Magneto-Optical Trap: Catch Atoms with Light, Then Let Them Fly
Almost every cold-atom experiment starts the same way. A glass cell holds a thin vapour of rubidium at room temperature, with atoms flying around at about 300 m/s. Six laser beams and a pair of magnetic coils catch a small fraction of them, slow them to a few centimetres per second and hold them in a glowing ball about a millimetre across, at a few hundred microkelvin. This is a magneto-optical trap, or MOT. It was first demonstrated in 1987 by Eric Raab, Mara Prentiss, Alex Cable, Steven Chu and David Pritchard, and it is the first step on the way to a Bose-Einstein condensate.
The simulator below follows a couple of thousand rubidium-87 atoms one by one, in three dimensions. You can tune the lasers and the magnetic field, load the trap from the vapour, switch the beams off and watch the atoms fly apart and fall, then switch them back on and see how many you catch again.
How light can slow an atom
Every photon carries momentum ħk. When an atom absorbs a photon from a laser beam it gets a small kick along the beam, about 6 mm/s for rubidium. It then re-emits the photon in a random direction, so the recoil from emission averages out. A rubidium atom can repeat this cycle millions of times per second, so the small kicks add up to a force about ten thousand times stronger than gravity.
The trick is to make the force depend on how the atom moves. The lasers are tuned slightly below the atomic resonance (red detuned). An atom moving toward a beam sees its light Doppler-shifted up, closer to resonance, so it scatters more photons from the beam it is running into than from the beam behind it. The net force always opposes the motion, like moving through syrup. Six beams along three axes give optical molasses, a friction force in every direction.
Friction cools but does not hold atoms in place. For that, two coils with opposite currents make a magnetic field that is zero at the center and grows in every direction. Through the Zeeman effect, the field shifts the atomic resonance more the further an atom is from the center. With the right circular polarisation in each beam, an atom that has wandered off scatters more light from the beam pushing it back. The result is a restoring force on top of the friction: a damped spring that holds the cloud at the field zero.
F = ħk (Γ/2) [ s / (1 + s_tot + 4δ₊²/Γ²) − s / (1 + s_tot + 4δ₋²/Γ²) ], δ± = δ ∓ kv ∓ μ_B B′x/ħ
Here δ is the laser detuning, Γ = 2π × 6.07 MHz is the natural linewidth of the rubidium D2 line, s is the beam intensity in units of the saturation intensity (1.67 mW/cm²) and B′ is the field gradient. The simulator applies this force along each of the three axes.
How to use the simulator
- Watch the trap. It starts loaded. The picture is a side view with gravity pointing down. Atoms glow in proportion to how many photons they scatter, the way a MOT looks through a camera.
- Turn the beams off. The atoms fly out in all directions and fall. Their spread of speeds is the temperature, and the “Flight and recapture” numbers measure it from the expansion, the same way experiments do. Turn the beams back on to catch whatever is still close.
- Release and recapture. This switches the beams off for the dark time you set, back on, and counts how many atoms are caught again. Repeat it with different dark times to build up a curve. The dashed line is a ballistic cloud at the measured temperature, with the capture radius fitted to your points.
- Load from the vapour. Empty the trap and watch atoms arrive from the walls of the cell. Slow ones are stopped and collect at the center; fast ones fly straight through. Switch to the wide view to see the whole beam region and the coils.
What to look for
1. There is a best detuning. Move the detuning toward zero and the cloud gets hotter: the friction gets weaker, while the random kicks from spontaneous emission do not. Move it far from resonance and it also gets hotter, because the atoms hardly scatter any light. Doppler theory says the coldest temperature is reached at δ = −Γ/2 with weak beams: the Doppler limit, kBT = ħΓ/2, which is 146 µK for rubidium. The preset “Weak beams, close to the Doppler limit” gets within a factor of two of it.
2. Temperature is a balance. The histogram of speeds is always a Gaussian. Its width is set by two competing effects: the friction that slows atoms down, and the random recoil from every emitted photon that heats them up. The dashed curve is the Doppler theory prediction for the current settings, and the simulation lands on it.
