Daniel Cohen Hillel

Daniel Cohen Hillel

Grad student

🔗 Coupling between the readout resonator and transmon

Modes

modeobject
0transmon
1cavity
2cavity
3cavity
4readout

Imports

%load_ext autoreload
%autoreload 2
%config IPCompleter.greedy = True

import sys
import numpy as np
from IPython.display import display, Math, Latex, display_markdown
from pathlib import Path
import pandas as pd
from scipy import constants

import pyEPR as epr
from pyEPR.calcs import Convert
from pyEPR.core import *
from pyEPR.ansys import *
import warnings
warnings.simplefilter("ignore")

path_to_project = 'D:\\Users\\Daniel\\Cavity-Analysis\\coupling'

🔷 Mode analysis

🔹 Connect to HFSS

pinfo = epr.Project_Info(project_path = path_to_project, 
                         project_name = 'coupling',
                         design_name  = 'design')

INFO 09:44PM [connect]: Connecting to Ansys Desktop API...
INFO 09:44PM [load_ansys_project]: 	File path to HFSS project found.
INFO 09:44PM [load_ansys_project]: 	Opened Ansys App
INFO 09:44PM [load_ansys_project]: 	Opened Ansys Desktop v2020.1.0
INFO 09:44PM [load_ansys_project]: 	Opened Ansys Project
	Folder:    D:/Users/Daniel/Cavity-Analysis/coupling/
	Project:   coupling
INFO 09:44PM [connect]: 	Opened active design
	Design:    design [Solution type: Eigenmode]
INFO 09:44PM [get_setup]: 	Opened setup `Setup1`  (<class 'pyEPR.ansys.HfssEMSetup'>)
INFO 09:44PM [connect]: 	Connection to Ansys established successfully. 😀

pad-RO gap

swp_var = 'ro_gap'  # Sweep ove 'ro_gap'
to_swp_val = lambda x: f'{x}mm' 

for swp_param in np.linspace(0.5, 2, 4):
    swp_val = to_swp_val(swp_param)
    epr.logger.info(f'Setting sweep variable {swp_var}={swp_val}')
    pinfo.project.set_variable(swp_var, swp_val)
    pinfo.setup.analyze()
# pinfo.setup.analyze()

INFO 09:44PM [<module>]: Setting sweep variable ro_gap=0.5mm
INFO 09:44PM [analyze]: Analyzing setup Setup1
INFO 09:44PM [<module>]: Setting sweep variable ro_gap=1.0mm
INFO 09:44PM [analyze]: Analyzing setup Setup1
INFO 09:45PM [<module>]: Setting sweep variable ro_gap=1.5mm
INFO 09:45PM [analyze]: Analyzing setup Setup1
INFO 09:46PM [<module>]: Setting sweep variable ro_gap=2.0mm
INFO 09:46PM [analyze]: Analyzing setup Setup1

pinfo.junctions['j1'] = {'Lj_variable' : 'Lj_1',
                         'rect'        : 'rect_jj1', 
                         'line'        : 'line_jj1', 
                         'length'      : epr.parse_units('100um')}


# Check that valid names of variables and objects have been supplied.
# An error is raised with a message if something is wrong.
pinfo.validate_junction_info()

eprh = epr.DistributedAnalysis(pinfo)

Design "design" info:
	# eigenmodes    5
	# variations    7

eprh.do_EPR_analysis(modes=[0,4]);

Variation 0  [1/7]

  Mode 0 at 4.49 GHz   [1/5]
    Calculating â„°_magnetic,â„°_electric
       (â„°_E-â„°_H)/â„°_E       â„°_E       â„°_H
               96.6%  1.302e-24 4.381e-26

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_0j   sign s_0j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 98.74%
	j1              0.964126  (+)        0.0122956
		(U_tot_cap-U_tot_ind)/mean=0.72%

  Mode 4 at 7.60 GHz   [5/5]
    Calculating â„°_magnetic,â„°_electric
       (â„°_E-â„°_H)/â„°_E       â„°_E       â„°_H
                3.0%  5.095e-23 4.944e-23

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_4j   sign s_4j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 96.48%
	j1              0.00842922  (+)        0.000307636
		(U_tot_cap-U_tot_ind)/mean=1.10%

Variation 1  [2/7]

  Mode 0 at 4.56 GHz   [1/5]
    Calculating â„°_magnetic,â„°_electric
       (â„°_E-â„°_H)/â„°_E       â„°_E       â„°_H
               97.1%   4.15e-24 1.187e-25

