def decoherence(self):
gamma = self.gamma
if self.d1 == 1:
j2 = 1.0 / 2.0
Gamma = 2 * np.pi * 4.575e6 #this is parameter for D1 line
else:
j2 = 3.0 / 2.0
Gamma = 2 * np.pi * 5.234e6
#Gamma = 2*np.pi*750.0e6
n = self.parameter['n']
self.parameter['decoherence_matrix'] = [[[] for i in range(n)]
for j in range(n)]
cs = Atom()
#gamma
for i in range(n):
for j in range(i, n):
d1 = self.index2lfm(i)
d2 = self.index2lfm(j)
if d1[0:2] == (0, 3) and d2[0:2] == (0, 3): #ground state
if i == j: # diagonal
for q in range(-4, 5):
ii = int(self.lfm2index(0, 4, q))
self.parameter['decoherence_matrix'][ii][
ii].append([ii, ii, -1 * gamma / 9.0])
self.parameter['decoherence_matrix'][ii][
ii].append([i, j, gamma / 9.0])
self.parameter['decoherence_matrix'][i][j].append(
[ii, ii, gamma / 9.0])
self.parameter['decoherence_matrix'][i][j].append(
[i, j, -1 * gamma / 9.0])
# self.graph.add_edge(pydot.Edge(self.l0subn[4][int(d1[2]+q+4)],self.l0subn[3][int(d1[2]+3)],label = 'gamma/9'))
if d2[0:2] == (0, 3):
for q in range(-4, 5):
allow_state = []
allow_state.append(self.lfm2index(0, 4, q))
# print allow_state ,self.index2lfm(i),self.index2lfm(j)
if i in allow_state:
# print('allowed non diagonal states')
self.parameter['decoherence_matrix'][i][j].append(
[i, j, -1.0 * gamma / 9.0])
#Gamma
for pair in self.egpair:
for i in range(n):
for j in range(i, n):
d1 = self.index2lfm(i)
d2 = self.index2lfm(j)
if d1[0:2] == pair[0] and d2[0:2] == pair[0] and i != j:
self.parameter['decoherence_matrix'][i][j].append(
[i, j, -1.0 * Gamma])
elif d1[0:2] == pair[0] and d2[0:2] == pair[1]:
self.parameter['decoherence_matrix'][i][j].append(
[i, j, -1.0 * Gamma / 2.0])
elif d1[0:2] == pair[1] and d2[0:2] == pair[0]:
self.parameter['decoherence_matrix'][i][j].append(
[i, j, -1.0 * Gamma / 2.0])
elif d1[0:2] == pair[1] and d2[0:2] == pair[1]:
for q in (-1.0, 0.0, 1.0):
f1 = pair[0][1]
if (d1[2] + q <= f1 and d1[2] + q >= -1 * f1) and (
d2[2] + q <= f1 and d2[2] + q >= -1 * f1):
coef1 = {
'q': q,
'L1': 0,
'L2': 1,
'F1': pair[1][1],
'F2': pair[0][1],
'mf1': d1[2],
'mf2': d1[2] + q,
'J1': 1.0 / 2.0,
'J2': j2,
'I': 7.0 / 2.0
}
coef2 = {
'q': q,
'L1': 0,
'L2': 1,
'F1': pair[1][1],
'F2': pair[0][1],
'mf1': d2[2],
'mf2': d2[2] + q,
'J1': 1.0 / 2.0,
'J2': j2,
'I': 7.0 / 2.0
}
#this correction coefficient (see equation 54) should be written to atom.py later
rev = (-1)**(pair[0][1] - pair[1][1] +
q) * math.sqrt(
(2 * pair[0][1] + 1) /
(2 * pair[1][1] + 1))
rev = rev**2
tmp = Gamma * cs.cg_coef(**coef1) * cs.cg_coef(
