Question

How to obtain a vector relation for the Rabi frequency?

Answer 1

In this paper by Golovach et al.: http://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.165319 there is the following equation for spin evolution:

⟨S˙⟩=(ωz+δω(t))×⟨S⟩,

where ωz=gμBBn/ℏ. When they consider a general driving field:

δω(t)=δωasin(ωact)+δωbcos(ωact)

they obtain the following expression for the Rabi frequency:

ωR(t)=12(δωa×n−[δωb×n]×n)

by using the rotating wave approximation. This last equation is what I really want to understand. The case for n=k is quite easy to prove but how do we obtain the relation for n at an arbitrary direction?

quantum-me

Answer 2

In rabi season it is usually taken as a main crop or rabi frequency.