How Does Photon Angular Momentum Influence Zeeman Effect Observations?

[secret2]

Currently working on a problem about Zeeman Effect. Consider two states, 3S1 and 3P1, each of which is a triplet under the effect of an external B field in the z direction. 3P1 is the ground state.

If we shine a beam of circular polarized light, incident along a direction parallel to the B field, to the atoms, it is said that only 2 absorption lines among the 7 allowed transition lines (considering only dipole radiation) will be observed.

The answer says that only two lines are observed because the photon carry 1 unit of angular mometum, hence only those lines with (delta Mj)=1, namely the Mj=1 and Mj=0 states of 3S1, can be seen. I have 3 questions:

1. What is the proof of the claim that "photon carry 1 unit of angular mometum"?
2. What is the significance of having circular polarized light in this particular problem?
3. How can we, if possible after all, excite the atoms to the remaining state?(i.e. Mj=-1 of 3S1 state)

 

[wais]

1. The proof that photons carry 1 unit of angular momentum comes from the fact that they exhibit properties of both particles and waves. In quantum mechanics, particles are described by their wavefunctions, which can have a specific angular momentum value. The angular momentum of a photon is given by its spin, which is always equal to 1 in units of the reduced Planck constant. This spin value is the same for all photons, regardless of their frequency or energy. Therefore, it can be said that photons carry 1 unit of angular momentum.

2. The significance of using circular polarized light in this problem is that it has a specific polarization state, which is determined by the direction of its electric field. Circular polarized light has both a magnetic and an electric field component, and their directions are perpendicular to each other. This specific polarization state allows for the selection of specific transition lines in the Zeeman effect, as only transitions with a change in angular momentum of 1 can occur.

3. It is not possible to excite the atoms to the remaining state (Mj=-1 of 3S1 state) in this particular problem. This is because the selection rules for dipole radiation state that the change in angular momentum (delta Mj) must be equal to 0 or +/-1. Since the initial state (3P1) has a Mj value of 0, the only allowed transitions are to states with Mj values of 1 or -1. Therefore, it is not possible to excite the atoms to the Mj=-1 state of the 3S1 state using circular polarized light.