Figure 1: Video from "Tout est quantique" at http://toutestquantique.fr/en/laser/. Scientific advisor: Julien Bobroff LPS, Université Paris-Sud et CNRS Orsay.
"In quantum physics, the energy of an atom displays discontinuous levels. If the atom is excited, its energy suddenly rises to the next level.
If a photon (a light bundle) with proper energy is sent to an excited atom, the atom falls into a lower energy level and emits a second photon perfectly identical to the first one.
In a laser, excited atoms are put between two mirrors. A first photon stimulates an atom which emits a second photon, and so on thanks to the mirrors.
The resulting photons are all identical. They have the same energy which gives them the same color and a unique direction. This is how a LASER works."
Please refer to the section "Absorption - Emission" for the notion of "spontaneous" and "stimulated" emission.
MacGyver and the Optical Pump
Figure 2: Video from the TV series "MacGyver" demonstrating an "optical pump".
In order to create a laser, first we need a material like for instance the element rubidium (Rb) or mixtures of the elements helium and neon (HeNe).
The material will be absorbing photons (light) i.e. the energy of the photons will be absorbed by the electrons/atoms (optical absorbance) of the material, and there will be stimulated emissions (cf. previous section) of photons.
We must have a way to energize the material or medium, in other words to "pump" it. We have to mediate optical absorbance in order to have optical emission. As energy is absorbed in the medium, excited states are created in its atoms. As more and more atoms are excited, we reach a point where the number of atoms in the excited state exceeds the number of particles in the ground state (or less-excited state). In statistical mechanics, this is called population inversion.
“If the number of photons being amplified per unit of time is greater than the number of photons being absorbed, then the net result is a continuously increasing number of photons being produced; the laser medium is said to have a gain (cf. optical gain) of greater than unity.”
Once this condition is achieved, via stimulated emission the medium can act as an optical amplifier or laser that from a certain number of photons generates laser power!
We refer to lasing or optical amplification.
The pump energy is usually provided in the form of light or electric current.
As mentioned in Wikipedia (https://en.wikipedia.org/wiki/Optical_pumping) “an optical pumping experiment is commonly found in physics undergraduate laboratories, using rubidium gas isotopes and displaying the ability of radiofrequency (MHz) electromagnetic radiation to effectively pump and unpump these isotopes.”
Such an exercise is available at this link http://www.teachspin.com/optical-pumping.html.
Alkali metals couple in a resonant fashion with light (D1 and D2 optical transitions)
In accordance with what was mentioned in the spin-orbit interaction section, the energy levels of the atoms consist of a gross structure, a fine structure (due to the spin-orbit interaction or the coupling of the electronic spin and the orbital angular momentum) and a hyperfine structure (due to the magnetic and electric moment interaction between the nuclear spin and electronic spin). [Ref. https://scholar.colorado.edu/phys_gradetds/125/ e-page 36 - 2.3 Alkali atoms.]
In the case of sodium, due to the spin-orbit interaction "the 3p level is split into states with total angular momentum j=3/2 and j=1/2 by the magnetic energy of the electron spin in the presence of the internal magnetic field caused by the orbital motion". [Ref. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/sodzee.html.]
The 3P3/2->3S1/2 is called the D2 transition and gives the 588.995 nm spectral D2 line and the 3P1/2->3S1/2 is called the D1 transition and gives the 589.592 D1 spectral line.
Similarly, the other alkali metal atoms are closed shells plus one valence electron in the next s state (l=0). These are 2S, 3S, 4S, 5S, 6S for Li, Na, K, Rb, and Cs, respectively. We are interested in the same transitions between the ground state and the excited states having the electron in the P state (same n, = 0 l = 1). The same D line notation is used for all alkali metals.
[Ref. from Columbia Physics Dept, home of Prof. I. I. Rabi cf. “Breit-Rabi” formula http://www.phys.columbia.edu/~w3081/exp_files/OpticalPumping.pdf.]
Due to their atomic properties, "alkali atoms couple in a resonant fashion to light, with frequency in the visible and near-infrared spectrum. The transitions between the ground state and excited state energy levels are often called optical transitions" (cf. D1 and D2 optical transitions). [Ref. https://scholar.colorado.edu/phys_gradetds/125/ e-page 36 - 2.3 Alkali atoms].
We also mentioned in previous sections, the effects of magnetic fields on atoms, cf. hyperfine structure splitting, spin excitation/flipping and Larmor precession.
