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half_JPC.py
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# -*- coding: utf-8 -*-
"""
Created on Mon May 30 15:11:49 2016
@author: leghtas
"""
import scipy.constants as sc
import numpy as np
import matplotlib.pyplot as plt
import circuit as cc
import circuit_half_JPC as cHJPC
import scipy.linalg as sl
import numpy.linalg as nl
from scipy.misc import factorial
import matplotlib
from matplotlib.animation import FuncAnimation
import sys
e = cc.e
def move_figure(f, x, y):
"""Move figure's upper left corner to pixel (x, y)"""
backend = matplotlib.get_backend()
if backend == 'TkAgg':
f.canvas.manager.window.wm_geometry("+%d+%d" % (x, y))
elif backend == 'WXAgg':
f.canvas.manager.window.SetPosition((x, y))
else:
# This works for QT and GTK
# You can also use window.setGeometry
f.canvas.manager.window.move(x, y)
plt.show()
pi = np.pi
plt.close('all')
wa, Za = [11e9*2*np.pi, 90]
wb, Zb = [4e9*2*np.pi, 90]
Cc = 3.7*1e-15
LJ = 10e-9 #Henri
L = 3e-9
Ls = 0.01e-9
c = cHJPC.CircuitPump2Snail(wa, Za, wb, Zb, Ls, LJ, L,)
max_freq_displayed = 15# GHz
min_phi = -1*2*pi
max_phi = 2*2*pi
Npts = 51
phi_Delta = np.linspace(min_phi, max_phi, Npts)
phi_Sum = np.linspace(min_phi, max_phi, Npts)
ng_sweep = np.linspace(-1, 1, 21)
min_Cca = 1e-15
max_Cca = 100000e-15
Npts = 101
CcaVec = np.linspace(min_Cca, max_Cca, Npts)
ECcaVec = e**2/2/CcaVec
#Plot potential
if 1==0:
fig, ax = plt.subplots(figsize = (12,12))
ax.set_xlabel(r'$\varphi_r$', fontsize = fs)
ax.set_ylabel(r'$\varphi_s$', fontsize = fs)
min_i = 0
max_i = 10
def update(i):
Phi_ext = np.linspace(0,2*np.pi, max_i-min_i)
phi_ext= Phi_ext[i]
U = c.get_U(phi_ext_0=phi_ext)
shape=(40,20)
Ps = np.linspace(-8*np.pi, 8*np.pi, shape[0])
Pr = np.linspace(-8*np.pi, 8*np.pi, shape[1])
U_color = np.empty(shape)
for ii, ps in enumerate(Ps):
for jj, pr in enumerate(Pr):
U_color[ii, jj] = U(np.array([ps, pr]))
ax.pcolor(Pr, Ps, U_color, vmin=vmin, vmax=vmax)
return ax
# move_figure(fig, -1900, 10)
anim = FuncAnimation(fig, update, frames=np.arange(min_i, max_i), interval=200)
# if len(sys.argv) > 1 and sys.argv[1] == 'save':
anim.save('line.html', dpi=80, writer='imagemagick')
# Get freqs and Kerrs v.s. flux
if 1==1:
n_modes = c.dim
print('Found %d modes...'%(n_modes))
max_solutions = 1
particulars = [(0,0,0,1), (0,0,1,1)]
factors_particulars = np.array([1])
Xi2 = np.zeros((len(phi_Delta), len(phi_Sum), max_solutions, n_modes))
Xi3 = np.zeros((len(phi_Delta), len(phi_Sum), max_solutions, n_modes))
Xi4 = np.zeros((len(phi_Delta), len(phi_Sum), max_solutions, n_modes))
