def calc_linresp(self, Nqp, hwread, D_0):
s_0 = kidcalc.cinduct(hwread, D_0, self.kbT)
Qi_0 = kidcalc.Qi(s_0[0], s_0[1], self.ak, self.kbT, D_0,
SC.Sheet(self.SC, self.d))
Q = Qi_0 * self.Qc / (Qi_0 + self.Qc)
beta = kidcalc.beta(self.kbT, D_0, SC.Sheet(self.SC, self.d))
kbTeff = kidcalc.kbTeff(Nqp / self.V, self.SC)
D = kidcalc.D(kbTeff, self.SC)
s1, s2 = kidcalc.cinduct(hwread, D, kbTeff)
lindA = self.ak * beta * Q * (s1 - s_0[0]) / s_0[1]
lintheta = -self.ak * beta * Q * (s2 - s_0[1]) / s_0[1]
return lindA, lintheta
def calc_S21(self, Nqp, hwread, s20, dhw=0):
kbTeff = kidcalc.kbTeff(Nqp / self.V, self.SC)
D = kidcalc.D(kbTeff, self.SC)
s1, s2 = kidcalc.cinduct(hwread + dhw, D, kbTeff)
Qi = interpolate.splev(kbTeff, self.Qispl)
hwres = kidcalc.hwres(s2, self.hw0, s20, self.ak, self.kbT, D,
SC.Sheet(self.SC, self.d))
return kidcalc.S21(Qi, self.Qc, hwread, dhw, hwres)
def calc_resp(self, Nqp, hwread, s20, D_0, dhw=0):
# Calculate S21
S21 = self.calc_S21(Nqp, hwread, s20, dhw)
# Define circle at this temperature:
s_0 = kidcalc.cinduct(hwread, D_0, self.kbT)
Qi_0 = kidcalc.Qi(s_0[0], s_0[1], self.ak, self.kbT, D_0,
SC.Sheet(self.SC, self.d))
S21min = self.Qc / (self.Qc + Qi_0) # Q/Qi
xc = (1 + S21min) / 2
# translate S21 into this circle:
dA = 1 - np.sqrt((np.real(S21) - xc) ** 2 + np.imag(S21) ** 2) / (1 - xc)
theta = np.arctan2(np.imag(S21), (xc - np.real(S21)))
return S21, dA, theta
def plot_freqsweep(self, start=None, stop=None, points=200):
hwread = self.hwread
D_0 = self.D_0
s20 = self.s20
s_0 = kidcalc.cinduct(hwread, D_0, self.kbT)
Qi_0 = kidcalc.Qi(s_0[0], s_0[1], self.ak, self.kbT, D_0,
SC.Sheet(self.SC, self.d))
Q = Qi_0 * self.Qc / (Qi_0 + self.Qc)
S21min = self.Qc / (self.Qc + Qi_0) # Q/Qi
xc = (1 + S21min) / 2
if start is None:
start = -self.hw0 / Q * 2
if stop is None:
stop = self.hw0 / Q * 2
for dhw in np.linspace(start, stop, points):
S21_0 = self.calc_S21(self.Nqp_0, hwread, s20, dhw=dhw)
plt.plot(np.real(S21_0), np.imag(S21_0), "r.")
plt.plot(xc, 0, "kx")
plt.plot(S21min, 0, "gx")
def minfunc(kbT, s2s1, hw, N0, kbTc, kbTD):
D_ = D(kbT, N0, kbTc, kbTD)
s1, s2 = cinduct(hw, D_, kbT)
return np.abs(s2s1 - s2 / s1)
def ak(S21data,
lbd0=0.092,
N0=1.72e4,
kbTD=37312.0,
plot=False,
reterr=False,
method='df'):
'''Calculates the kinetic induction fraction, based on Goa2008, PhD Thesis.
Arguments:
S21data -- the content of the .csv from the S21-analysis.
lbd0 -- penetration depth at T=0 in µm (default: 0.092, Al)
N0 -- Density of states in µeV^{-1}µm^{-3} (default: 1.72e4, Al)
kbTD -- Debye Energy in µeV (default 37312.0, Al)
plot -- boolean to plot the fit over temperature.
reterr -- boolean to return fitting error.
method -- either df or Qi, which is fitted linearly over temperature.
Returns:
ak
optionally: the error as well.'''