**coef2) * rev
if tmp != 0.0:
ii = self.lfm2index(
pair[0][0], pair[0][1], d1[2] + q)
jj = self.lfm2index(
pair[0][0], pair[0][1], d2[2] + q)
self.parameter['decoherence_matrix'][i][
j].append([ii, jj, tmp])
if ii == jj:
self.parameter['decoherence_matrix'][
int(ii)][int(jj)].append(
[ii, jj, -1 * tmp])
#add to graph
f1 = int(pair[0][1])
f2 = int(pair[1][1])
label = '%.2e' % tmp
self.graph.add_edge(
pydot.Edge(
self.l1subn[f1][int(d1[2] + q +
f1)],
self.l0subn[f2][int(d1[2] +
f2)],
label=label))
def decoherence(parameter):
Gamma = 2 * np.pi * 4.575e6 #this is parameter for D1 line
n = parameter['n']
parameter['decoherence_matrix'] = [[[] for i in range(n)]
for j in range(n)]
cs = Atom()
"""
e l=1 f=3 g l=0 f=4
e l=1 f=3 g l=0 f=3
"""
# for f in (3.0,4.0):
# for m in range(-1*f,f+1):
# for m2 in range(-3,4)
# for q in (-1.0,0.0,1.0):
# coef1 = {'q':q,
# 'L1':0,
# 'L2':1,
# 'F1':f,
# 'F2':3,
# 'mf1':m,
# 'mf2':m2,
# 'J1':1.0/2.0,
# 'J2':1.0/2.0,
# 'I':7.0/2.0}
# tmp = Gamma * pow(cs.cg_coef(**coef1),2)
# parameter['decoherence_matrix'][i][j].append([lfm2index(pair[0][0],pair[0][1],d1[2]+q),lfm2index(pair[0][0],pair[0][1],d2[2]+q),tmp])
#egpair=(((1,3),(0,4)),((1,3),(0,3)))
egpair = (((1, 3), (0, 4)), )
for pair in egpair:
for i in range(n):
for j in range(i, n):
d1 = index2lfm(i)
d2 = index2lfm(j)
if d1[0:2] == pair[0] and d2[0:2] == pair[0]:
parameter['decoherence_matrix'][i][j].append(
[i, j, -1.0 * Gamma])
elif d1[0:2] == pair[0] and d2[0:2] == pair[1]:
parameter['decoherence_matrix'][i][j].append(
[i, j, -1.0 * Gamma / 2.0])
elif d1[0:2] == pair[1] and d2[0:2] == pair[0]:
parameter['decoherence_matrix'][i][j].append(
[i, j, -1.0 * Gamma / 2.0])
elif d1[0:2] == pair[1] and d2[0:2] == pair[1]:
for q in (-1.0, 0.0, 1.0):
f1 = pair[0][1]
if (d1[2] + q <= f1 and d1[2] + q >= -1 * f1) and (
d2[2] + q <= f1 and d2[2] + q >= -1 * f1):
coef1 = {
'q': q,
'L1': 0,
'L2': 1,
'F1': pair[1][1],
'F2': pair[0][1],
'mf1': d1[2],
'mf2': d1[2] + q,
'J1': 1.0 / 2.0,
'J2': 1.0 / 2.0,
'I': 7.0 / 2.0
}
coef2 = {
'q': q,
'L1': 0,
'L2': 1,
'F1': pair[1][1],
'F2': pair[0][1],
'mf1': d2[2],
'mf2': d2[2] + q,
'J1': 1.0 / 2.0,
'J2': 1.0 / 2.0,
'I': 7.0 / 2.0
}
tmp = Gamma * cs.cg_coef(**coef1) * cs.cg_coef(
**coef2)
if tmp != 0.0:
parameter['decoherence_matrix'][i][j].append([
lfm2index(pair[0][0], pair[0][1],
d1[2] + q),
lfm2index(pair[0][0], pair[0][1],
d2[2] + q), tmp
])
return parameter
def decoherence(self):
gamma = self.gamma
if self.d1 == 1:
j2 = 1.0/2.0
