06} & -6.363\times10^{-08} & 1.423\times10^{-09} & -2.904\times10^{-11} & 0.0 & 0.0 & 0.0\\0.002 & -8.817\times10^{-05} & 3.117\times10^{-06} & -8.999\times10^{-08} & 2.250\times10^{-09} & -5.030\times10^{-11} & 1.027\times10^{-12} & 0.0 & 0.0 & 0.0\\-5.090\times10^{-05} & 2.545\times10^{-06} & -8.999\times10^{-08} & 2.598\times10^{-09} & -6.494\times10^{-11} & 1.452\times10^{-12} & 0.0 & 0.0 & 0.0 & 0.0\\1.273\times10^{-06} & -6.363\times10^{-08} & 2.250\times10^{-09} & -6.494\times10^{-11} & 1.624\times10^{-12} & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\-2.846\times10^{-08} & 1.423\times10^{-09} & -5.030\times10^{-11} & 1.452\times10^{-12} & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\5.809\times10^{-10} & -2.904\times10^{-11} & 1.027\times10^{-12} & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\-1.098\times10^{-11} & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\end{array}\right)\end{equation*}
==================== Lindblad steadystate dm
Quantum object: dims = [[10], [10]], shape = (10, 10), type = oper, isherm = True\begin{equation*}\left(\begin{array}{*{11}c}0.998 & (-0.050+5.953\times10^{-04}j) & (0.002-4.208\times10^{-05}j) & (-5.086\times10^{-05}+1.822\times10^{-06}j) & (1.271\times10^{-06}-6.072\times10^{-08}j) & (-2.840\times10^{-08}+1.697\times10^{-09}j) & (5.791\times10^{-10}-4.155\times10^{-11}j) & -1.093\times10^{-11} & 1.931\times10^{-13} & -3.213\times10^{-15}\\(-0.050-5.953\times10^{-04}j) & 0.002 & (-8.814\times10^{-05}+1.052\times10^{-06}j) & (2.544\times10^{-06}-6.074\times10^{-08}j) & (-6.357\times10^{-08}+2.277\times10^{-09}j) & (1.421\times10^{-09}-6.788\times10^{-11}j) & (-2.898\times10^{-11}+1.731\times10^{-12}j) & 5.471\times10^{-13} & -9.662\times10^{-15} & 1.608\times10^{-16}\\(0.002+4.208\times10^{-05}j) & (-8.814\times10^{-05}-1.052\times10^{-06}j) & 3.116\times10^{-06} & (-8.995\times10^{-08}+1.074\times10^{-09}j) & (2.248\times10^{-09}-5.368\times10^{-11}j) & (-5.025\times10^{-11}+1.800\times10^{-12}j) & 1.025\times10^{-12} & -1.936\times10^{-14} & 3.419\times10^{-16} & -5.691\times10^{-18}\\(-5.086\times10^{-05}-1.822\times10^{-06}j) & (2.544\times10^{-06}+6.074\times10^{-08}j) & (-8.995\times10^{-08}-1.074\times10^{-09}j) & 2.597\times10^{-09} & -6.490\times10^{-11} & 1.451\times10^{-12} & -2.960\times10^{-14} & 5.591\times10^{-16} & -9.877\times10^{-18} & 1.644\times10^{-19}\\(1.271\times10^{-06}+6.072\times10^{-08}j) & (-6.357\times10^{-08}-2.277\times10^{-09}j) & (2.248\times10^{-09}+5.368\times10^{-11}j) & -6.490\times10^{-11} & 1.623\times10^{-12} & -3.628\times10^{-14} & 7.403\times10^{-16} & -1.398\times10^{-17} & 2.471\times10^{-19} & -4.114\times10^{-21}\\(-2.840\times10^{-08}-1.697\times10^{-09}j) & (1.421\times10^{-09}+6.788\times10^{-11}j) & (-5.025\times10^{-11}-1.800\times10^{-12}j) & 1.451\times10^{-12} & -3.628\times10^{-14} & 8.112\times10^{-16} & -1.655\times10^{-17} & 3.127\times10^{-19} & -5.524\times10^{-21} & 9.192\times10^{-23}\\(5.791\times10^{-10}+4.155\times10^{-11}j) & (-2.898\times10^{-11}-1.731\times10^{-12}j) & 1.025\times10^{-12} & -2.960\times10^{-14} & 