# Extract relevant data
hw = S21data[:, 5] * 2 * np.pi * 0.6582 * 1e-9 #µeV
kbT = S21data[:, 1] * 86.17 #µeV
# Set needed constants
hw0 = hw[0]
d = S21data[0, 25]
kbTc = S21data[0, 21] * 86.17
D0 = 1.76 * kbTc
# define y to fit:
if method == 'df':
y = (hw - hw0) / hw0
elif method == 'Qi':
y = 1 / S21data[:, 4] - 1 / S21data[0, 4]
# Mask the double measured temperatures, and only fit from 250 mK
mask1 = np.zeros(len(y), dtype="bool")
mask1[np.unique(np.round(S21data[:, 1], decimals=2),
return_index=True)[1]] = True
mask = np.logical_and(mask1, (kbT >= .25 * 86.17))
if mask.sum() > 3:
y = y[mask]
else:
warnings.warn(
'Not enough high temperature S21data, taking the last 10 points')
y = y[mask1][-10:]
# define x to fit:
x = np.zeros(len(y))
i = 0
s0 = cinduct(hw0, D(kbT[0], N0, kbTc, kbTD), kbT[0])
for kbTi in kbT[mask]:
D_0 = D(kbTi, N0, kbTc, kbTD)
s = cinduct(hw[i], D_0, kbTi)
if method == 'df':
x[i] = (s[1] - s0[1]) / s0[1] * beta(lbd0, d, D_0, D0, kbTi) / 4
elif method == 'Qi':
x[i] = (s[0] - s0[0]) / s0[1] * beta(lbd0, d, D_0, D0, kbTi) / 2
i += 1
#do the fit:
fit = curve_fit(lambda t, ak: ak * t, x, y)
if plot:
plt.figure()
plt.plot(x, y, 'o')
plt.plot(x, fit[0] * x)
plt.legend(['Data', 'Fit'])
if method == 'df':
plt.ylabel(r'$\delta f/f_0$')
plt.xlabel(r'$\beta \delta \sigma_2/4\sigma_2 $')
elif method == 'Qi':
plt.ylabel(r'$\delta(1/Q_i)$')
plt.xlabel(r'$\beta \delta \sigma_1/2\sigma_2 $')
if reterr:
return fit[0][0], np.sqrt(fit[1][0])
else:
return fit[0][0]
def minfunc(kbT, s2s1, hw, SC):
D_ = kidcalc.D(kbT, SC)
s1, s2 = kidcalc.cinduct(hw, D_, kbT)
return np.abs(s2s1 - s2 / s1)
def ak(S21data, SC=None, plot=False, reterr=False, method="df", Tmin=.25):
"""Calculates the kinetic induction fraction, based on Goa2008, PhD Thesis.
Arguments:
S21data -- the content of the .csv from the S21-analysis.
SC -- Superconductor object, from SC module, default: Al
plot -- boolean to plot the fit over temperature.
reterr -- boolean to return fitting error.
method -- either df or Qi, which is fitted linearly over temperature.
Returns:
ak
optionally: the error in ak from fitting."""
if SC is None:
SC = SuperCond.Al(Tc=S21data[0, 21])
# Extract relevant data
hw = S21data[:, 5] * const.Planck / const.e * 1e6 # µeV
kbT = S21data[:, 1] * const.Boltzmann / const.e * 1e6 # µeV
hw0 = hw[0]
# define y to fit:
if method == "df":
y = (hw - hw0) / hw0
elif method == "Qi":
y = 1 / S21data[:, 4] - 1 / S21data[0, 4]
# Mask the double measured temperatures, and only fit from 250 mK
mask1 = np.zeros(len(y), dtype="bool")
mask1[np.unique(np.round(S21data[:, 1], decimals=2),
return_index=True)[1]] = True
mask = np.logical_and(mask1,
(kbT >= Tmin * const.Boltzmann / const.e * 1e6))
if mask.sum() > 3:
y = y[mask]
else:
warnings.warn(
"Not enough high temperature S21data, taking the last 10 points")
y = y[mask1][-10:]
# define x to fit:
x = np.zeros(len(y))
i = 0
s0 = kidcalc.cinduct(hw0, kidcalc.D(kbT[0], SC), kbT[0])
for kbTi in kbT[mask]:
D_0 = kidcalc.D(kbTi, SC)
s = kidcalc.cinduct(hw[i], D_0, kbTi)
if method == "df":
x[i] = (s[1] - s0[1]) / s0[1] * kidcalc.beta(
kbTi, D_0, SuperCond.Sheet(SC, d=S21data[0, 25])) / 4
elif method == "Qi":
x[i] = (s[0] - s0[0]) / s0[1] * kidcalc.beta(
kbTi, D_0, SuperCond.Sheet(SC, d=S21data[0, 25])) / 2
i += 1
# do the fit:
fit = curve_fit(lambda t, ak: ak * t, x, y)
if plot:
plt.figure()
plt.plot(x, y, "o")
plt.plot(x, fit[0] * x)
plt.legend(["Data", "Fit"])
if method == "df":
plt.ylabel(r"$\delta f/f_0$")
plt.xlabel(r"$\beta \delta \sigma_2/4\sigma_2 $")
elif method == "Qi":
plt.ylabel(r"$\delta(1/Q_i)$")
plt.xlabel(r"$\beta \delta \sigma_1/2\sigma_2 $")
if reterr:
return fit[0][0], np.sqrt(fit[1][0])
else:
return fit[0][0]
def s20(self):
D_0 = kidcalc.D(self.kbT0, self.SC)
return kidcalc.cinduct(self.hw0, D_0, self.kbT0)[1]
def Qi_0(self):
hwread = self.hwread
s_0 = kidcalc.cinduct(hwread, self.D_0, self.kbT)
return kidcalc.Qi(s_0[0], s_0[1], self.ak, self.kbT, self.D_0,
SC.Sheet(self.SC, self.d))