n_particulars = len(particulars)
Xip = np.zeros((len(phi_Delta), len(phi_Sum), max_solutions, n_particulars))
comp = np.zeros((len(phi_Sum), max_solutions, n_modes, n_modes))
for ll, yy in enumerate(phi_Delta):
for kk, xx in enumerate(phi_Sum):
_res = c.get_freqs_kerrs(particulars=particulars, return_components=True, max_solutions=max_solutions, sort=False, pext_1=(xx+yy)/2, pext_2=(xx-yy)/2)
res1, res2, Xi2s, Xi3s, Xi4s, Xips, P= _res
Xi2[ll, kk] = Xi2s
# Xi3[kk] = Xi3s
Xi4[ll,kk] = 2*Xi4s
Xip[ll, kk] = Xips
# comp[kk] = np.moveaxis(P, 1, -1)
Xi2 = np.moveaxis(Xi2, -1, 0)
Xi3 = np.moveaxis(Xi3, -1, 0)
Xi4 = np.moveaxis(Xi4, -1, 0)
Xip = np.moveaxis(Xip*factors_particulars, -1, 0)
#2D freq_map
if 1==1:
plt.close('all')
_phi_Sum, _phi_Delta = cc.to_pcolor(phi_Sum, phi_Delta)
# Xi2[3] = np.where(Xi2[3]<10e9, Xi2[3], Xi2[1])
colors = ['b', 'r', 'y', 'g', 'o']
fig0, ax0 = plt.subplots(2,figsize=(12,6))
figkerr, axkerr = plt.subplots(3,figsize=(12,6))
# figpumping, axpumping = plt.subplots(2, figsize=(12,6))
f = Xi2[:,:,:,0]/1e9 #MHz
kerr = Xi4[:,:,:,0]/1e6 #GHz
pumping = Xip[0,:,:,0]/1e6 #MHz
crosskerr = Xip[1,:,:,0]/1e6 #MHz
for ii in range(len(f)):
if ii<1:
cc.pcolor_z(ax0[ii], _phi_Sum/2/pi, _phi_Delta/2/pi, f[ii])#, '.', label= 'f'+str(ii), color = colors[ii])
ax0[ii].set_title('f%d'%(ii))
if ii==0:
extremum = (np.nanvar(kerr[ii])**0.5)
print(extremum)
else:
extremum = (np.nanvar(kerr[ii])**0.5)*5
cc.pcolor_z(axkerr[ii], _phi_Sum/2/pi, _phi_Delta/2/pi, kerr[ii], vmin= -extremum, vmax = extremum, cmap='bwr')#, '.', label= 'f'+str(ii), color = colors[ii])
axkerr[ii].set_title('c4%d'%(ii))
mean = np.nanmean(pumping)
extremum = (np.nanvar(pumping)**0.5)
print(extremum)
cc.pcolor_z(axkerr[1], _phi_Sum/2/pi, _phi_Delta/2/pi, pumping, vmin= -extremum, vmax = extremum, cmap='bwr')
cc.pcolor_z(axkerr[2], _phi_Sum/2/pi, _phi_Delta/2/pi, crosskerr, vmin= -extremum, vmax = extremum, cmap='bwr')
# ax0.plot(phiVec/2/pi, Xi2[2,:]/1e9, '.', label= 'f2')
# ax0.plot(phiVec/2/pi, Xi2[3,:]/1e9, '.', label= 'f3')
# ax0.legend()
# ax0.set_ylabel('GHz')
# ax0.set_ylim(0,max_freq_displayed)
# PLOT
if 1==0:
colors = ['b', 'r', 'y', 'g', 'o']
fig0, ax0 = plt.subplots(1, 2, figsize=(6,6))
for ii, f in enumerate(Xi2):
ax0.plot(phiVec/2/pi, f/1e9, '.', label= 'f'+str(ii), color = colors[ii])
# ax0.plot(phiVec/2/pi, Xi2[2,:]/1e9, '.', label= 'f2')
# ax0.plot(phiVec/2/pi, Xi2[3,:]/1e9, '.', label= 'f3')
ax0.legend()
ax0.set_ylabel('GHz')
ax0.set_ylim(0,max_freq_displayed)
index = np.argmin(np.abs(Xi2[1,:]-Xi2[0,:]-1e9))
fig, ax = plt.subplots(n_modes, 3, figsize=(16,8), sharex=True)