7.403\times10^{-16} & -1.655\times10^{-17} & 3.378\times10^{-19} & -6.370\times10^{-21} & 1.120\times10^{-22} & -1.841\times10^{-24}\\-1.093\times10^{-11} & 5.471\times10^{-13} & -1.936\times10^{-14} & 5.591\times10^{-16} & -1.398\times10^{-17} & 3.127\times10^{-19} & -6.370\times10^{-21} & 1.188\times10^{-22} & -1.992\times10^{-24} & 2.766\times10^{-26}\\1.931\times10^{-13} & -9.662\times10^{-15} & 3.419\times10^{-16} & -9.877\times10^{-18} & 2.471\times10^{-19} & -5.524\times10^{-21} & 1.120\times10^{-22} & -1.992\times10^{-24} & 2.369\times10^{-26} & 3.484\times10^{-28}\\-3.213\times10^{-15} & 1.608\times10^{-16} & -5.691\times10^{-18} & 1.644\times10^{-19} & -4.114\times10^{-21} & 9.192\times10^{-23} & -1.841\times10^{-24} & 2.766\times10^{-26} & 3.484\times10^{-28} & -8.010\times10^{-29}\\\end{array}\right)\end{equation*}
==================== Steadystate expectation values
R_ob: [0.0024999999999958857, -0.09999999999983651]
R_eb: [0.0024999999999999467, -0.09999999999999895]
L : [0.0024996438434595246, -0.09998575373839921]
==================== Dynamics final states
R: [0.0034899627568894909, -0.097648226112852135]
L: [0.0034896231351718215, -0.097634314487055257]
In [29]:
n_th = 1.5
c_ops = [np.sqrt(kappa * (n_th + 1)) * a, np.sqrt(kappa * n_th) * a.dag()]
w_th = w0/np.log(1 + 1/n_th)
def S_w_func(w):
if w >= 0:
return (n_th + 1) * kappa
else:
return (n_th + 1) * kappa * np.exp(w / w_th)
a_ops = [[a + a.dag(), S_w_func]]
In [30]:
solve(H, psi0, c_ops, a_ops, e_ops)
==================== Bloch-Redfield tensor:
Quantum object: dims = [[[10], [10]], [[10], [10]]], shape = (100, 100), type = super, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}-0.225 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 4.815\times10^{-25}\\0.0 & (-0.525-6.283j) & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & (-0.825-12.566j) & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & (-1.125-18.850j) & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & (-1.425-25.133j) & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & (-3.400+25.288j) & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & (-3.700+19.005j) & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & (-3.999+12.722j) & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & (-4.231+6.437j) & 0.0\\4.792\times10^{-27} & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & -3.215\\\end{array}\right)\end{equation*}
==================== Lindblad liouvilllian:
Quantum object: dims = [[[10], [10]], [[10], [10]]], shape = (100, 100), type = super, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}-0.225 & -0.314j & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\-0.314j & (-0.525-6.283j) & -0.444j & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & -0.444j & (-0.825-12.566j) & -0.544j & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & -0.544j & (-1.125-18.850j) & -0.628j & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & -0.628j & (-1.425-25.133j) & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & (-3.300+25.133j) & -0.770j & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & -0.770j & (-3.600+18.850j) & -0.831j & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & -0.831j & (-3.900+12.566j) & -0.889j & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & -0.889j & (-4.200+6.283j) & -0.942j\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & -0.942j & -3.375\\\end{array}\right)\end{equation*}