These effects can be deployed on a population of atoms for different applications.
In general, the electron spin magnetic momentum of paramagnetic atoms is considered to be one of the most sensitive magnetic field probes.
By directing the spins of a medium along a specific axis, a specific pole, it is possible to produce a macroscopic magnetization. It is said that the medium becomes spin polarized.
This can be induced using light or a magnetic field.
An effective method to induce spin polarized media is optical pumping and this can be accomplished using for instance circularly polarized light corresponding to the D1 transition of alkali metals. Also, linearly polarized light (D2 transition line of alkali metals) can be used to study the changes in atomic polarization.
[Ref. Effect of light polarization on the absorption index of alkali metal vapor in optical pumping phenomenon https://www.researchgate.net/figure/The-optical-pumping-process-with-circularly-s-polarized-light-1_fig1_270703906]
For the Population Dynamics of Optical Pumping please refer to the section "Details" of this reference: http://demonstrations.wolfram.com/OpticalPumpingPopulationDynamics/
Some general comments:
Alkali metal atoms are characterized by D1 and D2 (optical) transitions that are resonant to linearly or circularly polarized light.
Electrons of atoms transition to higher energetic levels (magnetic sublevels - cf. hyperfine splitting & Zeeman effect) and then proceed to relaxation.
Depending on the use of linearly of circularly polarized light, specific transitions are anticipated (notion of "selection rule").
The video that follows presents the demonstration included at the above link.
Figure 3: Video of the Wolfram demonstration on "Optical Pumping: Population Dynamics" (https://youtu.be/kHIJ-Uz6Z2U).
Note that a relevant demonstration entitled "Optical Pumping: Visualization of Steady State Populations and Polarizations" is found at the link:
"Demonstrations can be created with just a few short lines of code. This opens the door for researchers, educators, students, and professionals at any level to create their own sophisticated mini-applications, then publish and share them with the world using Wolfram's Computable Document Format (CDF)."
At this link https://collaps.web.cern.ch/beta-nmr/spin-polarization there is an important figure on selection rules or transition rules (cf. https://en.wikipedia.org/wiki/Selection_rule)
"The mechanism of polarizing the spin of atoms is based on the selection rules for electromagnetic radiation from atomic transition. If the excitation by the photon of the proper wavelength is done with circular polarized light, only transitions with Δm = +1, -1 are allowed. If the light is right circularly polarized, only transitions with Δm = +1 are allowed.
The two effects - levels splitting up in a weak magnetic field in combination with circular polarized light - can be used to selectively change the population of the electronic levels:
The excitation always causes an transition towards the HIGHER m(F), whereas the decay can take place with all allowed transitions: Δm = +1, -1, 0.
If the atom goes through many excitation / decay cycles, the electron will move up and stay up in the state with the highest quantum number m(F). As a result, the atom gets spin polarized with respect to the quantization axis - the direction of the magnetic field. If one looks at a large number of atoms, the net effect is a change in population of the different levels towards the level with the highest spin."
For the mathematics of the process of optical pumping i.e. resonance behavior of the optical transition which may include homogeneous collisional broadening or Doppler broadening refer to the following thesis on “Atomic Magnetometers” by R. Jimenez Martinez, University of Colorado at Boulder (in collaboration with NIST) https://scholar.colorado.edu/phys_gradetds/125/
[e-page 45] Physically, the matrix elements of the operator α describe the promotion of an atom in the ground state |Fgµ> into an excited state |Fem> by the absorption of a photon with angular momentum (m − µ) * h , and the subsequent population of the ground state |F’gµ’> by the stimulated decay of the excited state |Fem> accompanied by the emission of a photon with angular momentum (µ − m) * h.
[e-page 47] Figure 2.4: (a) Energy splittings contributing to the profile factor in Eq. (2.44) for alkali atoms with nuclear spin I = 3/2. (b) Sketch of optical absorption as a function of light detuning for the case where Doppler broadening and collisional broadening dominate the width of the optical line.
Relevant note from a previous section: “Given the fact that ground states relax at a much slower rate than excited states, the authors assume that the excited states reach a quasi-steady-state much faster than the ground states do and follow them adiabatically. They consider Doppler broadening and collisional damping of the excited state and assume that the interaction due to magnetic fields is much smaller than any other atom interaction, but not necessarily the light-atom interaction .