display_factor = 2
for ii in range(n_modes):
ax[ii, 0].plot(phiVec/2/pi, Xi2[ii]/1e9, '.', label= 'f'+str(ii))
ax[ii, 0].legend()
ax[ii, 0].set_ylabel('GHz')
ax[ii, 1].plot(phiVec/2/pi, Xi3[ii]/1e6)
ax[ii, 1].set_ylabel('MHz')
mean = np.nanmean(Xi3[ii]/1e6)
std = np.nanmean(Xi3[ii]/1e6)
ax[ii, 1].set_ylim(mean-display_factor*std, mean+display_factor*std)
ax[ii, 2].plot(phiVec/2/pi, Xi4[ii]/1e6)
ax[ii, 2].set_ylabel('MHz')
mean = np.nanmean(Xi4[ii]/1e6)
std = np.nanmean(Xi4[ii]/1e6)
ax[ii, 2].set_ylim(mean-display_factor*std, mean+display_factor*std)
ax[0,0].set_title('$a^{+}a$')
ax[0,1].set_title('$a^{+}a^2$')
ax[0,2].set_title('$a^{+2}a^2/2$')
#
#
# dphiVec = (phiVec[1:]+phiVec[:-1])/2
# figp, axp = plt.subplots(n_particulars,2, figsize=(16,8), sharex=True)
# display_factor = 2
# for ii in range(n_particulars):
# axp[ii, 0].plot(phiVec/2/pi, Xip[ii]/1e6, '.', label= str(particulars[ii]))
# axp[ii, 0].legend()
# axp[ii, 0].set_ylabel('MHz')
# mean = np.nanmean(Xip[ii]/1e6)
# std = np.nanmean(Xip[ii]/1e6)
# axp[ii, 0].set_ylim(mean-display_factor*std, mean+display_factor*std)
#
# dXip=np.diff(Xip[ii], axis=0)/(phiVec[1]-phiVec[0])*pi/10
# axp[ii, 1].plot(dphiVec/2/pi, dXip/1e6, '.', label= str(particulars[ii]))
# axp[ii, 1].legend()
# axp[ii, 1].set_ylabel('MHz')
# mean = np.nanmean(dXip/1e6)
# std = np.nanmean(dXip/1e6)
# axp[ii, 1].set_ylim(mean-display_factor*std, mean+display_factor*std)
#
#
#
## print('\nf0 = %.3f GHz\n'%(Xi2[0,:][0]/1e9)+'f1 = %.3f GHz'%(Xi2[1,:][0]/1e9))
## print('k0 = %.3f MHz\n'%(Xi4[0,:][0]/1e6)+'k1 = %.3f MHz\n'%(Xi4[1,:][0]/1e6)+'k01 = %.3f MHz'%(Xi_a2s2[0]/1e6))
##
## print('\nphi_ext_opt = %.3f'%(phiVec[index]/2/pi))
## print('f0 = %.3f GHz\n'%(Xi2[0,index]/1e9)+'f1 = %.3f GHz'%(Xi2[1,index]/1e9))
## print('k0 = %.3f MHz\n'%(Xi4[0,index]/1e6)+'k1 = %.3f MHz\n'%(Xi4[1,index]/1e6)+'k01 = %.3f MHz'%(Xi_a2s2[index]/1e6))
#
# fig, ax = plt.subplots(2, 4, figsize=(16,8))
# ax[0,0].plot(phiVec/2/pi, Xi2[0]/1e9, '.', label= 'f0')
# ax[1,0].plot(phiVec/2/pi, Xi2[1]/1e9, '.', label= 'f1')
# ax[0,0].set_title('freq')
#
# ax[0,0].legend()
# ax[1,0].legend()
#
# ax[0,1].plot(phiVec/2/pi, Xi3[0]/1e6)
# ax[1,1].plot(phiVec/2/pi, Xi3[1]/1e6)
# ax[0,1].set_title('c3')
#
# ax[0,2].plot(phiVec/2/pi, Xi4[0]/1e6)
# ax[1,2].plot(phiVec/2/pi, Xi4[1]/1e6)
# ax[0,2].set_title('c4')
#
# fig2, ax2 = plt.subplots(2,2, figsize=(16,8))
# ax2[0,0].plot(phiVec/2/pi, Xip[0,:,0]/1e6, '.', label= '$a^2b^{+}$')
#
# dXi_a2s=np.diff(Xip[0,:,0])/(phiVec[1]-phiVec[0])*pi/10
# dphiVec = (phiVec[1:]+phiVec[:-1])/2
#