==================== Bloch-Redfield steadystate dm
Quantum object: dims = [[10], [10]], shape = (10, 10), type = oper, isherm = True\begin{equation*}\left(\begin{array}{*{11}c}0.402 & -0.008 & 1.137\times10^{-04} & -1.313\times10^{-06} & 1.313\times10^{-08} & -1.174\times10^{-10} & 0.0 & 0.0 & 0.0 & 0.0\\-0.008 & 0.241 & -0.007 & 1.182\times10^{-04} & -1.576\times10^{-06} & 1.762\times10^{-08} & -1.726\times10^{-10} & 1.521\times10^{-12} & 0.0 & 0.0\\1.137\times10^{-04} & -0.007 & 0.145 & -0.005 & 1.003\times10^{-04} & -1.495\times10^{-06} & 1.831\times10^{-08} & -1.938\times10^{-10} & 1.827\times10^{-12} & 0.0\\-1.313\times10^{-06} & 1.182\times10^{-04} & -0.005 & 0.087 & -0.003 & 7.773\times10^{-05} & -1.269\times10^{-06} & 1.679\times10^{-08} & -1.899\times10^{-10} & 1.899\times10^{-12}\\1.313\times10^{-08} & -1.576\times10^{-06} & 1.003\times10^{-04} & -0.003 & 0.052 & -0.002 & 5.713\times10^{-05} & -1.007\times10^{-06} & 1.425\times10^{-08} & -1.709\times10^{-10}\\-1.174\times10^{-10} & 1.762\times10^{-08} & -1.495\times10^{-06} & 7.773\times10^{-05} & -0.002 & 0.031 & -0.002 & 4.057\times10^{-05} & -7.647\times10^{-07} & 1.147\times10^{-08}\\0.0 & -1.726\times10^{-10} & 1.831\times10^{-08} & -1.269\times10^{-06} & 5.713\times10^{-05} & -0.002 & 0.019 & -9.946\times10^{-04} & 2.811\times10^{-05} & -5.619\times10^{-07}\\0.0 & 1.521\times10^{-12} & -1.938\times10^{-10} & 1.679\times10^{-08} & -1.007\times10^{-06} & 4.057\times10^{-05} & -9.946\times10^{-04} & 0.011 & -6.382\times10^{-04} & 1.912\times10^{-05}\\0.0 & 0.0 & 1.827\times10^{-12} & -1.899\times10^{-10} & 1.425\times10^{-08} & -7.647\times10^{-07} & 2.811\times10^{-05} & -6.382\times10^{-04} & 0.007 & -4.059\times10^{-04}\\0.0 & 0.0 & 0.0 & 1.899\times10^{-12} & -1.709\times10^{-10} & 1.147\times10^{-08} & -5.619\times10^{-07} & 1.912\times10^{-05} & -4.059\times10^{-04} & 0.004\\\end{array}\right)\end{equation*}
==================== Lindblad steadystate dm
Quantum object: dims = [[10], [10]], shape = (10, 10), type = oper, isherm = True\begin{equation*}\left(\begin{array}{*{11}c}0.402 & (-0.008+9.596\times10^{-05}j) & (1.137\times10^{-04}-2.714\times10^{-06}j) & (-1.312\times10^{-06}+4.705\times10^{-08}j) & (1.312\times10^{-08}-6.319\times10^{-10}j) & (-1.178\times10^{-10}+6.493\times10^{-12}j) & 9.423\times10^{-13} & -4.294\times10^{-15} & -7.474\times10^{-17} & 1.605\times10^{-18}\\(-0.008-9.596\times10^{-05}j) & 0.241 & (-0.007+8.146\times10^{-05}j) & (1.181\times10^{-04}-2.818\times10^{-06}j) & (-1.574\times10^{-06}+5.621\times10^{-08}j) & (1.756\times10^{-08}-8.970\times10^{-10}j) & (-1.757\times10^{-10}+1.454\times10^{-11}j) & 1.853\times10^{-12} & -2.153\times10^{-14} & 4.078\times10^{-17}\\(1.137\times10^{-04}+2.714\times10^{-06}j) & (-0.007-8.146\times10^{-05}j) & 