def fixed_S(self):
w=2*pi*self.fixed_freq
L_arr=self._get_L(fq=self.fixed_fq)
if self.S_type=="simple":
return array([self._get_simple_S(f=self.fixed_freq, YL=-1.0j/(w*L)) for L in L_arr])
P=self.fixed_P[0]
#return self.PtoS(*P, YL=self.YL)
return array([self.PtoS(*P, YL=-1.0j/(w*L)) for L in L_arr])
def fixed_S(self):
w = 2 * pi * self.fixed_freq
L_arr = self._get_L(fq=self.fixed_fq)
if self.S_type == "simple":
return array([
self._get_simple_S(f=self.fixed_freq, YL=-1.0j / (w * L))
for L in L_arr
])
P = self.fixed_P[0]
#return self.PtoS(*P, YL=self.YL)
return array([self.PtoS(*P, YL=-1.0j / (w * L)) for L in L_arr])
def _get_S11(self, f, couple_mult, f0, K2, Np, C, L):
Ga=self._get_Ga(f=f, couple_mult=couple_mult, f0=f0, K2=K2, Np=Np, C=C)
Ba=self._get_Ba(f=f, couple_mult=couple_mult, f0=f0, K2=K2, Np=Np, C=C)
w=2*pi*f
try:
return Ga/(Ga+1j*Ba+1j*w*C+1.0/(1j*w*L))
except ValueError:
return array([Ga/(Ga+1j*Ba+1j*w*C+1.0/(1j*w*qL)) for qL in L])
def test_plot(**kwargs):
rho=Rho.process_kwargs(kwargs)
rho.ft="single"
kdiv2pi=(rho.fixed_freq[1]-rho.fixed_freq[0])/rho.vf
k=2*pi*rho.fixed_freq/rho.vf
lbda0=1.0 #rho.lbda0
xx=linspace(-1.75*lbda0, 1.75*lbda0, 201)
rhox=array([sum(2*kdiv2pi*rho.fixed_alpha*cos(k*x)) for x in xx])
pl=line(xx, rhox, linewidth=0.5)[0]
return pl
def test_plot(**kwargs):
rho = Rho.process_kwargs(kwargs)
rho.ft = "single"
kdiv2pi = (rho.fixed_freq[1] - rho.fixed_freq[0]) / rho.vf
k = 2 * pi * rho.fixed_freq / rho.vf
lbda0 = 1.0 #rho.lbda0
xx = linspace(-1.75 * lbda0, 1.75 * lbda0, 201)
rhox = array([sum(2 * kdiv2pi * rho.fixed_alpha * cos(k * x)) for x in xx])
pl = line(xx, rhox, linewidth=0.5)[0]
return pl
def _get_ls_f(self, f, couple_mult, f0, K2, Np):
try:
return array([
sqrt(qf * (qf - 2 * self._get_Lamb_shift(
f=qf, couple_mult=couple_mult, f0=f0, K2=K2, Np=Np)))
for qf in f
])
except TypeError:
return sqrt(f * (f - 2 * self._get_Lamb_shift(
f=f, couple_mult=couple_mult, f0=f0, K2=K2, Np=Np)))
def update_EkdivEc(self, ng, Ec, Ej, Nstates, order):
"""calculates transmon energy level with N states (more states is better approximation)
effectively solves the mathieu equation but for fractional inputs (which doesn't work in scipy.special.mathieu_a)"""
# if type(ng) not in (int, float):
# d=zeros((order, len(ng)))
# elif type(Ec) not in (int, float):
# d=zeros((order, len(Ec)))
# elif type(Ej) not in (int, float):
# d=zeros((order, len(Ej)))
if type(ng) in (int, float):
ng = array([ng])
d1 = []
d2 = []
d3 = []
Ej = Ej / Ec
Ec = 1.0 #/4.0
for a in ng:
NL = 2 * Nstates + 1
A = zeros((NL, NL))
for b in range(0, NL):
A[b, b] = 4.0 * Ec * (b - Nstates - a)**2
if b != NL - 1:
A[b, b + 1] = -Ej / 2.0
if b != 0:
A[b, b - 1] = -Ej / 2.0
#w,v=eig(A)
w = eigvalsh(A)
d = w[0:order]
# d1.append(min(w))#/h*1e-9)
# w=delete(w, w.argmin())
# d2.append(min(w))#/h*1e-9)
# w=delete(w, w.argmin())
# d3.append(min(w))#/h*1e-9)
return array([array(d1), array(d2), array(d3)]).transpose()
def surface_charge_plot(pl="surface charge", **kwargs):
rho=Rho.process_kwargs(kwargs)