# ax2[0,0].plot(dphiVec/2/pi, dXi_a2s/1e6, '.', label= r'$\frac{\pi}{10}*da^2b^{+}$')
# ax2[0,0].legend()
# ax2[0,0].set_ylabel('MHz')
#
# Xi4_0 = (Xi4[0,1:,0]+Xi4[0,:-1,0])/2
# ax2[1,0].plot(dphiVec/2/pi, Xi4_0/1e6, '.', label= '$a^2a^{+2}$')
# ax2[1,0].plot([min(dphiVec/2/pi), max(dphiVec/2/pi)], [0,0])
# ax2[1,0].legend()
# ax2[1,0].set_ylabel('MHz')
#
# ax2[1,1].plot(phiVec/2/pi, Xip[1,:,0]/1e6, '.', label= r'$a^{+}ac^{+}c$')
## ax2[1,1].plot(phiVec/2/pi, Xi_bc/1e6, '.', label= r'$b^{+}bc^{+}c$')
# ax2[1,1].legend()
## print('a2b = %.3f MHz\n'%(dXi_a2s[index]/1e6))
#
# ax2[0,1].plot(dphiVec/2/pi, dXi_a2s/Xi4_0, '.', label= '$da^2b^{+}/a^2a^{+2}$')
## ax[3,1].plot(phiVec/2/pi, Xi4[1,:]/1e6, label= '$b^2b^{+2}$')
# ax2[0,1].legend()
#
# index = np.argmin(np.abs(Xi4[0,:500,0]))
# print('index_0c4')
# print(index)
# index = np.argmin(np.abs(Xip[1,:500,0]))
# print(index)
# print('da^+a^2 = %.3f MHz'%(dXi_a2s[index]*1e-6))
# print('f_snail = %.3f GHz'%(Xi2[1,index,0]*1e-9))
# print('\n')
# index_max = np.argmax(dXi_a2s[:400])
# print('index_max_c3')
# print(index_max)
# print('a^2c^+ = %.3f MHz'%(dXi_a2s[index_max]*1e-6))
# print('a^+2a^2 = %.3f MHz'%(Xi4[0,index_max,0]*1e-6))
# print('a^+ac^+c = %.3f MHz'%(Xip[1,index_max,0]*1e-6))
# print('f_snail = %.3f GHz'%(Xi2[1,index_max,0]*1e-9))
#
# print('\n')
# index_max = np.argmin(np.abs(Xi2[1,:500,0]-Xi2[0,:500,0]+2e9))
# print('index_2GHz')
# print(index_max)
# print('da^2c^+ = %.3f MHz'%(dXi_a2s[index_max]*1e-6))
# print('a^+2a^2 = %.3f MHz'%(Xi4[0,index_max,0]*1e-6))
# print('a^+ac^+c = %.3f MHz'%(Xip[1,index_max,0]*1e-6))
# print('f_snail = %.3f GHz'%(Xi2[1,index_max,0]*1e-9))
# print('f_mem = %.3f GHz'%(Xi2[0,index_max,0]*1e-9))
# AS A FUNCTION OF COUPLING
if 1==0:
Xi2 = np.zeros((4, len(CcaVec)))
Xi3 = np.zeros((4, len(CcaVec)))
Xi4 = np.zeros((4, len(CcaVec)))
check_Xi2 = np.zeros((4, len(CcaVec)))
Xi_pa2pb = np.zeros(len(CcaVec))
Xi_ac = np.zeros(len(CcaVec))
Xi_bc = np.zeros(len(CcaVec))
resx = np.zeros(len(CcaVec))
resy = np.zeros(len(CcaVec))
comp0 = np.zeros((4, len(CcaVec)))
comp1 = np.zeros((4, len(CcaVec)))
comp2 = np.zeros((4, len(CcaVec)))
comp3 = np.zeros((4, len(CcaVec)))
for kk, xx in enumerate(ECcaVec):
_res = c.get_freqs_kerrs(particulars=[(1,1,2), (1,1,3,3), (2,2,3,3)], return_components=True, ECca=xx)
res1, res2, Xi2s, Xi3s, Xi4s, Xi_p, P = _res
Xi2[:, kk] = Xi2s
Xi3[:, kk] = Xi3s
Xi4[:, kk] = Xi4s
Xi_pa2pb[kk] = Xi_p[0]
Xi_ac[kk] = 4*Xi_p[1]
Xi_bc[kk] = 4*Xi_p[2]
resx[kk] = res1[0]
resy[kk] = res1[1]
comp0[:, kk] = (P.T)[0]
comp1[:, kk] = (P.T)[1]
comp2[:, kk] = (P.T)[2]
comp3[:, kk] = (P.T)[3]