Copyright by Kirsten Viering 2006 - Raizen Lab - The University of ...

Chapter 2
Interaction of atoms with
non-resonant light
In this chapter we give a brief introduction into the theory of the interaction of atoms
with non-resonant light. We restrict the treatment to purely monochromatic light and
use a semi-classical expression for the interaction Hamiltonian.
2.1 Time-dependant Schrödinger equation
A dynamical quantum mechanical system is described by the time-dependant Schrödinger-
equation
H|Ψ(r, t)〉 = i ∂
|Ψ(r, t)〉. (2.1)
∂t
For the interaction of atoms with light this equation cannot be solved analytically.
Hence we will use perturbation theory and treat the time-dependant electro-magnetic
light field as a perturbation [6]. We separate the total Hamiltonian H(t) into two terms,
H(t) = H0 +H ′ (t), where H0 is time independant; the explicit time dependance is treated
in H ′ (t) as perturbation to the solution of the stationary Schrödinger-equation.
The solution to the time-independant Schrödinger equation is given by the
3