def test_fit_exp_decay():
parameters = [0, 1, 1]
x_data = np.arange(0, 10., .1)
y_data = exp_function(x_data, *parameters)
fitted = fit_exp_decay(x_data, y_data)
np.testing.assert_array_almost_equal(fitted, parameters, decimal=3)
fitted = fit_exp_decay(x_data, y_data, offset_parameter=0.1)
np.testing.assert_array_almost_equal(fitted, [.1, .95, 1.4], decimal=1)
def test_fit_exp_decay_upward():
parameters = [0, -1, 1]
x_data = np.arange(0, 10., .1)
y_data = exp_function(x_data, *parameters)
fitted = fit_exp_decay(x_data, y_data)
np.testing.assert_array_almost_equal(fitted, np.array(
[5.38675880e-05, -9.99998574e-01, 9.99760970e-01]), decimal=3)
def _fit_and_plot_decay(bincentres, counts, label, fig_label):
""" Fitting and plotting of exponential decay for level """
A_fit, B_fit, gamma_fit = fit_exp_decay(bincentres, counts)
tunnelrate = gamma_fit / 1000
other_label = 'up' if label == 'down' else 'down'
if verbose:
print(f'Tunnel rate {label} to {other_label}: %.1f kHz' %
tunnelrate)
time_scaling = 1e3
if fig_label:
title = f'Fitted exponential decay, level {label}'
Fig = plt.figure(fig_label)
plt.clf()
plt.plot(time_scaling * bincentres,
counts,
'o',
label=f'Counts {label}')
plt.plot(
time_scaling * bincentres,
exp_function(bincentres, A_fit, B_fit, gamma_fit),
'r',
label=
r'Fitted exponential decay $\Gamma_{\mathrm{%s\ to\ %s}}$: %.1f kHz'
% (label, other_label, tunnelrate))
plt.xlabel('Lifetime (ms)')
plt.ylabel('Counts per bin')
plt.legend()
plt.title(title)
if ppt:
addPPTslide(title=title, fig=Fig)
fit_parameters = [A_fit, B_fit, gamma_fit]
return tunnelrate, fit_parameters
def tunnelrates_RTS(data,
samplerate=None,
min_sep=2.0,
max_sep=7.0,
min_duration=5,
num_bins=None,
plungers=[],
fig=None,
ppt=None,
verbose=0):
"""
This function takes an RTS dataset, fits a double gaussian, finds the split between the two levels,
determines the durations in these two levels, fits a decaying exponantial on two arrays of durations,
which gives the tunneling frequency for both the levels.
Args:
data (array): qcodes DataSet (or 1d data array) with the RTS data
plungers ([str, str]): array of the two plungers used to perform the RTS measurement
samplerate (int or float): sampling rate of either the fpga or the digitizer, optional if given in the metadata
of the measured data
min_sep (float): if the separation found for the fit of the double gaussian is less then this value, the fit probably failed
and a FittingException is raised
max_sep (float): if the separation found for the fit of the double gaussian is more then this value, the fit probably failed
and a FittingException is raised
min_duration (int): minimal number of datapoints a duration should last to be taking into account for the analysis
fig (None or int): shows figures and sends them to the ppt when is not None
ppt (None or int): determines if the figures are send to a powerpoint presentation
verbose (int): prints info to the console when > 0
Returns:
tunnelrate_dn (numpy.float64): tunneling rate of the down level (kHz)
tunnelrate_up (numpy.float64): tunneling rate of the up level (kHz)
parameters (dict): dictionary with relevent (fit) parameters
"""
if type(data) == qcodes.data.data_set.DataSet:
try:
plungers = plungers
metadata = data.metadata
gates = metadata['allgatevalues']
plungervalue = gates[plungers[0]]
except:
plungervalue = []
if samplerate is None:
metadata = data.metadata
samplerate = metadata['samplerate']
data = np.array(data.measured)
else:
plungervalue = []
if samplerate is None:
raise Exception('samplerate is None')
# plotting a 2d histogram of the RTS
if fig:
xdata = np.array(range(0, len(data))) / samplerate * 1000
Z, xedges, yedges = np.histogram2d(
xdata,
data,
bins=[int(np.sqrt(len(xdata))) / 2,
int(np.sqrt(len(data))) / 2])
title = '2d histogram RTS'
plt.figure(title)
plt.clf()
plt.pcolormesh(xedges, yedges, Z.T)
cb = plt.colorbar()
cb.set_label('Data points per bin')
plt.xlabel('Time (ms)')
plt.ylabel('Signal sensing dot (a.u.)')
