def draw_bloch_sphere(ax,
R=1,
color='yellow',
npts=30,
elev=15,
azim=15,
lim=None):
from numpy import linspace, sin, cos, pi, outer, ones, size
# Set up the basic 3d plot
ax.set_aspect("equal")
ax.view_init(elev=elev, azim=azim)
# Draw the sphere
u = linspace(0, 2 * pi, npts)
v = linspace(0, pi, npts)
x = R * outer(cos(u), sin(v))
y = R * outer(sin(u), sin(v))
z = R * outer(ones(size(u)), cos(v))
ax.plot_surface(x,
y,
z,
rstride=1,
cstride=1,
color=color,
alpha=0.1,
linewidth=0)
# Draw the axes
c = 'black'
draw_vec(ax, [1, 0, 0], color=c, label=r'$|+x\rangle$', fudge=1.75)
draw_vec(ax, [0, 1, 0], color=c, label=r'$|+y\rangle$')
draw_vec(ax, [0, 0, 1], color=c, label=r'$|+z\rangle$')
draw_vec(ax, [0, 0, -1], color=c, label=r'$|-z\rangle$', fudge=1.2)
# Draw a dashed line around the "equator."
N = 100
x = []
y = []
z = []
sin_theta = sin(pi / 2)
cos_theta = cos(pi / 2)
phi = 0
for n in range(N + 1):
x += [
R * sin_theta * cos(phi),
]
y += [
R * sin_theta * sin(phi),
]
z += [
R * cos_theta,
]
phi += 2 * pi / N
ax.plot(x, y, z, color='gray', linestyle='--')
if lim != None:
ax.set_xlim3d(-lim, lim)
ax.set_ylim3d(-lim, lim)
ax.set_zlim3d(-lim, lim)
def __init__(self, ax, alpha, beta, bs_lim=None):
from numpy import sin, cos, arccos, angle
from matplotlib import pyplot as pl
self.clr = 'green'
self.ax = ax
draw_bloch_sphere(ax, lim=bs_lim)
theta = 2 * arccos(abs(alpha))
phi = angle(beta) - angle(alpha)
x = cos(phi) * sin(theta)
y = sin(phi) * sin(theta)
z = cos(theta)
# Label for the Psi vector (if we want one)
self.vlabel = r'$|\psi\rangle$'
self.vlabel = '' # Don't notate psi for now.
# last_vec holds pointers to the vector and text objects.
# Delete them with last_vec[0].remove(), etc ...
self.last_vec = draw_vec(ax, [x, y, z],
color=self.clr,
label=self.vlabel,
fudge=1.3)
pl.draw()
pl.show()
def update(self, time, alpha, beta):
from numpy import sin, cos, arccos, angle
from matplotlib import pyplot as pl
ax = self.ax
self.last_vec[0].remove()
self.last_vec[1].remove()
theta = 2*arccos(abs(alpha))
phi = angle(beta)-angle(alpha)
x = cos(phi)*sin(theta)
y = sin(phi)*sin(theta)
z = cos(theta)
self.last_vec = draw_vec(
ax,[x,y,z],color=self.clr,label=self.vlabel,fudge=1.3)
pl.draw()
pl.show()
def update(self, time, alpha, beta):
from numpy import sin, cos, arccos, angle
ax = self.ax
self.last_vec[0].remove()
self.last_vec[1].remove()
theta = 2 * arccos(abs(alpha))
phi = angle(beta) - angle(alpha)
x = cos(phi) * sin(theta)
y = sin(phi) * sin(theta)
z = cos(theta)
self.last_vec = draw_vec(ax, [x, y, z],
color=self.clr,
label=self.vlabel,
fudge=1.3)
pl.draw()
pl.show()
def draw_bloch_sphere(ax,
R=1, color='yellow', npts=30, elev=15, azim=15, lim=None):
from numpy import linspace, sin, cos, pi, outer, ones, size
# Set up the basic 3d plot
ax.set_aspect("equal")
ax.view_init(elev=elev, azim=azim)
# Draw the sphere
u = linspace(0, 2 * pi, npts)
v = linspace(0, pi, npts)
x = R*outer(cos(u), sin(v))
y = R*outer(sin(u), sin(v))
z = R*outer(ones(size(u)), cos(v))
ax.plot_surface(
x, y, z, rstride=1, cstride=1, color=color, alpha = 0.1,
linewidth = 0)
# Draw the axes
c = 'black'
draw_vec(ax, [1,0,0], color=c, label=r'$|+x\rangle$', fudge=1.75)
draw_vec(ax, [0,1,0], color=c, label=r'$|+y\rangle$')
draw_vec(ax, [0,0,1], color=c, label=r'$|+z\rangle$')
draw_vec(ax, [0,0,-1], color=c, label=r'$|-z\rangle$', fudge=1.2)
# Draw a dashed line around the "equator."
N=100
x = []; y = []; z = []
sin_theta = sin(pi/2)
cos_theta = cos(pi/2)
phi = 0
for n in range(N+1):
x += [ R*sin_theta*cos(phi), ]
y += [ R*sin_theta*sin(phi), ]
z += [ R*cos_theta, ]
phi += 2*pi/N
ax.plot(x, y, z, color='gray', linestyle='--')
if lim != None:
ax.set_xlim3d(-lim,lim)
ax.set_ylim3d(-lim,lim)
ax.set_zlim3d(-lim,lim)
def draw_xyz(ax, v, color='green', draw_box=True):
from sglib import draw_vec
# Draw the axes
draw_vec(ax, [1, 0, 0], color='black', label='x')
draw_vec(ax, [0, 1, 0], color='black', label='y')
draw_vec(ax, [0, 0, 1], color='black', label='z')
# Draw the spin vectors
draw_vec(ax, v, label=r'$\vec{v}$', color=color)
if draw_box: pass
else: ax.set_axis_off()
# If you use "equal" then the last parm on position sets size?
# But this causes it to fail outsize a notebook!
#ax.set_position([1,1,1,2])
ax.set_aspect("equal")
ax.view_init(elev=5, azim=25)
pl.draw()
pl.show()
def draw_xyz(ax, v, color='green', draw_box=True):
import matplotlib.pyplot as pl
from sglib import draw_vec
# Draw the axes
draw_vec(ax, [1,0,0], color='black', label='x')
draw_vec(ax, [0,1,0], color='black', label='y')
draw_vec(ax, [0,0,1], color='black', label='z')
# Draw the spin vectors
draw_vec(ax, v, label=r'$\vec{v}$', color=color)
if draw_box: pass
else: ax.set_axis_off()
# If you use "equal" then the last parm on position sets size?
# But this causes it to fail outsize a notebook!
#ax.set_position([1,1,1,2])
ax.set_aspect("equal")
ax.view_init(elev=5, azim=25)
pl.draw()
pl.show()
def __init__(self, ax, alpha, beta, bs_lim=None):
from numpy import sin, cos, arccos, angle
from matplotlib import pyplot as pl
self.clr = 'green'
self.ax = ax
draw_bloch_sphere(ax, lim=bs_lim)
theta = 2*arccos(abs(alpha))
phi = angle(beta)-angle(alpha)
x = cos(phi)*sin(theta)
y = sin(phi)*sin(theta)
z = cos(theta)
# Label for the Psi vector (if we want one)
self.vlabel = r'$|\psi\rangle$'
self.vlabel = '' # Don't notate psi for now.
# last_vec holds pointers to the vector and text objects.
# Delete them with last_vec[0].remove(), etc ...
self.last_vec = draw_vec(
ax,[x,y,z],color=self.clr,label=self.vlabel,fudge=1.3)
pl.draw()
pl.show()