0.145 & (-0.005+5.991\times10^{-05}j) & (1.003\times10^{-04}-2.396\times10^{-06}j) & (-1.495\times10^{-06}+5.069\times10^{-08}j) & (1.800\times10^{-08}-7.440\times10^{-10}j) & (-1.758\times10^{-10}+2.574\times10^{-11}j) & (1.790\times10^{-12}-1.344\times10^{-12}j) & -4.383\times10^{-14}\\(-1.312\times10^{-06}-4.705\times10^{-08}j) & (1.181\times10^{-04}+2.818\times10^{-06}j) & (-0.005-5.991\times10^{-05}j) & 0.087 & (-0.003+4.153\times10^{-05}j) & (7.770\times10^{-05}-1.924\times10^{-06}j) & (-1.279\times10^{-06}+4.505\times10^{-08}j) & (1.710\times10^{-08}+1.921\times10^{-10}j) & (-1.533\times10^{-10}-4.118\times10^{-11}j) & -6.294\times10^{-13}\\(1.312\times10^{-08}+6.319\times10^{-10}j) & (-1.574\times10^{-06}-5.621\times10^{-08}j) & (1.003\times10^{-04}+2.396\times10^{-06}j) & (-0.003-4.153\times10^{-05}j) & 0.052 & (-0.002+2.718\times10^{-05}j) & (5.688\times10^{-05}-1.483\times10^{-06}j) & (-1.015\times10^{-06}+6.915\times10^{-08}j) & (1.666\times10^{-08}-1.361\times10^{-09}j) & (-2.725\times10^{-10}-3.558\times10^{-11}j)\\(-1.178\times10^{-10}-6.493\times10^{-12}j) & (1.756\times10^{-08}+8.970\times10^{-10}j) & (-1.495\times10^{-06}-5.069\times10^{-08}j) & (7.770\times10^{-05}+1.924\times10^{-06}j) & (-0.002-2.718\times10^{-05}j) & 0.031 & (-0.002+1.615\times10^{-05}j) & (4.000\times10^{-05}-4.783\times10^{-07}j) & (-6.958\times10^{-07}+6.183\times10^{-08}j) & (1.025\times10^{-08}-4.287\times10^{-09}j)\\9.423\times10^{-13} & (-1.757\times10^{-10}-1.454\times10^{-11}j) & (1.800\times10^{-08}+7.440\times10^{-10}j) & (-1.279\times10^{-06}-4.505\times10^{-08}j) & (5.688\times10^{-05}+1.483\times10^{-06}j) & (-0.002-1.615\times10^{-05}j) & 0.019 & (-0.001+1.302\times10^{-05}j) & (2.875\times10^{-05}+9.020\times10^{-07}j) & (-5.015\times10^{-07}-5.299\times10^{-08}j)\\-4.294\times10^{-15} & 1.853\times10^{-12} & (-1.758\times10^{-10}-2.574\times10^{-11}j) & (1.710\times10^{-08}-1.921\times10^{-10}j) & (-1.015\times10^{-06}-6.915\times10^{-08}j) & (4.000\times10^{-05}+4.783\times10^{-07}j) & (-0.001-1.302\times10^{-05}j) & 0.011 & (-6.459\times10^{-04}+2.824\times10^{-05}j) & (2.157\times10^{-05}-9.632\times10^{-07}j)\\-7.474\times10^{-17} & -2.153\times10^{-14} & (1.790\times10^{-12}+1.344\times10^{-12}j) & (-1.533\times10^{-10}+4.118\times10^{-11}j) & (1.666\times10^{-08}+1.361\times10^{-09}j) & (-6.958\times10^{-07}-6.183\times10^{-08}j) & (2.875\times10^{-05}-9.020\times10^{-07}j) & (-6.459\times10^{-04}-2.824\times10^{-05}j) & 0.007 & (-3.735\times10^{-04}+5.327\times10^{-05}j)\\1.605\times10^{-18} & 4.078\times10^{-17} & -4.383\times10^{-14} & -6.294\times10^{-13} & (-2.725\times10^{-10}+3.558\times10^{-11}j) & (1.025\times10^{-08}+4.287\times10^{-09}j) & (-5.015\times10^{-07}+5.299\times10^{-08}j) & (2.157\times10^{-05}+9.632\times10^{-07}j) & (-3.735\times10^{-04}-5.327\times10^{-05}j) & 0.004\\\end{array}\right)\end{equation*}
==================== Steadystate expectation values
R_ob: [1.441172521173384, -0.09593514655834637]
R_eb: [1.4411725211733848, -0.0959351465583464]