plt.title(title)
if ppt:
addPPTslide(title=title, fig=plt.figure(title))
# binning the data and determining the bincentres
if num_bins is None:
num_bins = int(np.sqrt(len(data)))
counts, bins = np.histogram(data, bins=num_bins)
bincentres = np.array([(bins[i] + bins[i + 1]) / 2
for i in range(0,
len(bins) - 1)])
# fitting the double gaussian and finding the split between the up and the down state, separation between the max of the two gaussians measured in the sum of the std
par_fit, result_dict = fit_double_gaussian(bincentres, counts)
separation = result_dict['separation']
split = result_dict['split']
if verbose:
print('Fit parameters double gaussian:\n mean down: %.3f counts' %
par_fit[4] + ', mean up:%.3f counts' % par_fit[5] +
', std down: %.3f counts' % par_fit[2] +
', std up:%.3f counts' % par_fit[3])
print('Separation between peaks gaussians: %.3f std' % separation)
print('Split between two levels: %.3f' % split)
# plotting the data in a histogram, the fitted two gaussian model and the split
if fig:
title = 'Histogram of two levels RTS'
plt.figure(title)
plt.clf()
counts, bins, _ = plt.hist(data, bins=num_bins)
plt.plot(bincentres,
double_gaussian(bincentres, par_fit),
'r',
label='Fitted double gaussian')
plt.plot(split,
double_gaussian(split, par_fit),
'ro',
markersize=8,
label='split: %.3f' % split)
plt.xlabel('Measured value (a.u.)')
plt.ylabel('Data points per bin')
plt.legend()
plt.title(title)
if ppt:
addPPTslide(
title=title,
fig=plt.figure(title),
notes='Fit paramaters double gaussian:\n mean down: %.3f counts'
% par_fit[4] + ', mean up:%.3f counts' % par_fit[5] +
', std down: %.3f counts' % par_fit[2] +
', std up:%.3f counts' % par_fit[3] +
'.Separation between peaks gaussians: %.3f std' % separation +
'. Split between two levels: %.3f' % split)
if separation < min_sep:
raise FittingException(
'Separation between the peaks of the gaussian %.1f is less then %.1f std, indicating that the fit was not succesfull.'
% (separation, min_sep))
if separation > max_sep:
raise FittingException(
'Separation between the peaks of the gaussian %.1f is more then %.1f std, indicating that the fit was not succesfull.'
% (separation, max_sep))
# count the number of transitions and their duration
durations_dn_idx, durations_up_idx = transitions_durations(data, split)
# throwing away the durations with less data points then min_duration
durations_up_min_duration = durations_up_idx > min_duration
durations_up = durations_up_idx[durations_up_min_duration]
durations_dn_min_duration = durations_dn_idx > min_duration
durations_dn = durations_dn_idx[durations_dn_min_duration]
if len(durations_up) < 1:
raise FittingException(
'All durations_up are shorter than the minimal duration.')
if len(durations_dn) < 1:
raise FittingException(
'All durations_dn are shorter than the minimal duration.')
# calculating durations in seconds
durations_dn = durations_dn / samplerate
durations_up = durations_up / samplerate
# sorting the durations
durations_dn_srt = np.sort(durations_dn)
durations_up_srt = np.sort(durations_up)
# calculating the number of bins and counts for down level
numbins_dn = int(np.sqrt(len(durations_dn_srt)))
counts_dn, bins_dn = np.histogram(durations_dn_srt, bins=numbins_dn)
if counts_dn[0] < 400:
warnings.warn(
'Number of datapoints might not be enough to make an acurate fit of the exponantial decay for level down.'
)
if counts_dn[0] < 50:
raise FittingException(
'Number of datapoints is not be enough to make an acurate fit of the exponantial decay for level down.'
)
bincentres_dn = np.array([(bins_dn[i] + bins_dn[i + 1]) / 2
for i in range(0,
len(bins_dn) - 1)])
# fitting exponantial decay for down level
A_dn_fit, B_dn_fit, gamma_dn_fit = fit_exp_decay(bincentres_dn, counts_dn)
tunnelrate_dn = gamma_dn_fit / 1000
if verbose:
print('Tunnel rate down: %.1f kHz' % tunnelrate_dn)
if fig:
title = 'Fitted exponantial decay, level down'
plt.figure(title)
plt.clf()
plt.plot(bincentres_dn, counts_dn, 'o', label='Counts down')
plt.plot(bincentres_dn,
exp_function(bincentres_dn, A_dn_fit, B_dn_fit, gamma_dn_fit),
'r',
label='Fitted exponantial decay \n $\Gamma_{dn}$: %.1f kHz' %
tunnelrate_dn)
plt.xlabel('Lifetime (s)')
plt.ylabel('Counts per bin')
plt.legend()
plt.title(title)
if ppt:
addPPTslide(title=title, fig=plt.figure(title))
# calculating the number of bins and counts for up level
numbins_up = int(np.sqrt(len(durations_up_srt)))
counts_up, bins_up = np.histogram(durations_up_srt, bins=numbins_up)
if counts_up[0] < 50:
warnings.warn(
'Number of datapoints might not be enough to make an acurate fit of the exponantial decay for level up.'
