DOI : 10.1119/1.1935926

This paper is easy to read and give a very easy understanding on optical pumping. it also demonstrated an experimental setup on detecting this effect. worth to read.

i am not going to reveal the detail and the experiment on the paper this time, but i just share my understanding on this subject.

The electron’s spin is polarized by optical pumping. Photon has intrinsic spin 1, and, it can be liner polarized or circular polarized. A linear polarized photon carries 0 magnetic angular momentum, and a circular polarized photon carries ±1 magnetic angular momentum. Therefore, an absorption of a circular polarized photon will make an electron undergoes ΔJ=±1and Δm=±1 transition.

In atomic energy level, a ground state is 3S½ and the next level is 3P½ and 3P3/2, the splitting of the P state is due to spin-orbital coupling between electron spin and the magnetic field generated by the orbital motion of the electron. Due to hyperfine coupling with the nuclear spin, the sub-shell will further split up. The good quantum numbers for hyper structure are |I-J|≤ F≤I+J and -F ≤ m_F≤F. The following graph demonstrated the I=3/2. The selection rule is ΔF=±1 and Δm_F=±1.

The red line is the transition by absorbed a circular polarized photon, and the black lines are possible de-excitation. Since there are 2/3 chance for the lowest state to the higher states, then, the population will move and become unbalanced. If we set up a set of rate equations, we can find out the population of each state.

A magnetic field is not necessary for optical pumping, as the graph demonstrated. The magnetic field for optical pumping is for measuring the effect. When a magnetic field is applied, the population will unbiased to, say, m_F=+1 state. Since there is no more state for absorption of the circular polarized light, then, the medium will become transparent. If we switch the magnetic field, the population will be inverted absorption will occur, and the medium become no-transparent. By measuring the intensity of the light pass through the medium, we can observe the effect of the pumping.

we can see, if the number higher energy state is more than the number of lower energy state, the maximum state has an escape channel. Look at the graph, if we have transition from F=1 to F=2 state, the m_F=+1 can absorb a photon and go to the m_F=+2 state (red dotted line). Due to relaxation, the m_F=+2 can transit to the F=2, at 3S½ state ( the black dotted lines).

Due to the lamb shift, the S-state is always little higher than the P-state in same shell. therefore, is it not possible to polarize the electron for Zero nuclear spin.