#rho.ft="single" #"double"
#charge=real(fft.fftshift(fft.ifft(rho.fixed_alpha)))#.astype(float64)
print rho.a, rho.g
#print rho.surface_charge.dtype
#print max(rho.surface_voltage/rho.epsinf)
#x=linspace()
#x=linspace(-rho.N_fixed/2+.001, rho.N_fixed/2+0.0, rho.N_fixed)/800.0
print rho.surface_charge.shape, rho.surface_x.shape
pieta=pi*rho.eta
#a=0.25 #rho.a
lbda0=1.0 #rho.lbda0
x=linspace(-1.75*10*lbda0, 1.75*10*lbda0, 20001)
s=linspace(0.0,1.0, 20001)
def rh(x):
m=int(2*x/(lbda0))
if absolute(2*x/lbda0-m)<1.0/4.0:
theta=4*pi*x/lbda0
return 2/lbda0*2*sqrt(2.0)*((1.0)**m)/sqrt(cos(theta)-cos(pieta))*trapz(sin(pi*s)*cos((s-1/2)*theta)/rho.lgf1.Pv(-s),s)
if absolute(2*x/lbda0-m-1)<1.0/4.0:
theta=4*pi*x/lbda0
return 2/lbda0*2*sqrt(2.0)*((1.0)**m)/sqrt(cos(theta)-cos(pieta))*trapz(sin(pi*s)*cos((s-1/2)*theta)/rho.lgf1.Pv(-s),s)
if absolute(2*x/lbda0-m+1)<1.0/4.0:
theta=4*pi*x/lbda0
return 2/lbda0*2*sqrt(2.0)*((1.0)**m)/sqrt(cos(theta)-cos(pieta))*trapz(sin(pi*s)*cos((s-1/2)*theta)/rho.lgf1.Pv(-s),s)
return 0.0
rgh=array([rh(xx) for xx in x])/1.694
line(1*x, rgh, linewidth=0.5, pl=pl)
#line(real(fft.fft(rgh)))
#line(imag(fft.fft(rgh)))
line(rho.fixed_freq, rho.fixed_alpha)
print "line done"
pl=line(rho.surface_x, rho.surface_charge*rgh[10000]/rho.surface_charge[rho.N_fixed/2], plotter=pl, plot_name="single", color="blue", label="single finger", **kwargs)
#charge=real(fft.fftshift(fft.ifft(rho.fixed_alpha/rho.fixed_freq*rho.f0)))#.astype(float64)
pl=line(rho.surface_x, rho.surface_voltage*1e6, plotter=pl, plot_name="singled", color="red", label="single finger2", **kwargs)
xprime=linspace(-2.000001, 2.0, 200) #[0.01, 1.01] #range(10)
print "trapz"
#line(xprime, array([trapz(rho.surcharge/absolute(x-xp), x) for xp in xprime]))
print "trapz done"
pl.xlabel="frequency/center frequency"
pl.ylabel="element factor"
#pl.legend()
return pl
def center_coupling_vs_eta(pl="f0_vs_eta", **kwargs):
idt=Rho.process_kwargs(kwargs)
idt.couple_type="full expr"
idt.fixed_update=True
idt.N_fixed=1000
idt.fixed_freq_max=2*idt.f0
idt.ft="single"
eta_arr=linspace(0.1, 0.9, 21)
alpha_arr1=[]
alpha_arr2=[]
alpha_arr3=[]
for eta in eta_arr:
idt.eta=eta
alpha=idt._get_alpha(f=idt.f0, eta=eta)
alpha_arr1.append(alpha)
alpha=idt._get_alpha(f=3*idt.f0, eta=eta)
alpha_arr2.append(alpha)
alpha=idt._get_alpha(f=5*idt.f0, eta=eta)
alpha_arr3.append(alpha)
pl=line(eta_arr, array(alpha_arr1), plotter=pl)
line(eta_arr, array(alpha_arr2), plotter=pl, color="red")
line(eta_arr, array(alpha_arr3), plotter=pl, color="green")
return pl #line(eta, idt._get_alpha(f=3*idt.f0, eta=eta))[0]
def center_coupling_vs_eta(pl="f0_vs_eta", **kwargs):
idt = Rho.process_kwargs(kwargs)
idt.couple_type = "full expr"
idt.fixed_update = True
idt.N_fixed = 1000
idt.fixed_freq_max = 2 * idt.f0
idt.ft = "single"
eta_arr = linspace(0.1, 0.9, 21)
alpha_arr1 = []
alpha_arr2 = []
alpha_arr3 = []
for eta in eta_arr:
idt.eta = eta
alpha = idt._get_alpha(f=idt.f0, eta=eta)
alpha_arr1.append(alpha)
alpha = idt._get_alpha(f=3 * idt.f0, eta=eta)
alpha_arr2.append(alpha)