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_0j   sign s_0j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 98.70%
	j1              0.968695  (+)        0.0127119
		(U_tot_cap-U_tot_ind)/mean=0.77%

  Mode 4 at 7.61 GHz   [5/5]
    Calculating â„°_magnetic,â„°_electric
       (â„°_E-â„°_H)/â„°_E       â„°_E       â„°_H
                2.7%  3.684e-22 3.586e-22

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_4j   sign s_4j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 96.47%
	j1              0.00391719  (+)        0.000143314
		(U_tot_cap-U_tot_ind)/mean=1.15%

Variation 2  [3/7]

  Mode 0 at 4.55 GHz   [1/5]
    Calculating â„°_magnetic,â„°_electric
       (â„°_E-â„°_H)/â„°_E       â„°_E       â„°_H
               97.3%   2.99e-24 8.192e-26

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_0j   sign s_0j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 98.71%
	j1              0.969892  (+)        0.0126869
		(U_tot_cap-U_tot_ind)/mean=0.77%

  Mode 4 at 7.61 GHz   [5/5]
    Calculating â„°_magnetic,â„°_electric
       (â„°_E-â„°_H)/â„°_E       â„°_E       â„°_H
                2.3%  5.349e-22 5.228e-22

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_4j   sign s_4j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 96.47%
	j1              0.00195276  (+)        7.15183e-05
		(U_tot_cap-U_tot_ind)/mean=1.05%

Variation 3  [4/7]

  Mode 0 at 4.54 GHz   [1/5]
    Calculating â„°_magnetic,â„°_electric
       (â„°_E-â„°_H)/â„°_E       â„°_E       â„°_H
               97.5%  2.018e-24 5.134e-26

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_0j   sign s_0j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 98.71%
	j1              0.971791  (+)        0.0126685
		(U_tot_cap-U_tot_ind)/mean=0.77%

  Mode 4 at 7.61 GHz   [5/5]
    Calculating â„°_magnetic,â„°_electric
       (â„°_E-â„°_H)/â„°_E       â„°_E       â„°_H
                2.2%  6.485e-22 6.345e-22

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_4j   sign s_4j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 96.47%
	j1              0.000955591  (+)        3.49657e-05
		(U_tot_cap-U_tot_ind)/mean=1.05%

Variation 4  [5/7]

  Mode 0 at 4.54 GHz   [1/5]
    Calculating â„°_magnetic,â„°_electric
       (â„°_E-â„°_H)/â„°_E       â„°_E       â„°_H
               97.5%  2.018e-24 5.134e-26

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_0j   sign s_0j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 98.71%
	j1              0.971791  (+)        0.0126685
		(U_tot_cap-U_tot_ind)/mean=0.77%

  Mode 4 at 7.61 GHz   [5/5]
    Calculating â„°_magnetic,â„°_electric
       (â„°_E-â„°_H)/â„°_E       â„°_E       â„°_H
                2.2%  6.485e-22 6.345e-22

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_4j   sign s_4j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 96.47%
	j1              0.000955591  (+)        3.49657e-05
		(U_tot_cap-U_tot_ind)/mean=1.05%

Variation 5  [6/7]

  Mode 0 at 4.54 GHz   [1/5]
    Calculating â„°_magnetic,â„°_electric
       (â„°_E-â„°_H)/â„°_E       â„°_E       â„°_H
               97.5%  2.018e-24 5.134e-26

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_0j   sign s_0j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 98.71%
	j1              0.971791  (+)        0.0126685
		(U_tot_cap-U_tot_ind)/mean=0.77%

  Mode 4 at 7.61 GHz   [5/5]
    Calculating â„°_magnetic,â„°_electric
       (â„°_E-â„°_H)/â„°_E       â„°_E       â„°_H
                2.2%  6.485e-22 6.345e-22

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_4j   sign s_4j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 96.47%
	j1              0.000955591  (+)        3.49657e-05
		(U_tot_cap-U_tot_ind)/mean=1.05%

Variation 6  [7/7]

  Mode 0 at 4.54 GHz   [1/5]
    Calculating â„°_magnetic,â„°_electric
       (â„°_E-â„°_H)/â„°_E       â„°_E       â„°_H
               97.5%  2.018e-24 5.134e-26

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_0j   sign s_0j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 98.71%
	j1              0.971791  (+)        0.0126685
		(U_tot_cap-U_tot_ind)/mean=0.77%

