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)

 

[anathema]

1. The proof of the claim that "photon carry 1 unit of angular mometum" comes from the principles of quantum mechanics. In quantum mechanics, particles can have both particle-like and wave-like properties. Photons, which are the fundamental particles of light, are described as having both energy and momentum. The angular momentum of a photon is related to its spin, which is always equal to 1. Therefore, the photon carries 1 unit of angular momentum.

2. The significance of having circular polarized light in this particular problem lies in its ability to selectively excite certain states of the atoms. Circular polarized light has a specific orientation of its electric field, which causes the atoms to interact differently with the light depending on their orientation. In this case, the circular polarized light can only excite transitions between states with a difference in angular momentum of 1, making it useful for studying the Zeeman Effect.

3. It is possible to excite the atoms to the remaining state (Mj=-1 of 3S1 state) by using a different type of light, such as linearly polarized light. Linearly polarized light has a different orientation of its electric field, allowing it to interact with atoms in a different way. This can result in transitions between states with a difference in angular momentum of 2, allowing for the excitation of the Mj=-1 state. Additionally, other techniques such as using higher energy photons or applying an external electric field can also lead to the excitation of this 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.