Thesis (pdf) - Swinburne University of Technology

Chapter 2: Theoretical Background
The difference in the energies ±¯hΩ due to the applied light field is called the
ac-Stark shift. In the limit of small frequencies ΩR, the Ω in equation (2.8) can
be expanded around ΩR/(4|∆|). This results in energy shifts of ¯hΩ 2 R /(4|∆|)
of the ground and excited state. For negative detunings ∆ < 0 (red detuned
light), the energy of the ground state is lowered by this amount, while the
energy of the excited state is raised by the same amount. In this limit we have
θ → 0, and the dressed states become identical to their respective unperturbed
eigenstates.
Ε
e, n
g, n+1
e, n-1
g, n
h∆
h∆
ω
h 0
Figure 2.1: Energy of the system atom-light without interaction between
the atomic states and the light field (left side) and including the interaction
(“dressed states”, right side). The notation is explained in the text. The cou-
pling increases the energy gap of the doublet states and in case of resonance
will cause an “avoided crossing”.
hΩ
hΩ
1, n
2, n
1, n-1
2, n-1
The Rabi frequency of a light field is a function of its intensity,
Ω 2 R = 1
2 Γ2 · I
17
I0
(2.11)