/
periodic_detuning.py
125 lines (102 loc) · 2.86 KB
/
periodic_detuning.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
import numpy as np
from numpy import ceil, sin, sqrt
from numpy.linalg import eig
from plotting import *
from utils import get_eig, get_H_eff, inner, get_x, get_prob
FIG_PATH = "figs/periodic_detuning/"
V0 = 1e2
N = 10_000
eps = 1
def V(x, Vr, V0 = V0):
n = len(x)
m = int(ceil(n/3))
V = np.zeros(n)
V[m:2*m] = V0*np.ones(m)
V[2*m:] = Vr*np.ones(n-2*m)
return V
def plot_vecs(N, Vr):
l, v = get_eig(N, lambda x: V(x, Vr), 2)
x = get_x(N)
fig, ax = plt.subplots()
v1 = v[:, 0]
v2 = v[:, 1]
print(inner(v1, V(x, Vr, 0)*v1))
print(inner(v2, V(x, Vr, 0)*v1))
print(inner(v2, V(x, Vr, 0)*v2))
print(inner(v1, V(x, Vr, 0)*v2))
ax.plot(x, v1)
ax.plot(x, v2)
ax2 = ax.twinx()
ax2.plot(x, V(x, Vr), "k--")
y1 = np.max(abs(v))
y2 = np.max(abs(V(x, Vr)))
# ax.set_ylim(-y1*1.1, y1*1.1)
ax2.set_ylim(-y2*1.1, y2*1.1)
plt.plot()
plt.show()
def plot_diff_vals(N, Vrs):
n = len(Vrs)
diff1 = []
diff2 = []
l0, v0 = get_eig(N, lambda x: V(x, 0, V0), 2)
for i in range(n):
Vr = Vrs[i]
l1, _ = get_eig(N, lambda x: V(x, Vr), 2)
H_eff = get_H_eff(N, l0, v0, V, Vr)
l2, _ = eig(H_eff)
diff1.append(l1[1] - l1[0])
diff2.append(l2[1] - l2[0])
fig, ax = plt.subplots()
ax.plot(Vrs, diff1, label="full system")
ax.plot(Vrs, diff2, label="effective system")
ax.legend()
ax.set_ylabel("$\Delta E/ [2mL/\hbar^2]$")
ax.set_xlabel("$V_r/ [2mL/\hbar^2]$")
plt.show()
def plot_H_eff_vecs(N, Vrs):
n = len(Vrs)
fig, ax = plt.subplots(2)
for i in range(n):
Vr = Vrs[i]
H_eff = get_H_eff(N, V, Vr)
l, v = eig(H_eff)
indx = np.argsort(l)
v = v[:, indx]
l, v2 = get_eig(N, lambda x:V(x, Vr), 2)
x = get_x(N)
ax[0].plot([0.25, 0.75], abs(v[:, 0])**2, "kx")
ax2 = ax[0].twinx()
ax2.plot(x, abs(v2[:, 0])**2, color=color(i, n))
ax[1].plot([0.25, 0.75], abs(v[:, 1])**2, "kx")
ax3 = ax[1].twinx()
ax3.plot(x, abs(v2[:, 1])**2, color=color(i, n))
plt.show()
def plot_prob():
N = 10_000
T = 1_000
tau = 0.01
ws = [0.96, 0.98, 1., 1.01, 1.03]
v0 = np.array([1, 0])
t = np.linspace(0, T, N)
fig, ax = plt.subplots(figsize=(10, 4))
for i, w, in enumerate(ws):
p = get_prob(v0, N, T, tau, w)
ax.plot(
t, p,
color=cm.viridis(i/len(ws)),
label="$\\omega = {}$".format(w)
)
ax.plot(
t, sin(t*tau/2)**2, "-.k",
label="$\sin^2(t \\tau /2)$"
)
ax.set_xlabel("$t/[2mL^2/\\hbar]$")
ax.set_ylabel("$|a_1|^2$")
ax.legend()
plt.tight_layout()
plt.savefig(FIG_PATH + "rabi_osc.pdf")
Vrs = np.linspace(-10, 10, 51)
# plot_vecs(N, 0.0001)
# plot_diff_vals(N, Vrs)
# plot_H_eff_vecs(N, [-0.05])
plot_prob()