)
if counts_dn[0] < 50:
raise FittingException(
'Number of datapoints is not be enough to make an acurate fit of the exponantial decay for level down.'
)
bincentres_up = np.array([(bins_up[i] + bins_up[i + 1]) / 2
for i in range(0,
len(bins_up) - 1)])
# fitting exponantial decay for up level
A_up_fit, B_up_fit, gamma_up_fit = fit_exp_decay(bincentres_up, counts_up)
tunnelrate_up = gamma_up_fit / 1000
if verbose:
print('Tunnel rate up: %.1f kHz' % tunnelrate_up)
if fig:
title = 'Fitted exponantial decay, level up'
plt.figure(title)
plt.plot(bincentres_up, counts_up, 'o', label='Counts up')
plt.plot(bincentres_up,
exp_function(bincentres_up, A_up_fit, B_up_fit, gamma_up_fit),
'r',
label='Fitted exponantial decay \n $\Gamma_{up}$: %.1f kHz' %
tunnelrate_up)
plt.xlabel('Lifetime (s)')
plt.ylabel('Data points per bin')
plt.legend()
plt.title(title)
if ppt:
addPPTslide(title=title, fig=plt.figure(title))
parameters = {
'plunger value': plungervalue,
'sampling rate': samplerate,
'fit parameters double gaussian': par_fit,
'separations between peaks gaussians': separation,
'split between the two levels': split,
'fit parameters exp. decay down': [A_dn_fit, B_dn_fit, gamma_dn_fit],
'fit parameters exp. decay up': [A_up_fit, B_up_fit, gamma_up_fit]
}
return tunnelrate_dn, tunnelrate_up, parameters
def tunnelrates_RTS(data,
samplerate=None,
min_sep=2.0,
max_sep=7.0,
min_duration=5,
num_bins=None,
plungers=None,
fig=None,
ppt=None,
verbose=0):
"""
This function takes an RTS dataset, fits a double gaussian, finds the split between the two levels,
determines the durations in these two levels, fits a decaying exponential on two arrays of durations,
which gives the tunneling frequency for both the levels. If the number of datapoints is too low to get enough points per bin
for the exponential fit (for either the up or the down level), this analysis step is passed over. tunnelrate_dn and tunnelrate_up
are returned as None, but similar information can be substracted from parameters['down_segments'] and parameters['up_segments'].
Args:
data (array): qcodes DataSet (or 1d data array) with the RTS data
plungers ([str, str]): array of the two plungers used to perform the RTS measurement
samplerate (int or float): sampling rate of the acquisition device, optional if given in the metadata
of the measured data
min_sep (float): if the separation found for the fit of the double gaussian is less then this value, the fit probably failed
and a FittingException is raised
max_sep (float): if the separation found for the fit of the double gaussian is more then this value, the fit probably failed
and a FittingException is raised
min_duration (int): minimal number of datapoints a duration should last to be taking into account for the analysis
fig (None or int): shows figures and sends them to the ppt when is not None
ppt (None or int): determines if the figures are send to a powerpoint presentation
verbose (int): prints info to the console when > 0
Returns:
tunnelrate_dn (numpy.float64): tunneling rate of the down level to the up level (kHz) or None in case of not enough datapoints
tunnelrate_up (numpy.float64): tunneling rate of the up level to the down level (kHz) or None in case of not enough datapoints
parameters (dict): dictionary with relevent (fit) parameters. this includes:
tunnelrate_down (float): tunnel rate in Hz
tunnelrate_up (float): tunnel rate up in Hz
"""
if plungers is None:
plungers = []
if isinstance(data, qcodes.data.data_set.DataSet):
try:
plungers = plungers
metadata = data.metadata
gates = metadata['allgatevalues']
plungervalue = gates[plungers[0]]
except BaseException:
plungervalue = []
if samplerate is None:
metadata = data.metadata
samplerate = metadata['samplerate']
data = np.array(data.measured)
else:
plungervalue = []
if samplerate is None:
raise Exception('samplerate is None')
# plotting a 2d histogram of the RTS
if fig:
xdata = np.array(range(0, len(data))) / samplerate * 1000
Z, xedges, yedges = np.histogram2d(
xdata,
data,
bins=[int(np.sqrt(len(xdata))) / 2,
int(np.sqrt(len(data))) / 2])
title = '2d histogram RTS'
Fig = plt.figure(fig)
plt.clf()
plt.pcolormesh(xedges, yedges, Z.T)
cb = plt.colorbar()
cb.set_label('Data points per bin')
plt.xlabel('Time (ms)')
plt.ylabel('Signal sensing dot (a.u.)')
