Six red-detuned laser beams cross at the trap center; an anti-Helmholtz coil pair adds a magnetic field that grows linearly with distance. Together they make the scattering force both velocity-dependent (cooling) and position-dependent (trapping).
1D scattering force on one axis:
F(x,v) = F0 · [ s0/(1+s0+(2Δ₋/Γ)²) − s0/(1+s0+(2Δ₊/Γ)²) ]
Δ± = δ ± k·v ± (μ'B'/ħ)·x (Zeeman-shifted Doppler detuning)
Doppler cooling limit (low intensity, δ = -Γ/2):
T_D = ħΓ / (2·k_B) ≈ 145 μK (Rb-87 D2 line, Γ/2π = 6.07 MHz)
General Doppler temperature:
k_B·T = (ħΓ/4) · (1 + s0 + (2δ/Γ)²) / (2|δ|/Γ)
- Trap ON/OFF — toggles the magnetic gradient and light forces off to show free ballistic expansion, then recaptures the cloud.
- Detuning δ/Γ — how far the laser sits red of atomic resonance; too small gives weak cooling, too large gives weak capture. The sweet spot is near -Γ/2.
- Magnetic gradient B' — sets the trap's spring constant; the coil axis (vertical) gets twice the gradient of the two radial axes, exactly as in a real anti-Helmholtz pair.
- Saturation s₀ — beam intensity relative to the atomic transition's saturation intensity; higher s₀ scatters more photons (faster capture) but also reheats the cloud via photon recoil.
This is the same technique used to load atoms into optical lattices and atomic clocks, and the first cooling stage before evaporative cooling to Bose-Einstein condensation.