3. The field holds the atoms; the light cools them. Turn the field off and the atoms stay just as cold, but nothing holds them any more. They wander off in a slow random walk, still glowing, and gently sink under gravity. This is optical molasses. Turn the field back on and they are pulled back to the center.
4. The cloud is flatter vertically. The field gradient along the coil axis is twice as steep as in the horizontal plane, so the trap is stiffer vertically and the cloud is squeezed into a flattened ball. Gravity also pulls it down by a few micrometres, which the simulator reports next to the theoretical sag, g/ω².
5. The wrong side of resonance. Set the detuning above zero (blue detuned). Now atoms scatter more light from the beam behind them, so the light speeds them up instead of slowing them, and the cloud blows apart within milliseconds. Use the slowest speed to watch it.
The numbers
| Quantity | Formula | What it tells you |
|---|---|---|
| Doppler temperature | kBT = (ħΓ/8) (1 + s_tot + 4δ²/Γ²) / |δ/Γ| | Where heating from random recoils balances friction. Lowest, 146 µK, at δ = −Γ/2 and low intensity. |
| Friction coefficient | β = −8ħk² s (δ/Γ) / (1 + s_tot + 4δ²/Γ²)² | How strongly motion is damped. m/β is the time it takes, typically a fraction of a millisecond. |
| Spring constant | κ = β μ_B B′ / ħk | The restoring force per unit distance. With the mass it gives a trap frequency of a few hundred hertz. |
| Cloud size | σ = √(kBT / κ) | The rms radius of the trapped cloud: a few hundred micrometres. |
| Expansion in the dark | σ(t)² = σ₀² + (kBT/m) t² | How time-of-flight measures temperature: the cloud’s width grows at the thermal speed. |
How the simulation works
Each atom has a position and velocity in 3D, updated every 10 microseconds. For each of the six beams the simulator works out the detuning the atom sees, including its Doppler shift and its Zeeman shift, and from that the scattering rate. The beams have Gaussian profiles, so atoms far from the center feel weaker light. The average force is ħk times the difference in scattering rates for each pair of beams. The randomness of absorption and emission is added as random kicks with the matching size: an atom scattering N photons gets a random walk of N steps of ħk. Gravity acts on every atom all the time.
Nothing here is fitted to the expected answer. The temperature, the cloud size, the trap frequency and the gravitational sag all come out of the random walk of individual atoms, and they match the Doppler-theory formulas in the table to within a few percent. With the beams off, the expansion follows σ(t)² = σ₀² + (kBT/m) t² exactly.
What the model leaves out
- Sub-Doppler cooling. Real rubidium molasses gets much colder than the Doppler limit, down to around 10 µK. In 1988, Paul Lett and colleagues in Bill Phillips’s group used release and recapture to measure sodium molasses far below the Doppler limit, to everyone’s surprise. The explanation, polarisation-gradient cooling by Jean Dalibard and Claude Cohen-Tannoudji, needs the atom’s multiple ground-state sublevels, which this two-level model does not have. Chu, Cohen-Tannoudji and Phillips shared the 1997 Nobel Prize in Physics for laser cooling and trapping.
- Atoms do not affect each other. In a dense MOT, atoms re-absorb light scattered by their neighbours, which pushes them apart and makes real MOTs larger than the simple formula predicts. Real MOTs also hold around a hundred million atoms, not a few thousand.
- Simplified field and loading. Each beam sees the field component along its own axis, the standard textbook approximation. Only the slowest atoms of the vapour are launched, because faster ones are never caught, so loading here is much quicker than the second or so a real MOT takes to fill. There is no repump laser and no loss from collisions.
Where stable optics comes in
A MOT only works when all six beams cross at the zero of the magnetic field and their intensities are balanced. If a mirror drifts and a beam walks off, the forces no longer balance at the center: the cloud shifts, changes shape, loads fewer atoms, and every later step of the experiment inherits the problem. Cold-atom labs often realign their MOT beams after every temperature change in the room. Mounts that hold their angle through thermal cycles remove that chore.
That is what Physiverse mounts are built for: monolithic flexure mounts that hold their alignment through temperature changes and long experiments. See the product line.