alpha = idt._get_alpha(f=5 * idt.f0, eta=eta)
alpha_arr3.append(alpha)
pl = line(eta_arr, array(alpha_arr1), plotter=pl)
line(eta_arr, array(alpha_arr2), plotter=pl, color="red")
line(eta_arr, array(alpha_arr3), plotter=pl, color="green")
return pl #line(eta, idt._get_alpha(f=3*idt.f0, eta=eta))[0]
def update_EkdivEc(self, ng, Ec, Ej, Nstates, order):
"""calculates transmon energy level with N states (more states is better approximation)
effectively solves the mathieu equation but for fractional inputs (which doesn't work in scipy.special.mathieu_a)"""
# if type(ng) not in (int, float):
# d=zeros((order, len(ng)))
# elif type(Ec) not in (int, float):
# d=zeros((order, len(Ec)))
# elif type(Ej) not in (int, float):
# d=zeros((order, len(Ej)))
if type(ng) in (int, float):
ng=array([ng])
d1=[]
d2=[]
d3=[]
Ej=Ej/Ec
Ec=1.0#/4.0
for a in ng:
NL=2*Nstates+1
A=zeros((NL, NL))
for b in range(0,NL):
A[b, b]=4.0*Ec*(b-Nstates-a)**2
if b!=NL-1:
A[b, b+1]= -Ej/2.0
if b!=0:
A[b, b-1]= -Ej/2.0
#w,v=eig(A)
w=eigvalsh(A)
d=w[0:order]
# d1.append(min(w))#/h*1e-9)
# w=delete(w, w.argmin())
# d2.append(min(w))#/h*1e-9)
# w=delete(w, w.argmin())
# d3.append(min(w))#/h*1e-9)
return array([array(d1), array(d2), array(d3)]).transpose()
def _get_S11(self, f, couple_mult, f0, K2, Np, C, L):
Ga = self._get_Ga(f=f,
couple_mult=couple_mult,
f0=f0,
K2=K2,
Np=Np,
C=C)
Ba = self._get_Ba(f=f,
couple_mult=couple_mult,
f0=f0,
K2=K2,
Np=Np,
C=C)
w = 2 * pi * f
try:
return Ga / (Ga + 1j * Ba + 1j * w * C + 1.0 / (1j * w * L))
except ValueError:
return array([
Ga / (Ga + 1j * Ba + 1j * w * C + 1.0 / (1j * w * qL))
for qL in L
])
def surface_charge_plot(pl="surface charge", **kwargs):
rho = Rho.process_kwargs(kwargs)
#rho.ft="single" #"double"
#charge=real(fft.fftshift(fft.ifft(rho.fixed_alpha)))#.astype(float64)
print rho.a, rho.g
#print rho.surface_charge.dtype
#print max(rho.surface_voltage/rho.epsinf)
#x=linspace()
#x=linspace(-rho.N_fixed/2+.001, rho.N_fixed/2+0.0, rho.N_fixed)/800.0
print rho.surface_charge.shape, rho.surface_x.shape
pieta = pi * rho.eta
#a=0.25 #rho.a
lbda0 = 1.0 #rho.lbda0
x = linspace(-1.75 * 10 * lbda0, 1.75 * 10 * lbda0, 20001)
s = linspace(0.0, 1.0, 20001)
def rh(x):
m = int(2 * x / (lbda0))
if absolute(2 * x / lbda0 - m) < 1.0 / 4.0:
theta = 4 * pi * x / lbda0
return 2 / lbda0 * 2 * sqrt(2.0) * (
(1.0)**m) / sqrt(cos(theta) - cos(pieta)) * trapz(
sin(pi * s) * cos(
(s - 1 / 2) * theta) / rho.lgf1.Pv(-s), s)
if absolute(2 * x / lbda0 - m - 1) < 1.0 / 4.0:
theta = 4 * pi * x / lbda0
return 2 / lbda0 * 2 * sqrt(2.0) * (
(1.0)**m) / sqrt(cos(theta) - cos(pieta)) * trapz(
sin(pi * s) * cos(
(s - 1 / 2) * theta) / rho.lgf1.Pv(-s), s)
if absolute(2 * x / lbda0 - m + 1) < 1.0 / 4.0:
theta = 4 * pi * x / lbda0
return 2 / lbda0 * 2 * sqrt(2.0) * (
(1.0)**m) / sqrt(cos(theta) - cos(pieta)) * trapz(
sin(pi * s) * cos(
(s - 1 / 2) * theta) / rho.lgf1.Pv(-s), s)
return 0.0
rgh = array([rh(xx) for xx in x]) / 1.694
line(1 * x, rgh, linewidth=0.5, pl=pl)
#line(real(fft.fft(rgh)))
#line(imag(fft.fft(rgh)))
