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Short introduction to Doppler cooling

Need three ingredients to understand Doppler cooling:
1. Three elementary processes of atom-light interaction:

\includegraphics[height=3.5cm,width=14cm,angle=0]{elprocess.eps}

2. Momentum conservation

\includegraphics[height=1.5cm,width=10cm,angle=0]{momcons.eps}

v typically a few cm/s 3. Doppler shift

\includegraphics[height=1.5cm,width=10cm,angle=0]{dopplersh.eps}

$\omega_{A}=\omega\pm \vec{k}\cdot\vec{v}$






Construct velocity-dependent dissipative force on atom with two red detuned laser beams:

\includegraphics[height=10cm,width=3cm,angle=-90]{cool.eps}

Red detuned
$\Rightarrow$ absorption preferentially from laser beam opposing velocity (Doppler shift towards resonance)
$\Rightarrow$ slows atom down towards v=0 if de-excitation mainly due to isotropic spontaneous emission (low intensity limit)

\includegraphics[height=12cm,width=6cm,angle=90]{force.ps}

($\Gamma$=natural line width)
Force
$\propto (-v) \Rightarrow$ energy dissipation


Ultimate limit for Doppler cooling
Atom cannot be cooled to v=0 because of random recoil from spontaneous emission (random walk in momentum space with increments
$\hbar k$)
$\Rightarrow$ heating rate associated with recoil

Landmark energy: Recoil energy
$E_{R}=\frac{\hbar^{2}k^{2}}{2m}$

ER corresponds to temperature $\frac{1}{2}kT=\frac{\hbar^{2}k^{2}}{2m}$ ( $\approx 20\mu K$ for Na)

Note: Omitted discussion of so-called Sub-doppler cooling

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Next: Two sub-recoil cooling methods Up: No Title Previous: No Title
Birger Bergersen
1998-12-12