Editing Dark state (section)

===In theory===
Whether or not we say a transition between a state <math>|1\rangle</math> and a state <math>|2\rangle</math> is allowed often depends on how detailed the model is that we use for the atom-light interaction. From a particular model follow a set of [[selection rules]] that determine which transitions are allowed and which are not. Often these selection rules can be boiled down to conservation of angular momentum (the photon has angular momentum). In most cases we only consider an atom interacting with the electric dipole field of the photon. Then some transitions are not allowed at all, others are only allowed for photons of a certain polarization. 
Consider for example the hydrogen atom. The transition from the state <math>1^2S_{1/2}</math> with ''m<sub>j</sub>=-1/2''  to the state <math>2^2P_{3/2}</math> with ''m<sub>j</sub>=-1/2'' is only allowed for light with polarization along the z axis (quantization axis) of the atom. The state <math>2^2P_{3/2}</math> with ''m<sub>j</sub>=-1/2'' therefore appears dark for light of other polarizations.
Transitions from the ''2S'' level to the ''1S'' level are not allowed at all. The ''2S'' state can not decay to the ground state by emitting a single photon. It can only decay by collisions with other atoms or by emitting multiple photons. Since these events are rare, the atom can remain in this excited state for a very long time, such an excited state is called a [[metastable state]].