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

d
dt ρgg = iΩ
2 ( ˜ρge − ˜ρeg) + Γρee
d
dt ρee = − iΩ
2 ( ˜ρge − ˜ρeg) − Γρee
(4.1)
(4.2)
d
dt ρge = − iΩ
2 (ρee − ρgg) − ( Γ
2 + i∆) ˜ρge, (4.3)
where ρij are the matrix elements of the density operator, Ω = µ·E
is the resonant
Rabi frequency, µ the dipole operator, E the electric field, Γ the natural decay rate of the
excited state e and ˜ρge ≡ ρgeexp(−i∆t), ˜ρge = ˜ρ ∗ eg. The total steady-state photon scattering
rate is then given by Γρee [20]
Rsc = Γ
2
I/Isat
1 + (2 ∆
Γ )2 + I
Isat
, (4.4)
where I
Isat = 2
Ω
2
Γ . This approximation is valid if the detuning ∆ from the optical
resonance is large, ∆ ≫ Γ.
An additional light field causing an AC-Stark shift, corresponding to a detuning
from resonance, should therefore decrease the scattering rate and consequently the
amount of scattered light. Fig. 4.1 shows the scattering rate as a function of the
detuning ∆ for several values of I . The natural decay rate Γ is taken to be 2π·9.795MHz,
Isat
corresponding to the Sodium D2-line, which we use to trap and cool the atoms.
4.2 Experimental Setup
4.2.1 Oven and Zeeman-slower
Because of the low vapor pressure of Sodium (Pv = 2.2 · 10 −11 torr [20]) it is necessary to
heat the Sodium in an oven to about 500K. Our oven is not recirculating and therefore
it has to be refilled after a few hundred hours of operation [21].
In order to be able to trap the atoms in a magneto-optical trap (MOT) (see section
4.2.2) the atoms in the effusive beam have to be decelerated to a few meters per second.
19