  Mode 4 at 7.61 GHz   [5/5]
    Calculating â„°_magnetic,â„°_electric
       (â„°_E-â„°_H)/â„°_E       â„°_E       â„°_H
                2.2%  6.485e-22 6.345e-22

    Calculating junction energy participation ration (EPR)
	method=`line_voltage`. First estimates:
	junction        EPR p_4j   sign s_4j    (p_capacitive)
		Energy fraction (Lj over Lj&Cj)= 96.47%
	j1              0.000955591  (+)        3.49657e-05
		(U_tot_cap-U_tot_ind)/mean=1.05%

ANALYSIS DONE. Data saved to:

D:\data-pyEPR\coupling\design\2020-05-19 21-46-30.npz

epra = epr.QuantumAnalysis(eprh.data_filename)
epra.analyze_all_variations(cos_trunc = 8, fock_trunc = 15);

	 Differences in variations:
variation0123456
_$ro_gap0.5mm1mm1.5mm2mm0.5mm1mm1.5mm
_ro_gap0.5mm1mm1.5mm2mm2mm2mm2mm
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
Variation 0

Starting the diagonalization
Finished the diagonalization
Pm_norm=
modes
0    1.014820
4    2.311961
dtype: float64

Pm_norm idx =
      j1
0   True
4  False

*** Different parameters



_$ro_gap    0.5mm
_ro_gap     0.5mm
Name: 0, dtype: object




*** P (participation matrix, not normlz.)
         j1
0  0.952416
4  0.008427

*** S (sign-bit matrix)
   s_j1
0     1
4     1
*** P (participation matrix, normalized.)
      0.97
    0.0084

*** Chi matrix O1 PT (MHz)
    Diag is anharmonicity, off diag is full cross-Kerr.
       115      3.4
       3.4   0.0251

*** Chi matrix ND (MHz) 
       123     3.23
      3.23   0.0222

*** Frequencies O1 PT (MHz)
0    4376.239072
1    7599.526246
dtype: float64

*** Frequencies ND (MHz)
0    4372.959363
1    7599.542598
dtype: float64

*** Q_coupling
Empty DataFrame
Columns: []
Index: [0, 4]

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
Variation 1

Starting the diagonalization
Finished the diagonalization
Pm_norm=
modes
0    1.015695
4    3.956376
dtype: float64

Pm_norm idx =
      j1
0   True
4  False

*** Different parameters



_$ro_gap    1mm
_ro_gap     1mm
Name: 1, dtype: object




*** P (participation matrix, not normlz.)
         j1
0  0.956536
4  0.003917

*** S (sign-bit matrix)
   s_j1
0     1
4     1
*** P (participation matrix, normalized.)
      0.97
    0.0039

*** Chi matrix O1 PT (MHz)
    Diag is anharmonicity, off diag is full cross-Kerr.
       120     1.62
      1.62  0.00544

*** Chi matrix ND (MHz) 
       128     1.53
      1.53  0.00478

*** Frequencies O1 PT (MHz)
0    4437.194074
1    7609.766145
dtype: float64

*** Frequencies ND (MHz)
0    4433.796616
1    7609.775105
dtype: float64

*** Q_coupling
Empty DataFrame
Columns: []
Index: [0, 4]

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
Variation 2

Starting the diagonalization
Finished the diagonalization
Pm_norm=
modes
0    1.015655
4    6.364569
dtype: float64

Pm_norm idx =
      j1
0   True
4  False

*** Different parameters



_$ro_gap    1.5mm
_ro_gap     1.5mm
Name: 2, dtype: object




*** P (participation matrix, not normlz.)
         j1
0  0.957741
4  0.001953

*** S (sign-bit matrix)
   s_j1
0     1
4     1
*** P (participation matrix, normalized.)
      0.97
     0.002

*** Chi matrix O1 PT (MHz)
    Diag is anharmonicity, off diag is full cross-Kerr.
       120    0.805
     0.805  0.00135

*** Chi matrix ND (MHz) 
       128    0.761
     0.761  0.00119

*** Frequencies O1 PT (MHz)
0    4430.398622
1    7614.146050
dtype: float64

*** Frequencies ND (MHz)
0    4427.049027
1    7614.150419
dtype: float64

*** Q_coupling
Empty DataFrame
Columns: []
Index: [0, 4]

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
Variation 3

Starting the diagonalization
Finished the diagonalization
Pm_norm=
modes
0     1.015684
4    11.958356
dtype: float64