L : [1.4415837865925414, -0.09581420257265144]
==================== Dynamics final states
R: [1.4412697964611352, -0.094946706436505962]
L: [1.4416807381001973, -0.094807209086397559]
In [34]:
N = 10
a = tensor(destroy(N), identity(2))
sm = tensor(identity(N), destroy(2))
psi0 = ket2dm(tensor(basis(N, 1), basis(2, 0)))
a_ops = [[a + a.dag(),lambda w : kappa*(w > 0)]]
e_ops = [a.dag() * a, sm.dag() * sm]
In [35]:
w0 = 1.0 * 2 * np.pi
g = 0.05 * 2 * np.pi
kappa = 0.05
times = np.linspace(0, 150 * 2 * np.pi / g, 1000)
c_ops = [np.sqrt(kappa) * a]
H = w0 * a.dag() * a + w0 * sm.dag() * sm + g * (a + a.dag()) * (sm + sm.dag())
In [36]:
solve(H, psi0, c_ops, a_ops, e_ops)
==================== Bloch-Redfield tensor:
Quantum object: dims = [[[10, 2], [10, 2]], [[10, 2], [10, 2]]], shape = (400, 400), type = super, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & (-0.013-5.969j) & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & (-0.012-6.597j) & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & (-0.039-12.122j) & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & (-0.036-13.010j) & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & (-0.419+13.531j) & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & (-0.413+11.758j) & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & (-0.441+7.263j) & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & (-0.436+5.382j) & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & -0.457\\\end{array}\right)\end{equation*}
==================== Lindblad liouvilllian:
Quantum object: dims = [[[10, 2], [10, 2]], [[10, 2], [10, 2]]], shape = (400, 400), type = super, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & -0.314j & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & -6.283j & -0.314j & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & -0.314j & (-0.025-6.283j) & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\-0.314j & 0.0 & 0.0 & (-0.025-12.566j) & -0.444j & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & -0.444j & (-0.050-12.566j) & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & (-0.400+12.566j) & -0.889j & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & -0.889j & (-0.425+12.566j) & 0.0 & 0.0 & -0.942j\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & (-0.425+6.283j) & -0.942j & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & -0.942j & (-0.450+6.283j) & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & -0.942j & 0.0 & 0.0 & -0.450\\\end{array}\right)\end{equation*}
==================== Bloch-Redfield steadystate dm
Quantum object: dims = [[10, 2], [10, 2]], shape = (20, 20), type = oper, isherm = True\begin{equation*}\left(\begin{array}{*{11}c}0.999 & 0.0 & 0.0 & -0.025 & 8.842\times10^{-04} & \cdots & -3.013\times10^{-12} & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\-0.025 & 0.0 & 0.0 & 6.254\times10^{-04} & -2.212\times10^{-05} & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\8.842\times10^{-04} & 0.0 & 0.0 & -2.212\times10^{-05} & 7.822\times10^{-07} & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots\\-3.013\times10^{-12} & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\end{array}\right)\end{equation*}