plt.title(title)
if ppt:
addPPTslide(title=title, fig=Fig)
# binning the data and determining the bincentres
if num_bins is None:
num_bins = int(np.sqrt(len(data)))
counts, bins = np.histogram(data, bins=num_bins)
bincentres = np.array([(bins[i] + bins[i + 1]) / 2
for i in range(0,
len(bins) - 1)])
# fitting the double gaussian and finding the split between the up and the
# down state, separation between the max of the two gaussians measured in
# the sum of the std
par_fit, result_dict = fit_double_gaussian(bincentres, counts)
separation = result_dict['separation']
split = result_dict['split']
if verbose:
print('Fit parameters double gaussian:\n mean down: %.3f counts' %
par_fit[4] + ', mean up:%.3f counts' % par_fit[5] +
', std down: %.3f counts' % par_fit[2] +
', std up:%.3f counts' % par_fit[3])
print('Separation between peaks gaussians: %.3f std' % separation)
print('Split between two levels: %.3f' % split)
# plotting the data in a histogram, the fitted two gaussian model and the split
if fig:
figure_title = 'Histogram of two levels RTS'
Fig = plt.figure(fig + 1)
plt.clf()
_plot_rts_histogram(data, num_bins, par_fit, split, figure_title)
if ppt:
addPPTslide(
title=title,
fig=Fig,
notes='Fit parameters double gaussian:\n mean down: %.3f counts'
% par_fit[4] + ', mean up:%.3f counts' % par_fit[5] +
', std down: %.3f counts' % par_fit[2] +
', std up:%.3f counts' % par_fit[3] +
'.Separation between peaks gaussians: %.3f std' % separation +
'. Split between two levels: %.3f' % split)
if separation < min_sep:
raise FittingException(
'Separation between the peaks of the gaussian %.1f is less then %.1f std, indicating that the fit was not succesfull.'
% (separation, min_sep))
if separation > max_sep:
raise FittingException(
'Separation between the peaks of the gaussian %.1f is more then %.1f std, indicating that the fit was not succesfull.'
% (separation, max_sep))
# count the number of transitions and their duration
durations_dn_idx, durations_up_idx = transitions_durations(data, split)
# throwing away the durations with less data points then min_duration
durations_up_min_duration = durations_up_idx >= min_duration
durations_up = durations_up_idx[durations_up_min_duration]
durations_dn_min_duration = durations_dn_idx >= min_duration
durations_dn = durations_dn_idx[durations_dn_min_duration]
if len(durations_up) < 1:
raise FittingException(
'All durations_up are shorter than the minimal duration.')
if len(durations_dn) < 1:
raise FittingException(
'All durations_dn are shorter than the minimal duration.')
def _create_histogram(durations, level, verbose=0):
""" Calculate number of bins, bin edges and histogram for durations
This method works if the data is sampled at integer durations.
"""
numbins = int(np.sqrt(len(durations)))
bin_size = int(np.ceil((durations.max() - durations.min()) / numbins))
# choose bins carefully, since our data is sampled only an discrete times
bins = np.arange(durations.min() - .5,
durations.max() + bin_size, bin_size)
counts, bins = np.histogram(durations, bins=bins)
if verbose:
print(' _create_histogram level ' + level +
': number of bins %d, %d' % (numbins, bin_size))
return counts, bins
# calculating the number of bins and counts for down level
counts_dn, bins_dn = _create_histogram(durations_dn,
level='down',
verbose=verbose >= 2)
# calculating the number of bins and counts for up level
counts_up, bins_up = _create_histogram(durations_up,
level='up',
verbose=verbose >= 2)
# calculating durations in seconds
durations_dn = durations_dn / samplerate
durations_up = durations_up / samplerate
bins_dn = bins_dn / samplerate
bins_up = bins_up / samplerate
if verbose >= 2:
print('counts_dn %d, counts_up %d' % (counts_dn[0], counts_up[0]))
tunnelrate_dn = None
tunnelrate_up = None
if counts_dn[0] < 50:
tunnelrate_dn = None
tunnelrate_up = None
warnings.warn(
'Number of down datapoints %d is not be enough to make an acurate fit of the exponential decay for level down.'