#Gamma = 2*np.pi*4.575e6 #Decay Rate/Natural Line Width (rad)
else:
j2 = 3.0/2.0
#Gamma = 2*np.pi*5.234e6 #Decay Rate/Natural Line Width (rad)
#Gamma = 2*np.pi*750.0e6
Gamma = 2*np.pi*9e7
n=self.parameter['n']
self.parameter['decoherence_matrix'] = [[[] for i in range(n)] for j in range(n)]
cs = Atom()
#gamma
for i in range(n):
for j in range(i,n):
d1 = self.index2lfm(i)
d2 = self.index2lfm(j)
if d1[0:2] == (0,4) and d2[0:2] == (0,3): #ground state
#if np.abs(d1[2]-d2[2]) <= 2: #no selection rule
self.parameter['decoherence_matrix'][i][i].append([i,i,-1.0*gamma])
self.parameter['decoherence_matrix'][i][i].append([j,j,gamma])
self.parameter['decoherence_matrix'][j][j].append([j,j,-1.0*gamma])
self.parameter['decoherence_matrix'][j][j].append([i,i,gamma])
self.parameter['decoherence_matrix'][i][j].append([i,j,-1.0*gamma])
# self.graph.add_edge(pydot.Edge(self.l0subn[4][int(d1[2]+q+4)],self.l0subn[3][int(d1[2]+3)],label = 'gamma/9'))
if d2[0:2] == (0,3):
for q in range(-4,5):
allow_state = []
allow_state.append(self.lfm2index(0,4,q))
# print allow_state ,self.index2lfm(i),self.index2lfm(j)
if i in allow_state:
# print('allowed non diagonal states')
self.parameter['decoherence_matrix'][i][j].append([i,j,-1.0*gamma/9.0])
#Gamma
for pair in self.egpair:
for i in range(n):
for j in range(i,n):
d1 = self.index2lfm(i)
d2 = self.index2lfm(j)
if d1[0:2] == pair[0] and d2[0:2] == pair[0] and i != j: #both are excited
self.parameter['decoherence_matrix'][i][j].append([i,j,-1.0*Gamma])
elif d1[0:2] == pair[0] and d2[0:2] == pair[1]:#d1 is excited d2 is ground
self.parameter['decoherence_matrix'][i][j].append([i,j,-1.0*Gamma/2.0])
elif d1[0:2] == pair[1] and d2[0:2] == pair[0]:# d2 is excited d1 is ground
self.parameter['decoherence_matrix'][i][j].append([i,j,-1.0*Gamma/2.0])
elif d1[0:2] == pair[1] and d2[0:2] == pair[1]:# both ground
for q in (-1.0,0.0,1.0):
f1 = pair[0][1]
if (d1[2]+q <= f1 and d1[2]+q >= -1*f1) and (d2[2]+q <= f1 and d2[2]+q >= -1*f1):
coef1 = {'q':q,
'L1':0,
'L2':1,
'F1':pair[1][1],
'F2':pair[0][1],
'mf1':d1[2],
'mf2':d1[2]+q,
'J1':1.0/2.0,
'J2':j2,
'I':7.0/2.0}
coef2 = {'q':q,
'L1':0,
'L2':1,
'F1':pair[1][1],
'F2':pair[0][1],
'mf1':d2[2],
'mf2':d2[2]+q,
'J1':1.0/2.0,
'J2':j2,
'I':7.0/2.0}
#this correction coefficient (see equation 54) should be written to atom.py later
rev = (-1)**(pair[0][1]-pair[1][1]+q)*math.sqrt((2*pair[0][1]+1)/(2*pair[1][1]+1))
rev = rev**2 #-1's power doesn't matter now, but still need to be checked
tmp = Gamma*cs.cg_coef(**coef1)*cs.cg_coef(**coef2)*rev