line(rho.fixed_freq, rho.fixed_alpha)
print "line done"
pl = line(rho.surface_x,
rho.surface_charge * rgh[10000] /
rho.surface_charge[rho.N_fixed / 2],
plotter=pl,
plot_name="single",
color="blue",
label="single finger",
**kwargs)
#charge=real(fft.fftshift(fft.ifft(rho.fixed_alpha/rho.fixed_freq*rho.f0)))#.astype(float64)
pl = line(rho.surface_x,
rho.surface_voltage * 1e6,
plotter=pl,
plot_name="singled",
color="red",
label="single finger2",
**kwargs)
xprime = linspace(-2.000001, 2.0, 200) #[0.01, 1.01] #range(10)
print "trapz"
#line(xprime, array([trapz(rho.surcharge/absolute(x-xp), x) for xp in xprime]))
print "trapz done"
pl.xlabel = "frequency/center frequency"
pl.ylabel = "element factor"
#pl.legend()
return pl
fixed_freq_max=7e9,
fixed_fq_min=1e9,
fixed_fq_max=10e9,
Cc=30e-15,
gate_type="capacitive",
Cground=100e-12)
a._get_simple_S(f=7e9)
#a.K2=0.01
#a.Np=3
a.fitter.gamma = 0.05
if 0:
pl = colormesh(a.fixed_freq, a.fixed_fq, a.MagAbs)
colormesh(a.fixed_freq, a.fixed_fq, a.MagAbsFit, pl=pl) #.show()
pl = line(a.fixed_freq,
array([fp[1] for fp in a.fitter.fit_params]) * 1e9,
label="center S33")
line(a.fixed_freq,
a.fixed_fq[argmin(a.MagAbs**2, axis=0)],
pl=pl,
label="min S33",
color="red")
line(a.fixed_freq,
a.fixed_freq - a.fixed_Lamb_shift,
pl=pl,
label="theory",
color="green") #.show()
#a.gate_type="constant"
line(a.fixed_freq,
a.fixed_freq - a._get_Lamb_shift(f=a.fixed_freq),
pl=pl,
def _get_ls_f(self, f, couple_mult, f0, K2, Np):
try:
return array([sqrt(qf*(qf-2*self._get_Lamb_shift(f=qf, couple_mult=couple_mult, f0=f0, K2=K2, Np=Np))) for qf in f])
except TypeError:
return sqrt(f*(f-2*self._get_Lamb_shift(f=f, couple_mult=couple_mult, f0=f0, K2=K2, Np=Np)))
# except ValueError:
# return array([1j*sqrt(2.0*Ga*GL)/(Ga+1j*Ba+1j*w*Ct+1.0/(1j*w*qL)) for qL in L])
if 0:
a=QDT(#Ga_type="sinc", Ba_type="formula",
magabs_type="S33",
fixed_freq_min=3e9, fixed_freq_max=7e9, fixed_fq_min=1e9, fixed_fq_max=10e9,
Cc=30e-15, gate_type="capacitive", Cground=100e-12)
a._get_simple_S(f=7e9)
#a.K2=0.01
#a.Np=3
a.fitter.gamma=0.05
if 0:
pl=colormesh(a.fixed_freq, a.fixed_fq, a.MagAbs)
colormesh(a.fixed_freq, a.fixed_fq, a.MagAbsFit, pl=pl)#.show()
pl=line(a.fixed_freq, array([fp[1] for fp in a.fitter.fit_params])*1e9, label="center S33")
line(a.fixed_freq, a.fixed_fq[argmin(a.MagAbs**2, axis=0)], pl=pl, label="min S33", color="red")
line(a.fixed_freq, a.fixed_freq-a.fixed_Lamb_shift, pl=pl, label="theory", color="green")#.show()
#a.gate_type="constant"
line(a.fixed_freq, a.fixed_freq-a._get_Lamb_shift(f=a.fixed_freq), pl=pl, label="theory", color="purple")#.show()
#-array([fp[1] for fp in a.fitter.fit_params])*1e9+a.fixed_freq=-a._get_Lamb_shift(f=a.fixed_freq)
#a.gate_type="capacitive"
pl=line(a.fixed_freq, a.fixed_coupling, label="width S33")
#a.gate_type="constant"
line(a.fixed_freq, a._get_coupling(f=a.fixed_freq), pl=pl, color="red", label="theory").show()
def energy_level_plot(qdt, fig_width=9.0, fig_height=6.0):
pl=Plotter(fig_width=fig_width, fig_height=fig_height)
EjdivEc=linspace(0.1, 300, 3000)