Pm_norm idx =
      j1
0   True
4  False

*** Different parameters



_$ro_gap    2mm
_ro_gap     2mm
Name: 3, dtype: object




*** P (participation matrix, not normlz.)
         j1
0  0.959634
4  0.000956

*** S (sign-bit matrix)
   s_j1
0     1
4     1
*** P (participation matrix, normalized.)
      0.97
   0.00096

*** Chi matrix O1 PT (MHz)
    Diag is anharmonicity, off diag is full cross-Kerr.
       120    0.394
     0.394 0.000324

*** Chi matrix ND (MHz) 
       128    0.373
     0.373 0.000285

*** Frequencies O1 PT (MHz)
0    4422.793687
1    7610.866029
dtype: float64

*** Frequencies ND (MHz)
0    4419.452986
1    7610.868134
dtype: float64

*** Q_coupling
Empty DataFrame
Columns: []
Index: [0, 4]

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
Variation 4

Starting the diagonalization
Finished the diagonalization
Pm_norm=
modes
0     1.015684
4    11.958356
dtype: float64

Pm_norm idx =
      j1
0   True
4  False

*** Different parameters



_$ro_gap    0.5mm
_ro_gap       2mm
Name: 4, dtype: object




*** P (participation matrix, not normlz.)
         j1
0  0.959634
4  0.000956

*** S (sign-bit matrix)
   s_j1
0     1
4     1
*** P (participation matrix, normalized.)
      0.97
   0.00096

*** Chi matrix O1 PT (MHz)
    Diag is anharmonicity, off diag is full cross-Kerr.
       120    0.394
     0.394 0.000324

*** Chi matrix ND (MHz) 
       128    0.373
     0.373 0.000285

*** Frequencies O1 PT (MHz)
0    4422.793687
1    7610.866029
dtype: float64

*** Frequencies ND (MHz)
0    4419.452986
1    7610.868134
dtype: float64

*** Q_coupling
Empty DataFrame
Columns: []
Index: [0, 4]

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
Variation 5

Starting the diagonalization
Finished the diagonalization
Pm_norm=
modes
0     1.015684
4    11.958356
dtype: float64

Pm_norm idx =
      j1
0   True
4  False

*** Different parameters



_$ro_gap    1mm
_ro_gap     2mm
Name: 5, dtype: object




*** P (participation matrix, not normlz.)
         j1
0  0.959634
4  0.000956

*** S (sign-bit matrix)
   s_j1
0     1
4     1
*** P (participation matrix, normalized.)
      0.97
   0.00096

*** Chi matrix O1 PT (MHz)
    Diag is anharmonicity, off diag is full cross-Kerr.
       120    0.394
     0.394 0.000324

*** Chi matrix ND (MHz) 
       128    0.373
     0.373 0.000285

*** Frequencies O1 PT (MHz)
0    4422.793687
1    7610.866029
dtype: float64

*** Frequencies ND (MHz)
0    4419.452986
1    7610.868134
dtype: float64

*** Q_coupling
Empty DataFrame
Columns: []
Index: [0, 4]

 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
Variation 6

Starting the diagonalization
Finished the diagonalization
Pm_norm=
modes
0     1.015684
4    11.958356
dtype: float64

Pm_norm idx =
      j1
0   True
4  False

*** Different parameters



_$ro_gap    1.5mm
_ro_gap       2mm
Name: 6, dtype: object




*** P (participation matrix, not normlz.)
         j1
0  0.959634
4  0.000956

*** S (sign-bit matrix)
   s_j1
0     1
4     1
*** P (participation matrix, normalized.)
      0.97
   0.00096

*** Chi matrix O1 PT (MHz)
    Diag is anharmonicity, off diag is full cross-Kerr.
       120    0.394
     0.394 0.000324

*** Chi matrix ND (MHz) 
       128    0.373
     0.373 0.000285

*** Frequencies O1 PT (MHz)
0    4422.793687
1    7610.866029
dtype: float64

*** Frequencies ND (MHz)
0    4419.452986
1    7610.868134
dtype: float64

*** Q_coupling
Empty DataFrame
Columns: []
Index: [0, 4]

epra.plot_hamiltonian_results();