if tmp != 0.0:
ii = self.lfm2index(pair[0][0],pair[0][1],d1[2]+q)
jj = self.lfm2index(pair[0][0],pair[0][1],d2[2]+q)
self.parameter['decoherence_matrix'][i][j].append([ii,jj,tmp])
if ii == jj:
self.parameter['decoherence_matrix'][int(ii)][int(jj)].append([ii,jj,-1*tmp])
def decoherence(self):
gamma = self.gamma
if self.d1 == 1:
j2 = 1.0/2.0
Gamma = 2*np.pi*4.575e6 #this is parameter for D1 line
else:
j2 = 3.0/2.0
Gamma = 2*np.pi*5.234e6
#Gamma = 2*np.pi*750.0e6
n=self.parameter['n']
self.parameter['decoherence_matrix'] = [[[] for i in range(n)] for j in range(n)]
cs = Atom()
#gamma
for i in range(n):
for j in range(i,n):
d1 = self.index2lfm(i)
d2 = self.index2lfm(j)
if d1[0:2] == (0,3) and d2[0:2] == (0,3): #ground state
if i == j: # diagonal
for q in range(-4,5):
ii = int(self.lfm2index(0,4,q))
self.parameter['decoherence_matrix'][ii][ii].append([ii,ii,-1*gamma/9.0])
self.parameter['decoherence_matrix'][ii][ii].append([i,j,gamma/9.0])
self.parameter['decoherence_matrix'][i][j].append([ii,ii,gamma/9.0])
self.parameter['decoherence_matrix'][i][j].append([i,j,-1*gamma/9.0])
# self.graph.add_edge(pydot.Edge(self.l0subn[4][int(d1[2]+q+4)],self.l0subn[3][int(d1[2]+3)],label = 'gamma/9'))
if d2[0:2] == (0,3):
for q in range(-4,5):
allow_state = []
allow_state.append(self.lfm2index(0,4,q))
# print allow_state ,self.index2lfm(i),self.index2lfm(j)
if i in allow_state:
# print('allowed non diagonal states')
self.parameter['decoherence_matrix'][i][j].append([i,j,-1.0*gamma/9.0])
#Gamma
for pair in self.egpair:
for i in range(n):
for j in range(i,n):
d1 = self.index2lfm(i)
d2 = self.index2lfm(j)
if d1[0:2] == pair[0] and d2[0:2] == pair[0] and i != j:
self.parameter['decoherence_matrix'][i][j].append([i,j,-1.0*Gamma])
elif d1[0:2] == pair[0] and d2[0:2] == pair[1]:
self.parameter['decoherence_matrix'][i][j].append([i,j,-1.0*Gamma/2.0])
elif d1[0:2] == pair[1] and d2[0:2] == pair[0]:
self.parameter['decoherence_matrix'][i][j].append([i,j,-1.0*Gamma/2.0])
elif d1[0:2] == pair[1] and d2[0:2] == pair[1]:
for q in (-1.0,0.0,1.0):
f1 = pair[0][1]
if (d1[2]+q <= f1 and d1[2]+q >= -1*f1) and (d2[2]+q <= f1 and d2[2]+q >= -1*f1):
coef1 = {'q':q,
'L1':0,
'L2':1,
'F1':pair[1][1],
'F2':pair[0][1],
'mf1':d1[2],
'mf2':d1[2]+q,
'J1':1.0/2.0,
'J2':j2,
'I':7.0/2.0}
coef2 = {'q':q,
'L1':0,
'L2':1,
'F1':pair[1][1],
'F2':pair[0][1],
'mf1':d2[2],
'mf2':d2[2]+q,
'J1':1.0/2.0,
'J2':j2,
'I':7.0/2.0}
#this correction coefficient (see equation 54) should be written to atom.py later
