.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/core/plot_EIT.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_core_plot_EIT.py: EIT === This examples employs a 3-level system to show the effect of EIT. EIT (electromagnetically-induced transparency). .. GENERATED FROM PYTHON SOURCE LINES 12-14 Import ------ .. GENERATED FROM PYTHON SOURCE LINES 14-20 .. code-block:: Python from MoleCool import System, np, plt, pi det_pump = 0*1e6 # pump laser detuning for for EIT resonance position in Hz I_probe = 0.2 # laser intensity of probe beam in W/m^2 I_pump = 5.0 # laser intensity of pump beam in W/m^2 gr_split = 1000 # splitting between both ground states in MHz .. GENERATED FROM PYTHON SOURCE LINES 21-23 Calculation routine ------------------- .. GENERATED FROM PYTHON SOURCE LINES 23-62 .. code-block:: Python Deltas = np.array([*np.arange(-3,-0.5,0.1),*np.arange(-0.5,0.,0.01)])*1e6 Deltas = np.array([*Deltas,*(-np.flip(Deltas[:-1]))]) + det_pump rho = np.zeros((2,len(Deltas)),dtype=complex) # steady state density matrix elements for i in range(2): system = System('testingEIT') system.levels.add_electronicstate('e', 'exs') # first add only excited state system.levels.e.add(F=1,mF=0) # add single mF=0 with F=1 as F=0 would be forbidden # simple two-level case: if i == 0: system.levels.add_electronicstate('g', 'gs') # ground electronic state system.levels.g.add(J=0.5,F=0,mF=0) # add a single level with F=0 # initial population can be specified but makes no difference for steady state system.N0 = [1,0] # Lambda-level scheme for EIT case: if i == 1: system.levels.add_electronicstate('g', 'gs') # ground electronic state system.levels.g.add(J=0.5,F=0,mF=0) # add two single levels with F=0 system.levels.g.add(J=1.5,F=0,mF=0) system.levels.g.freq.iloc[1] = -gr_split # detuning in MHz between both ground states # Iterating over all detunings of scanning probe laser: for j,Delta in enumerate(Deltas): del system.lasers[:] # delete laser instances in every iteration system.lasers.add(I=I_probe, freq_shift=Delta) # (weak) probe laser # only add pump laser for EIT case: if i == 1: system.lasers.add(I=I_pump, freq_shift=+gr_split*1e6+det_pump) T_Om = 2*pi/np.abs(system.calc_Rabi_freqs()).max() # period time of Rabi frequency # calculate dynamics until steady state is reached system.calc_OBEs(t_int=5*T_Om, steadystate=True, verbose=False) # transform density matrix elements (ymat) to the other rotating frame # which rotates with level's transition frequency instead laser frequency rho[i,j] = (system.ymat[0,-1,:] * np.exp(1j*system.t*Delta*2*pi)).mean() .. rst-class:: sphx-glr-script-out .. code-block:: none System is created with description: testingEIT /home/docs/checkouts/readthedocs.org/user_builds/molecool-py/checkouts/v3.7.2/MoleCool/Levelsystem.py:1573: UserWarning: Gamma must be defined for ElectronicState e! By default, it is now set to 1 MHz! warnings.warn(text) /home/docs/checkouts/readthedocs.org/user_builds/molecool-py/checkouts/v3.7.2/MoleCool/Levelsystem.py:293: UserWarning: There is no dipole matrix or reduced dipole matrix available!So a reduced matrix has been created only with ones: exs e F 1 gs J F g 0.5 0 1.0 warnings.warn(warn_txt) System is created with description: testingEIT /home/docs/checkouts/readthedocs.org/user_builds/molecool-py/checkouts/v3.7.2/MoleCool/Levelsystem.py:1573: UserWarning: Gamma must be defined for ElectronicState e! By default, it is now set to 1 MHz! warnings.warn(text) /home/docs/checkouts/readthedocs.org/user_builds/molecool-py/checkouts/v3.7.2/MoleCool/Levelsystem.py:293: UserWarning: There is no dipole matrix or reduced dipole matrix available!So a reduced matrix has been created only with ones: exs e F 1 gs J F g 1.5 0 1.0 0.5 0 1.0 warnings.warn(warn_txt) .. GENERATED FROM PYTHON SOURCE LINES 63-65 Plotting results ---------------- .. GENERATED FROM PYTHON SOURCE LINES 65-72 .. code-block:: Python plt.figure('Susceptibility') for i,case in enumerate(['1+1','2+1']): plt.plot(Deltas*1e-6,rho[i].imag,'--',label=f"Im, {case}", c='C'+str(i)) plt.plot(Deltas*1e-6,rho[i].real,'-',label=f"Re, {case}", c='C'+str(i)) plt.xlabel('Probe laser detuning ($\Gamma$)') plt.ylabel('Susceptibility $\\rho_{eg}$') plt.legend(loc='upper right') .. image-sg:: /auto_examples/core/images/sphx_glr_plot_EIT_001.png :alt: plot EIT :srcset: /auto_examples/core/images/sphx_glr_plot_EIT_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 7.596 seconds) .. _sphx_glr_download_auto_examples_core_plot_EIT.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_EIT.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_EIT.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_EIT.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_