% counts_dn[0] +
'Look therefore at the mean value of the measurement segments')
if counts_up[0] < 50:
tunnelrate_dn = None
tunnelrate_up = None
warnings.warn(
'Number of up datapoints %d is not be enough to make an acurate fit of the exponential decay for level up.'
% counts_dn[0] +
'Look therefore at the mean value of the measurement segments')
parameters = {
'plunger value': plungervalue,
'sampling rate': samplerate,
'fit parameters double gaussian': par_fit,
'separations between peaks gaussians': separation,
'split between the two levels': split
}
parameters['down_segments'] = {
'mean': np.mean(durations_dn_idx) / samplerate,
'p50': np.percentile(durations_dn_idx, 50) / samplerate,
'mean_filtered': np.mean(durations_dn_idx)
}
parameters['up_segments'] = {
'mean': np.mean(durations_up_idx) / samplerate,
'p50': np.percentile(durations_up_idx, 50) / samplerate,
'mean_filtered': np.mean(durations_up_idx)
}
parameters[
'tunnelrate_down_to_up'] = 1. / parameters['down_segments']['mean']
parameters[
'tunnelrate_up_to_down'] = 1. / parameters['up_segments']['mean']
if (counts_dn[0] > 50) and (counts_up[0] > 50):
bincentres_dn = np.array([(bins_dn[i] + bins_dn[i + 1]) / 2
for i in range(0,
len(bins_dn) - 1)])
# fitting exponential decay for down level
A_dn_fit, B_dn_fit, gamma_dn_fit = fit_exp_decay(
bincentres_dn, counts_dn)
tunnelrate_dn = gamma_dn_fit / 1000
if verbose:
print('Tunnel rate down: %.1f kHz' % tunnelrate_dn)
time_scaling = 1e3
if fig:
title = 'Fitted exponential decay, level down'
Fig = plt.figure(fig + 2)
plt.clf()
plt.plot(time_scaling * bincentres_dn,
counts_dn,
'o',
label='Counts down')
plt.plot(
time_scaling * bincentres_dn,
exp_function(bincentres_dn, A_dn_fit, B_dn_fit, gamma_dn_fit),
'r',
label=
r'Fitted exponential decay $\Gamma_{\mathrm{down\ to\ up}}$: %.1f kHz'
% tunnelrate_dn)
plt.xlabel('Lifetime (ms)')
plt.ylabel('Counts per bin')
plt.legend()
plt.title(title)
if ppt:
addPPTslide(title=title, fig=Fig)
bincentres_up = np.array([(bins_up[i] + bins_up[i + 1]) / 2
for i in range(0,
len(bins_up) - 1)])
# fitting exponential decay for up level
A_up_fit, B_up_fit, gamma_up_fit = fit_exp_decay(
bincentres_up, counts_up)
tunnelrate_up = gamma_up_fit / 1000
if verbose:
print('Tunnel rate up: %.1f kHz' % tunnelrate_up)
if fig:
title = 'Fitted exponential decay, level up'
Fig = plt.figure(fig + 3)
plt.clf()
plt.plot(time_scaling * bincentres_up,
counts_up,
'o',
label='Counts up')
plt.plot(
time_scaling * bincentres_up,
exp_function(bincentres_up, A_up_fit, B_up_fit, gamma_up_fit),
'r',
label=
r'Fitted exponential decay $\Gamma_{\mathrm{up\ to\ down}}$: %.1f kHz'
% tunnelrate_up)
plt.xlabel('Lifetime (ms)')
plt.ylabel('Data points per bin')
plt.legend()
plt.title(title)
if ppt:
addPPTslide(title=title, fig=Fig)
parameters['fit parameters exp. decay down'] = [
A_dn_fit, B_dn_fit, gamma_dn_fit
]
parameters['fit parameters exp. decay up'] = [
A_up_fit, B_up_fit, gamma_up_fit
]
parameters['tunnelrate_down_exponential_fit'] = tunnelrate_dn
parameters['tunnelrate_up_exponential_fit'] = tunnelrate_up
else:
parameters['tunnelrate_down_exponential_fit'] = None
parameters['tunnelrate_up_exponential_fit'] = None
return tunnelrate_dn, tunnelrate_up, parameters
