Doppler Cooling & Optical Molasses

Counter-propagating laser beams create a velocity-dependent viscous force. An atom moving right sees the left beam blue-shifted (closer to resonance) and experiences stronger radiation pressure — slowing it. Nobel Prize 1997.

Parameters

Force: F±(v) = ±ℏkΓ/2 · s/(1+s+(2(δ∓kv)/Γ)²)

Optimal detuning: δ = −Γ/2
gives max damping.

Doppler limit:
T_D = ℏΓ/2k_B ≈ 140 μK (Rb)

Below T_D: sub-Doppler cooling
via polarization gradients (Sisyphus).
RMS velocity:
T_eff: