Feshbach Resonance: Tuning Atomic Interactions

Magnetic Field

Field B 140.0 G

Resonance width Δ 25.0 G

Background length a_bg -1600 a₀

Gas temperature 1.0×

Live Readouts

Regime: weakly interacting

Scattering length a(B)

−1600 a₀

Cross-section σ = 4πa²

3.2×10⁷ a₀²

Bound molecules formed

0 / 60 pairs

How it works

Near a magnetic Feshbach resonance, an open scattering channel is coupled to a closed channel that supports a bound molecular state. Tuning the field B shifts that bound state across the open-channel threshold, and the s-wave scattering length follows:

a(B) = a_bg · ( 1 − Δ / (B − B₀) )
σ(B) = 4π a(B)²           (low-energy s-wave cross-section)
E_b  ≈ ħ² / (m a²)         (shallow-molecule binding energy, a > 0)

B₀ (fixed at 155 G here) is the pole of the resonance, Δ its width, and a_bg the off-resonance background scattering length. As B → B₀, a(B) diverges — the "unitarity" regime where the cross-section saturates at the largest value quantum mechanics allows for a given collision energy.

a > 0 — a shallow two-body bound state exists. Atom pairs that collide slowly enough within range capture into a molecule (gold, tethered pair) with binding energy E_b ∝ 1/a².
a < 0 — attractive interactions with no two-body bound state (the BCS side); atoms pull toward each other on approach but always separate again.
|a| large — near resonance, the effective interaction range and σ grow sharply; visualised here as a bigger capture radius and a wider glow around each atom.
Sweep button — ramps B slowly across B₀ so you can watch the gas cross from bound molecules, through the unitarity peak, to a purely repulsive/attractive atomic gas.

Real-world relevance: this exact knob — an external magnetic field near a Feshbach resonance — is how labs dial ultracold-atom interactions from strongly attractive to strongly repulsive, letting them build BCS-BEC crossover superfluids and Efimov trimers, and tune the Bose/Fermi-Hubbard models used in optical-lattice quantum simulation.

Free atom Bound molecule pair

B − B₀ = −15.0 G

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