(<Figure size 720x432 with 4 Axes>,
 array([[<matplotlib.axes._subplots.AxesSubplot object at 0x000001AB62D03E80>,
         <matplotlib.axes._subplots.AxesSubplot object at 0x000001AB6BE696D0>],
        [<matplotlib.axes._subplots.AxesSubplot object at 0x000001AB6BF173A0>,
         <matplotlib.axes._subplots.AxesSubplot object at 0x000001AB6BF39820>]],
       dtype=object))

png

🔹 Get HFSS mode and quality results

modes      = eprh.get_freqs_bare_pd(eprh.variations[0])
Fs, Qs     = np.array(modes['Freq. (GHz)']), np.array(modes['Quality Factor'])  # Get freqs and Q-factors
n_modes    = int(pinfo.setup.n_modes)
display(modes)
Freq. (GHz)Quality Factor
mode
04.4933269.981263e+05
14.8492615.716968e+10
27.0316345.873285e+07
37.0337786.987834e+08
47.6012531.018629e+05

🔹 Calculate the EPRs of the modes

eprh.set_mode(0)
p_cavity, (â„°_cav, â„°_total) = eprh.calc_p_electric_volume('cavity')
p_dirt,  (â„°_dirt, â„°_total) = eprh.calc_p_electric_volume('dirt')

print(f' 🔸 Energy in cavity = {100*p_cavity:.3f}% -> {ℰ_cav:0.2e} of the total energy in the system')
print(f' 🔸 Energy in dirt   = {100*p_dirt:.3f}% -> {ℰ_dirt:0.2e} of the total energy in the system')
print(f' 🔸 Total energy     = {ℰ_total:0.2e}')

---------------------------------------------------------------------------

com_error                                 Traceback (most recent call last)

<ipython-input-11-d62cbaa5fd11> in <module>
      1 eprh.set_mode(0)
----> 2 p_cavity, (â„°_cav, â„°_total) = eprh.calc_p_electric_volume('cavity')
      3 p_dirt,  (â„°_dirt, â„°_total) = eprh.calc_p_electric_volume('dirt')
      4 
      5 print(f' 🔸 Energy in cavity = {100*p_cavity:.3f}% -> {ℰ_cav:0.2e} of the total energy in the system')


D:\Users\Daniel\pyEPR\pyEPR\core_distributed_analysis.py in calc_p_electric_volume(self, name_dielectric3D, relative_to, E_total)
    653 
    654         logger.debug('Calculating â„°_object')
--> 655         â„°_object = self.calc_energy_electric(volume=name_dielectric3D)
    656 
    657         return â„°_object/â„°_total, (â„°_object, â„°_total)


D:\Users\Daniel\pyEPR\pyEPR\core_distributed_analysis.py in calc_energy_electric(self, variation, volume, smooth)
    596 
    597         lv = self._get_lv(variation)
--> 598         return A.evaluate(lv=lv)
    599 
    600     def calc_energy_magnetic(self,


D:\Users\Daniel\pyEPR\pyEPR\ansys.py in evaluate(self, phase, lv, print_debug)
   2750 
   2751     def evaluate(self, phase=0, lv=None, print_debug=False):  # , n_mode=1):
-> 2752         self.write_stack()
   2753         if print_debug:
   2754             print('---------------------')


D:\Users\Daniel\pyEPR\pyEPR\ansys.py in write_stack(self)
   2740                 getattr(self.calc_module, fn)(*arg)
   2741             else:
-> 2742                 getattr(self.calc_module, fn)(arg)
   2743 
   2744     def save_as(self, name):


~\Anaconda3\envs\lab\lib\site-packages\win32com\client\dynamic.py in EnterVol(self, geomName)


com_error: (-2147352567, 'Exception occurred.', (0, None, None, None, 0, -2147024365), None)

🔷 Life-times

Life-time from HFSS

Life time of a mode inside the cavity. Since in this exampole the cavity is perfect, the life time would be infinite

Fs_Hz  = np.array(Convert.toSI(Fs,'GHz'))  # Mode freqs in Hz
omegas = 2*np.pi*Fs_Hz                     # Freqs to angular freqs
taus   = Qs/omegas                         # Life times

print(f' 🔸 Life-time of mode = {taus[0]*1e3:.3f} ms')  # Should be inf since no resistive boundry and just inside a vacuum

Life-time from EPR

Life time calculation with the EPR method. This is highly dependent on the loss tangent of the dirt and cavity.

