from scipy.integrate import quad
from matplotlib_util import extract_params_from_file_name,\
read_column_names
from common_typeset_info import usetex, common_line_width
#Use matplotlib pre-2.0 version style
p.style.use('classic')
prefix = 'plot_data'
data_file_list = [
'cphase_fidelity_NAtoms_aE_a_opt_lambda_sagnac_g1d_0.05_OmegaScattering_1_OmegaStorageRetrieval_1_kd_0.5.txt',
'cphase_fidelity_NAtoms_aE_a_opt_dualv_sym_sagnac_g1d_0.05_OmegaScattering_1_OmegaStorageRetrieval_1_kd_0.266.txt',
]
usetex()
fig = p.figure(figsize=(3.375, 2.0))
data = []
column_dic = []
for file_name in data_file_list:
param_dict = extract_params_from_file_name(file_name)
full_path = os.path.join(prefix, file_name)
if not os.path.exists(full_path):
print('Path {} doesn\'t exist'.format(full_path))
continue
data.append(
np.loadtxt(full_path,
dtype=np.float64,
delimiter=';',
unpack=True,
skiprows=1))
def plot_r_and_t_Omega():
#Pick some incommensurate spacing between the atoms.
#This will ensure that no atoms will be exactly on
#the nodes of the standing wave
kd = 0.5 * np.pi
#We treat Delta, Deltac, g1d and gprime here as if they
#were scaled by the total decay rate
#\Gamma=\Gamma_{1D}+\Gamma'.
#Thus Delta is actually Delta/\Gamma etc.
min_Omega = 1
max_Omega = 100
num_Omega = 1000
NAtoms = 10000
g1d = 0.05
#Note that \Gamma'/\Gamma=1-\Gamma_{1D}/\Gamma.
gprime = 1 - g1d
gm = 0
Deltac = -10
usetex()
p.figure(figsize=(2 * 3.3, 2.5))
OmegaValues = np.linspace(min_Omega, max_Omega, num_Omega)
r = np.zeros(num_Omega, dtype=np.float64)
t = np.zeros(num_Omega, dtype=np.float64)
r_imp = np.zeros(num_Omega, dtype=np.float64)
t_imp = np.zeros(num_Omega, dtype=np.float64)
#r_diff2 = np.zeros(num_Omega, dtype=np.complex128)
t_diff2 = np.zeros(num_Omega, dtype=np.complex128)
deltaStart = 0.0025
for n, Omega in enumerate(OmegaValues):
delta = delta_for_minimal_r_0(deltaStart, NAtoms, kd, g1d, gprime, gm,
Deltac, Omega)
deltaStart = delta
Delta = delta + Deltac
#r_0_func = lambda x: r_0(x, NAtoms, kd, g1d, gprime, gm, Deltac, Omega)
#r_0_grad1 = grad(r_0_func)
#r_0_grad2 = grad(r_0_grad1)
t_0_func = lambda x: t_0(x, NAtoms, kd, g1d, gprime, gm, Deltac, Omega)
t_0_grad1 = grad(t_0_func)
t_0_grad2 = grad(t_0_grad1)
MensembleStandingWave\
= ensemble_transfer_matrix_pi_half(NAtoms, g1d, gprime, gm, Delta,
Deltac, Omega)
MHalfEnsembleStandingWave\
= ensemble_transfer_matrix_pi_half(NAtoms/2, g1d, gprime, gm, Delta,
Deltac, Omega)
M_impurity_cell = impurity_unit_cell_pi_half(g1d, gprime, gm, Delta,
Deltac, Omega)
MensembleStandingWaveImpurity = MHalfEnsembleStandingWave * M_impurity_cell * MHalfEnsembleStandingWave
r[n] = np.abs(-MensembleStandingWave[1,0]\
/MensembleStandingWave[1,1])**2
t[n] = np.abs(1.0 / MensembleStandingWave[1, 1])**2
r_imp[n] = np.abs(-MensembleStandingWaveImpurity[1,0]\
/MensembleStandingWaveImpurity[1,1])**2
t_imp[n] = np.abs(1.0 / MensembleStandingWaveImpurity[1, 1])**2
#r_diff2[n] = r_0_grad2(delta)
t_diff2[n] = t_0_grad2(delta)
t_analytical = (1 - (g1d * (1 - g1d) * NAtoms) / (16 * Deltac**2) -
(1 - g1d) * OmegaValues**2 * np.pi**2 /
(2 * Deltac**2 * g1d * NAtoms))**2
r_imp_analytical = (1 - 4 * np.pi**2 * Deltac**2 * (1 - g1d) /
(g1d**3 * NAtoms**2) + 32 * np.pi**4 * Deltac**2 *
(1 - g1d) * OmegaValues**2 / (g1d**5 * NAtoms**4))**2
w_analytical = 32 * np.sqrt(2) * Deltac**2 * OmegaValues**2 * np.pi**2 / (
g1d**3 * NAtoms**3)
ax = p.subplot(121)
#p.plot(OmegaValues, r, color='#000099', linestyle='-',
# label=r'$|r_0|^2$', linewidth=common_line_width)
p.plot(OmegaValues,
t,
color='#009900',
linestyle=':',
label=r'$|t_0|^2$ (full)',
linewidth=common_line_width)
p.plot(OmegaValues,
t_analytical - t_analytical[0] + t[0],
color='k',
linestyle='-.',
label=r'$|t_0|^2$ (approx)',
linewidth=common_line_width)
p.plot(OmegaValues,
r_imp,
color='#990000',
linestyle='--',
label=r'$|r_1|^2$ (full)',
linewidth=common_line_width)
p.plot(OmegaValues,
r_imp_analytical - r_imp_analytical[0] + r_imp[0],
color='#000099',
linestyle='-',
label=r'$|r_1|^2$ (approx)',
linewidth=common_line_width)
#p.plot(OmegaValues, t_imp, 'k-.',
# label=r'$|t_1|^2$', linewidth=common_line_width)
p.xlim(min_Omega, max_Omega)
p.ylim(0.0, 1)
p.xlabel(r'$\Omega_0/\Gamma$')
p.title('(a)')
p.legend(loc='lower right')
ax = p.subplot(122)
#r(\delta)=r(\delta_{res})+(2/w^2)(\delta-\delta_{res})^2
#Hence (d/d\delta)r(\delta) at \delta=\delta_{res}
#is equal to 4/w^2
#Upon solving r_diff2=4/w^2, we get w=\sqrt{4/r_diff2}
p.loglog(OmegaValues,
np.real(np.sqrt(4.0 / t_diff2)),
color='#009900',
linestyle=':',
label=r"full",
linewidth=common_line_width)
p.loglog(OmegaValues,
w_analytical,
color='k',
linestyle='-.',
label=r"approximate",
linewidth=common_line_width)
p.ylabel(r'$w/\Gamma$')
p.xlabel(r'$\Omega_0/\Gamma$')
p.legend(loc='lower right')
p.title('(b)')
p.tight_layout(pad=0.2)