==================== Lindblad steadystate dm
Quantum object: dims = [[10, 2], [10, 2]], shape = (20, 20), type = oper, isherm = True\begin{equation*}\left(\begin{array}{*{11}c}0.998 & 0.0 & 0.0 & (-0.025+4.974\times10^{-05}j) & (8.830\times10^{-04}-5.270\times10^{-06}j) & \cdots & -3.008\times10^{-12} & 5.318\times10^{-14} & 0.0 & 0.0 & -7.975\times10^{-16}\\0.0 & 6.282\times10^{-04} & (-3.128\times10^{-05}+4.971\times10^{-05}j) & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & -2.686\times10^{-16} & 5.694\times10^{-18} & 0.0\\0.0 & (-3.128\times10^{-05}-4.971\times10^{-05}j) & 6.250\times10^{-04} & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & -5.325\times10^{-15} & 9.983\times10^{-17} & 0.0\\(-0.025-4.974\times10^{-05}j) & 0.0 & 0.0 & 6.247\times10^{-04} & (-2.210\times10^{-05}+1.024\times10^{-07}j) & \cdots & 7.512\times10^{-14} & -1.326\times10^{-15} & 0.0 & 0.0 & 1.984\times10^{-17}\\(8.830\times10^{-04}+5.270\times10^{-06}j) & 0.0 & 0.0 & (-2.210\times10^{-05}-1.024\times10^{-07}j) & 9.114\times10^{-07} & \cdots & -7.964\times10^{-15} & 1.720\times10^{-16} & 0.0 & 0.0 & -3.048\times10^{-18}\\\vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots\\-3.008\times10^{-12} & 0.0 & 0.0 & 7.512\times10^{-14} & -7.964\times10^{-15} & \cdots & 1.865\times10^{-19} & -1.888\times10^{-18} & 0.0 & 0.0 & 9.101\times10^{-20}\\5.318\times10^{-14} & 0.0 & 0.0 & -1.326\times10^{-15} & 1.720\times10^{-16} & \cdots & -1.888\times10^{-18} & 2.620\times10^{-19} & 0.0 & 0.0 & 1.290\times10^{-20}\\0.0 & -2.686\times10^{-16} & -5.325\times10^{-15} & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & -6.197\times10^{-17} & 3.031\times10^{-18} & 0.0\\0.0 & 5.694\times10^{-18} & 9.983\times10^{-17} & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 3.031\times10^{-18} & -6.198\times10^{-17} & 0.0\\-7.975\times10^{-16} & 0.0 & 0.0 & 1.984\times10^{-17} & -3.048\times10^{-18} & \cdots & 9.101\times10^{-20} & 1.290\times10^{-20} & 0.0 & 0.0 & 3.143\times10^{-19}\\\end{array}\right)\end{equation*}
==================== Steadystate expectation values
R_ob: [0.0006269556884685608, 0.0006253905020122077]
R_eb: [0.0006269556893783309, 0.0006253905020103645]
L : [0.0012531197519054338, 0.0012536697716992462]
==================== Dynamics final states
R: [0.00062695568938809241, 0.00062539050201271512]
L: [0.0012531197519057469, 0.0012536697716989808]
In [37]:
w0 = 1.0 * 2 * np.pi
g = 0.75 * 2 * np.pi
kappa = 0.05
times = np.linspace(0, 150 * 2 * np.pi / g, 1000)
In [38]:
c_ops = [np.sqrt(kappa) * a]
H = w0 * a.dag() * a + w0 * sm.dag() * sm + g * (a + a.dag()) * (sm + sm.dag())
In [39]:
solve(H, psi0, c_ops, a_ops, e_ops)
==================== Bloch-Redfield tensor:
Quantum object: dims = [[[10, 2], [10, 2]], [[10, 2], [10, 2]]], shape = (400, 400), type = super, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & (-0.051-1.885j) & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & (-0.052-6.705j) & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & (-0.069-9.264j) & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & (-0.037-13.304j) & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & (-0.595+26.008j) & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & (-0.557+16.303j) & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & (-0.681+14.149j) & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & (-0.514+0.513j) & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & -0.948\\\end{array}\right)\end{equation*}
==================== Lindblad liouvilllian:
Quantum object: dims = [[[10, 2], [10, 2]], [[10, 2], [10, 2]]], shape = (400, 400), type = super, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & -4.712j & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & -6.283j & -4.712j & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & -4.712j & (-0.025-6.283j) & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\-4.712j & 0.0 & 0.0 & (-0.025-12.566j) & -6.664j & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & -6.664j & (-0.050-12.566j) & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & (-0.400+12.566j) & -13.329j & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & -13.329j & (-0.425+12.566j) & 0.0 & 0.0 & -14.137j\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & (-0.425+6.283j) & -14.137j & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & -14.137j & (-0.450+6.283j) & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & -14.137j & 0.0 & 0.0 & -0.450\\\end{array}\right)\end{equation*}
==================== Bloch-Redfield steadystate dm
Quantum object: dims = [[10, 2], [10, 2]], shape = (20, 20), type = oper, isherm = True\begin{equation*}\left(\begin{array}{*{11}c}0.795 & 0.0 & 0.0 & -0.345 & 0.195 & \cdots & -6.264\times10^{-04} & 1.696\times10^{-04} & 0.0 & 0.0 & -3.695\times10^{-05}\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\-0.345 & 0.0 & 0.0 & 0.150 & -0.085 & \cdots & 2.722\times10^{-04} & -7.370\times10^{-05} & 0.0 & 0.0 & 1.606\times10^{-05}\\0.195 & 0.0 & 0.0 & -0.085 & 0.048 & \cdots & -1.540\times10^{-04} & 4.170\times10^{-05} & 0.0 & 0.0 & -9.086\times10^{-06}\\\vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots\\-6.264\times10^{-04} & 0.0 & 0.0 & 2.722\times10^{-04} & -1.540\times10^{-04} & \cdots & 4.935\times10^{-07} & -1.336\times10^{-07} & 0.0 & 0.0 & 2.911\times10^{-08}\\1.696\times10^{-04} & 0.0 & 0.0 & -7.370\times10^{-05} & 4.170\times10^{-05} & \cdots & -1.336\times10^{-07} & 3.617\times10^{-08} & 0.0 & 0.0 & -7.882\times10^{-09}\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\-3.695\times10^{-05} & 0.0 & 0.0 & 1.606\times10^{-05} & -9.086\times10^{-06} & \cdots & 2.911\times10^{-08} & -7.882\times10^{-09} & 0.0 & 0.0 & 1.717\times10^{-09}\\\end{array}\right)\end{equation*}
==================== Lindblad steadystate dm