tan_dirt   = 4e-7                                         # Loss tangent of dirt

tau_epr    = lambda p, tan, omega: 1/(p*tan*omega)        # Easily calculate life time with EPR

tau_cavity = tau_epr(p_dirt, 0, omegas)[0]
tau_dirt   = tau_epr(p_cavity, tan_dirt, omegas)[0]

print(f' 🔸 Cavity life-time = {tau_cavity*1e6:.2f} ns')  # Should be infinite since the cavity is a pefect vacum
print(f' 🔸 Dirt life-time   = {tau_dirt*1e6:.2f} ns')

🔷 Losses

🔹 Surface loss

Calculating the energy precentage near the cavity walls by the surface integral. The total energy of the electromagnetic field at a layer of thickness dirt_widht would be approximated as:

\[\text{E}_{\text{cavity, boundry}} \approx \text{dirt_width} \cdot \int_{S_{cavity}} |E|^2\] \[\text{E}_{\text{cavity, volume}} = \int_{V_{cavity}} |E|^2\] \[\text{EPR}_{\text{cavity, boundry}} \approx \frac{\text{E}_{\text{cavity, boundry}}}{\text{E}_{\text{cavity, volume}}}\]

First we’ll setup a dictionary to store all the data

data = {
    "half":{
        "volume":{
            
        },
        "surface":{
           
        }
    },
    "full":{
        "volume":{
          
        },
        "surface":{
           
        }
    }
}

dirt_width = 0.1e-3
eps        = 1
tan_surf   = 5e-3

eprh.set_mode(0)

# --- Surface integral ---
surf = 'cavity'
calcobject = CalcObject([], eprh.setup)
vecE = calcobject.getQty("E").smooth()
A = vecE.times_eps()
B = vecE.conj()
A = A.dot(B)
A = A.real()
A = A.integrate_surf(name=surf)

E_subs = A.evaluate(lv=eprh._get_lv()) 
E_surf = E_subs*dirt_width*eps

# --- Volume integral ---
E_total = eprh.calc_energy_electric(smooth=True)

p_surf = E_surf/E_total      # EPR of surface 
Q_surf = 1/tan_surf/p_surf   # Q-fact of surface
tau_surf = Q_surf/omegas[0]  #  Life-time of surface

data['half']['surface'] = {
    "EPR": p_surf,
    "Q":   Q_surf,
    "tau":  tau_surf
}

print(f' 🔸 EPR surface       = {100*p_surf:.2f}%')
print(f' 🔸 Q-factor surface  = {Q_surf:.2e}')
print(f' 🔸 Life-time surface = {tau_surf:.2e} seconds \n')

🔹 Dirt (volume) loss

# Dirt is simulated as much thicker than it actually is (for computation reason). 
# Beacuase of that we reduce the loss tangent to an 'effective loss tangent' which is loss_tan*thick_factor
p_dirt, (â„°_dirt, â„°_total) = eprh.calc_p_electric_volume('dirt')
Q_dirt = 1/(tan_surf*p_dirt)
tau_dirt = Q_dirt/omegas[0]

data['half']['volume'] = {
    "EPR": p_dirt,
    "Q":   Q_dirt,
    "tau": tau_dirt
}

print(f'  🔸 EPR of dirt    = {100*p_dirt:0.2f}% ( {ℰ_dirt:.2e} / {ℰ_total:.2e} )')
print(f'  🔸 Quality factor = {Q_dirt:0.2e}')
print(f'  🔸 life time      = {tau_dirt:0.2e} seconds\n')

Figure what which mode is which

Es = []
for i in range(int(pinfo.setup.n_modes)):
    eprh.set_mode(i)

    calcobject = CalcObject([], eprh.setup)
    vecE   = calcobject.getQty("E").smooth()
    A      = vecE.times_eps()
    B      = vecE.conj()
    A      = A.dot(B)
    A      = A.real()
    ro     = A.integrate_surf(name='readout')
    cav    = A.integrate_vol(name='cavity')
    pad1   = A.integrate_surf(name='pad')
    pad2   = A.integrate_surf(name='pad_antenna')
    
    E_ro   = ro.evaluate(lv=eprh._get_lv()) 
    E_cav  = cav.evaluate(lv=eprh._get_lv()) 
    E_pad1 = pad1.evaluate(lv=eprh._get_lv()) 
    E_pad2 = pad2.evaluate(lv=eprh._get_lv()) 
    
    E = np.array([E_ro, E_cav, E_pad1, E_pad2])
    names = ['readout', 'cavity', 'transmon/pad', 'transmon/pad+antenna']
    print(i, ' --> ', names[np.argmax(E)])