Dark State Physics
Dark states are a very general property of quantum systems with three levels. These can be arranged energetically in Λ (lambda), V (vee), or ladder configuration, but what's needed is for one of the three (call it |c〉) to be coupled to the other two (call them |a〉 and |b〉), but |a〉 and |b〉 are not coupled to each other. The coupling can be by light and/or dc applied fields. The earliest observation was by Orriols and Arimondo in 1976 using resonant light and was subsequently called "coherent population trapping" (CPT). It was later followed by a demonstration in a magnetic field, and an electric field. The optical field case appears in many guises, including electromagnetically induced transparency (EIT), slow light, and laser action without inversion.
The coupling is characterized by off-diagonal elements in the Hamiltonian matrix, and diagonizing it results in new eigenstates given by |±〉 = (|a〉 ± |b〉)/√(2). The optical coupling between one of those superpositions with |c〉 vanishes because of the sign, so that superposition cannot absorb light, and is labelled a "dark state". It's rather surprising that an electric dipole transition will not occur even when resonant light is applied to an otherwise allowed transition, but the cancellation caused by the sign precludes it.
A description of laser cooling to very low temperatures requires inclusion of the atomic motion in the Hamiltonian, and this presents new concepts. In such cases, CPT becomes velocity selective (hence VSCPT) because the states |a〉 and |b〉 are degenerate only for the case of equal and opposite momenta. For these to be each coupled by the same light field to |c〉 as required, the momenta must be ±ℏk. Thus there is a family that comprises a "dark state" whose components have momenta 0 and ±ℏk.
Any deviation from this condition allows excitation, and then spontaneous decay can eventually populate the dark state where atoms necessarily remain trapped. With their momenta fixed, the sample of atoms becomes very cold. Our VSCPT experiments explored various ramifications of this phenomenon.