Quantum object: dims = [[10, 2], [10, 2]], shape = (20, 20), type = oper, isherm = True\begin{equation*}\left(\begin{array}{*{11}c}0.595 & 0.0 & 0.0 & (-0.256+6.823\times10^{-04}j) & (0.143-9.396\times10^{-04}j) & \cdots & (-4.275\times10^{-04}+1.073\times10^{-05}j) & (1.136\times10^{-04}-3.328\times10^{-06}j) & 0.0 & 0.0 & (-2.435\times10^{-05}+8.046\times10^{-07}j)\\0.0 & 0.073 & (-0.092+6.046\times10^{-04}j) & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & (4.927\times10^{-05}-5.798\times10^{-07}j) & (-1.237\times10^{-05}+1.515\times10^{-07}j) & 0.0\\0.0 & (-0.092-6.046\times10^{-04}j) & 0.129 & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & (-6.825\times10^{-05}+2.628\times10^{-06}j) & (1.592\times10^{-05}-7.139\times10^{-07}j) & 0.0\\(-0.256-6.823\times10^{-04}j) & 0.0 & 0.0 & 0.114 & (-0.066+2.619\times10^{-04}j) & \cdots & (2.457\times10^{-04}-4.655\times10^{-06}j) & (-7.023\times10^{-05}+1.572\times10^{-06}j) & 0.0 & 0.0 & (1.610\times10^{-05}-4.199\times10^{-07}j)\\(0.143+9.396\times10^{-04}j) & 0.0 & 0.0 & (-0.066-2.619\times10^{-04}j) & 0.042 & \cdots & (-1.764\times10^{-04}+2.688\times10^{-06}j) & (4.798\times10^{-05}-8.212\times10^{-07}j) & 0.0 & 0.0 & (-1.033\times10^{-05}+2.020\times10^{-07}j)\\\vdots & \vdots & \vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots & \vdots & \vdots\\(-4.275\times10^{-04}-1.073\times10^{-05}j) & 0.0 & 0.0 & (2.457\times10^{-04}+4.655\times10^{-06}j) & (-1.764\times10^{-04}-2.688\times10^{-06}j) & \cdots & 1.254\times10^{-05} & (-6.267\times10^{-06}+5.402\times10^{-08}j) & 0.0 & 0.0 & (2.063\times10^{-06}-3.414\times10^{-08}j)\\(1.136\times10^{-04}+3.328\times10^{-06}j) & 0.0 & 0.0 & (-7.023\times10^{-05}-1.572\times10^{-06}j) & (4.798\times10^{-05}+8.212\times10^{-07}j) & \cdots & (-6.267\times10^{-06}-5.402\times10^{-08}j) & 3.769\times10^{-06} & 0.0 & 0.0 & (-1.360\times10^{-06}+9.785\times10^{-09}j)\\0.0 & (4.927\times10^{-05}+5.798\times10^{-07}j) & (-6.825\times10^{-05}-2.628\times10^{-06}j) & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & 3.466\times10^{-06} & (-1.444\times10^{-06}+1.217\times10^{-08}j) & 0.0\\0.0 & (-1.237\times10^{-05}-1.515\times10^{-07}j) & (1.592\times10^{-05}+7.139\times10^{-07}j) & 0.0 & 0.0 & \cdots & 0.0 & 0.0 & (-1.444\times10^{-06}-1.217\times10^{-08}j) & 7.649\times10^{-07} & 0.0\\(-2.435\times10^{-05}-8.046\times10^{-07}j) & 0.0 & 0.0 & (1.610\times10^{-05}+4.199\times10^{-07}j) & (-1.033\times10^{-05}-2.020\times10^{-07}j) & \cdots & (2.063\times10^{-06}+3.414\times10^{-08}j) & (-1.360\times10^{-06}-9.785\times10^{-09}j) & 0.0 & 0.0 & 6.148\times10^{-07}\\\end{array}\right)\end{equation*}
==================== Steadystate expectation values
R_ob: [0.267645307720865, 0.1560205514129042]
R_eb: [0.267645307720865, 0.1560205514129042]
L : [0.4465560981540205, 0.22225842348795147]
==================== Dynamics final states
R: [0.26764721566971927, 0.15602106817515593]
L: [0.44662603050034932, 0.22228388401493518]
In [40]:
from qutip.ipynbtools import version_table
version_table()
Out[40]:
Software Version QuTiP 4.2.0 Numpy 1.13.1 SciPy 0.19.1 matplotlib 2.0.2 Cython 0.25.2 Number of CPUs 2 BLAS Info INTEL MKL IPython 6.1.0 Python 3.6.1 |Anaconda custom (x86_64)| (default, May 11 2017, 13:04:09)
[GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)] OS posix [darwin] Wed Jul 19 22:06:57 2017 MDT
In [ ]:
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