rev = (-1)**(pair[0][1]-pair[1][1]+q)*math.sqrt((2*pair[0][1]+1)/(2*pair[1][1]+1))
rev = rev**2
tmp = Gamma*cs.cg_coef(**coef1)*cs.cg_coef(**coef2)*rev
if tmp != 0.0:
ii = self.lfm2index(pair[0][0],pair[0][1],d1[2]+q)
jj = self.lfm2index(pair[0][0],pair[0][1],d2[2]+q)
self.parameter['decoherence_matrix'][i][j].append([ii,jj,tmp])
if ii == jj:
self.parameter['decoherence_matrix'][int(ii)][int(jj)].append([ii,jj,-1*tmp])
#add to graph
f1 = int(pair[0][1])
f2 = int(pair[1][1])
label = '%.2e'%tmp
self.graph.add_edge(pydot.Edge(self.l1subn[f1][int(d1[2]+q+f1)],self.l0subn[f2][int(d1[2]+f2)],label = label))
def decoherence(parameter):
Gamma = 2 * np.pi * 4.575e6 # this is parameter for D1 line
n = parameter["n"]
parameter["decoherence_matrix"] = [[[] for i in range(n)] for j in range(n)]
cs = Atom()
"""
e l=1 f=3 g l=0 f=4
e l=1 f=3 g l=0 f=3
"""
# for f in (3.0,4.0):
# for m in range(-1*f,f+1):
# for m2 in range(-3,4)
# for q in (-1.0,0.0,1.0):
# coef1 = {'q':q,
# 'L1':0,
# 'L2':1,
# 'F1':f,
# 'F2':3,
# 'mf1':m,
# 'mf2':m2,
# 'J1':1.0/2.0,
# 'J2':1.0/2.0,
# 'I':7.0/2.0}
# tmp = Gamma * pow(cs.cg_coef(**coef1),2)
# parameter['decoherence_matrix'][i][j].append([lfm2index(pair[0][0],pair[0][1],d1[2]+q),lfm2index(pair[0][0],pair[0][1],d2[2]+q),tmp])
# egpair=(((1,3),(0,4)),((1,3),(0,3)))
egpair = (((1, 3), (0, 4)),)
for pair in egpair:
for i in range(n):
for j in range(i, n):
d1 = index2lfm(i)
d2 = index2lfm(j)
if d1[0:2] == pair[0] and d2[0:2] == pair[0]:
parameter["decoherence_matrix"][i][j].append([i, j, -1.0 * Gamma])
elif d1[0:2] == pair[0] and d2[0:2] == pair[1]:
parameter["decoherence_matrix"][i][j].append([i, j, -1.0 * Gamma / 2.0])
elif d1[0:2] == pair[1] and d2[0:2] == pair[0]:
parameter["decoherence_matrix"][i][j].append([i, j, -1.0 * Gamma / 2.0])
elif d1[0:2] == pair[1] and d2[0:2] == pair[1]:
for q in (-1.0, 0.0, 1.0):
f1 = pair[0][1]
if (d1[2] + q <= f1 and d1[2] + q >= -1 * f1) and (d2[2] + q <= f1 and d2[2] + q >= -1 * f1):
coef1 = {
"q": q,
"L1": 0,
"L2": 1,
"F1": pair[1][1],
"F2": pair[0][1],
"mf1": d1[2],
"mf2": d1[2] + q,
"J1": 1.0 / 2.0,
"J2": 1.0 / 2.0,
"I": 7.0 / 2.0,
}
coef2 = {
"q": q,
"L1": 0,
"L2": 1,
"F1": pair[1][1],
"F2": pair[0][1],
"mf1": d2[2],
"mf2": d2[2] + q,
"J1": 1.0 / 2.0,
"J2": 1.0 / 2.0,
"I": 7.0 / 2.0,
}
tmp = Gamma * cs.cg_coef(**coef1) * cs.cg_coef(**coef2)
if tmp != 0.0:
parameter["decoherence_matrix"][i][j].append(
[
lfm2index(pair[0][0], pair[0][1], d1[2] + q),
lfm2index(pair[0][0], pair[0][1], d2[2] + q),
tmp,
]
)
return parameter
