Quantum Organ – Helium-Neon Laser

How do lasers actually work? It’s simple; you just need to press the button, and the show goes on. In the physical sense, however, there is much more to it. Let us discuss the helium–neon laser as an example of a gas laser.

There are two parallel mirrors at each end of a glass tube, which contains helium and neon. The mirrors must be perfectly parallel to each other; otherwise, the laser will not turn on.

Helium atoms are excited by shock waves created by electric discharge. The interesting feature here is that helium cannot give off energy by emitting radiation; it needs collisions to do so. This is because helium atoms are metastable.

When a helium atom collides with a neon atom, it gives its energy off. The neon atom, in turn, can immediately emit a photon to its surroundings. It then returns to its ground state.

The so-called inversion is a key mechanism in lasers. Excited helium is very durable. That’s why it is possible to generate many excited helium atoms simultaneously.

Excited helium atoms give energy off to many neon atoms, which then generate many photons – in stimulated emission. These coherent photons are reflected back and forth in the resonator by the two mirrors. That creates a standing wave, which is amplified further and further. A section of this standing wave is decoupled by the mirror, which does not reflect at 100%. That is the laser beam we can see.

Why is a helium atom unable to make a radiative transition? According to the Bohr atomic model, each electron should be able to jump from a higher shell to a lower one, emitting radiation in the process. We can see that Bohr cannot help us here.

In the model of a quantum organ, we specify not only shells n=1, 2, 3 …, but also the orbitals within the shells; that is, the s, p, d, and f orbitals, each with an additional azimuthal nodal line in the wave function.

An electron in the p orbital can emit a photon only by changing the orbital; for example, during the transition from 3p to 2s. These movements along the diagonal line are possible, while all other movements are forbidden. For example, a transition from 2s to 1s is forbidden. These are the so-called “selection rules”.

We can compare these rules with the movement of a bishop on a chess board. A white bishop can only move diagonally; it remains on white squares. The black bishop must move according to similar rules, so that only the transitions shown here are allowed.

Where do these selection rules come from? To explain this, we must consider the spatial wave function of the electron. At first, the spin plays no role here. We begin with the s and p orbitals. The wave function has no azimuthal nodal line in the s orbital; it has one in the p orbital. Here, we represent the three spatial orientation possibilities of the nodal line as one nodal line that rotates anti-clockwise, one that rotates clockwise, and one horizontal nodal line.

The wave function of the photon has one azimuthal nodal line. The electron “inherits” this line, so to speak. This is because this transition creates vertically polarized light, and the p orbital becomes an s orbital with less energy and with one azimuthal nodal line less.

From the anti-clockwise vibration in the p orbital, the photon inherits the anti-clockwise nodal line. This creates a left-circularly polarized photon. The electron can choose an s orbital with less energy, and with one azimuthal nodal line less.

From the clockwise vibration in the p orbital, the photon inherits the clockwise nodal line. The result is a right-circularly polarized photon. The electron can choose an s orbital with less energy, and with one azimuthal nodal line less.

A single photon is polarized, that is, it has a nodal line. When the electron has no nodal line initially, and it also has none afterwards, a photon won’t be created. This is because it must get its nodal line from somewhere.

And yet, an electron can emit radiation starting from the 3s orbital. We have seen a similar situation in U1 station 11 slide 6. A rotationally symmetric wave function without a nodal line can be understood as a superposition of orbitals that rotate clockwise and anti-clockwise. If an electron emits a right-hand polarized photon, it will get a p orbital rotating anti-clockwise.

If an electron emits a left-hand polarized photon, it will get a p orbital rotating clockwise.

We have thus explained the significance of the selection rules. The bishop moves along the diagonal, because an azimuthal nodal line can only be transferred to the photon when orbitals are changed. It is precisely for this reason that an excited electron in the 2s state is metastable. A photon cannot be emitted in the transition to the 1s orbital. The white bishop stays on the white square.

This is exactly what happened with the excited helium atoms. A helium atom can return back to its ground state without emitting radiation only when a so-called “collision of the second kind” takes place. It means the helium atom must transfer its excitation energy to the neon atom.

The many technical applications of gas lasers would be unthinkable without this subtle interplay of nodal lines between electrons and photons.