| Length form VS. Velocity form |
In approximated treatments of atom-radiation
interaction (ARI), the controversy over whether to use a velocity form
(as obtained from the Coulomb gauge) or a length form (as
obtained from the Multipolar gauge) was resolved by Kobe in 1979 for
identical-particle systems on the basis of gauge invariance. In quantum
coherent control of different-particle systems, it is still an issue of
which form to choose. Although the validity of the Multipolar gauge
treatment with the electric dipole approximation (EDA) is
controversial, it is a proper treatment. This paper shows that, for a
three-atom system, the transition rate between quantum states induced
by the electromagnetic field is the same for the two forms in a
resonant case with a local Hamiltonian. The paper also shows that there
is a transition rate difference between the two gauges for nonlocal
Hamiltonians. Reasons for a preference to the length form over the
velocity form will be explained based on gauge-invariant property of
the approximate molecular Hamiltonian. Link: My documentation on this topic My poster on this topic |
| Multipolar gauge with nonadiabatic terms |
To be able to control the chemical reaction, people
have shown great interest on the atom-radiation interaction. Different
derivations have been established for different gauges applied. On the
basis of gauge invariance property, Donald Kobe advocated the use
of the Multipolar gauge in 1979. However in the special case of
atom-diatiom system with laser, general theory has not been
established. What's more, the nonadiabatic cases have interested a lot
of people. It is also a challengle to include the nonadiabatic terms in
the atom-radiation interaction. Link: My documentation on this topic |