Laser cooling

Why does shining light on a cloud of atoms — pouring energy into it — leave the cloud colder than any refrigerator can make it?

Point six laser beams at a cloud of sodium vapour and within a millisecond it is colder than anything a dilution refrigerator can reach — a fraction of a thousandth of a degree above absolute zero. Yet lasers are how we cut steel. Energy is delivered continuously, and the result is cold.

The contradiction dissolves partly on inspecting the word "temperature". A cloud's temperature is not how much energy passes through it; it is how widely its atoms' velocities are spread. But that only relocates the puzzle: how does an untargeted, uniform beam narrow a distribution of velocities, when it cannot tell one atom from another?

Begin with what one photon can do mechanically. A photon of wavelength λ carries momentum h/λ; for sodium's resonance line at 589 nm — a recalled figure — that is 6.626 × 10⁻³⁴ / 589 × 10⁻⁹ ≈ 1.1 × 10⁻²⁷ kg m/s. A sodium atom has mass 23 × 1.66 × 10⁻²⁷ ≈ 3.8 × 10⁻²⁶ kg, so absorbing one photon changes its speed by about 0.03 m/s — three centimetres per second.

That looks hopeless. A sodium atom at room temperature moves at √(3*kT*/m) = √(3 × 1.38 × 10⁻²³ × 300 / 3.8 × 10⁻²⁶) ≈ 570 m/s, so stopping one takes about 570 / 0.03 ≈ 19,000 photons. But an excited atom re-emits and absorbs again at a rate of order Γ/2, where Γ ≈ 2π × 10 MHz is sodium's natural linewidth — another recalled figure. That is some 3 × 10⁷ absorptions per second, so 19,000 take roughly 0.6 milliseconds, at a deceleration of about 10⁶ m/s². Feeble per photon, overwhelming in aggregate.

But absorption pushes an atom along the beam, whatever it was doing. Why does that cool rather than blow the cloud away? Two observations do the work.

The first is about emission. Absorption is directional — always along the beam — but spontaneous emission is not: the atom radiates in a random direction each time, so those recoils average to nothing. The net force is one photon's momentum per absorption, along the beam.

The second is the Doppler shift, and it is the whole trick. Tune the laser slightly below resonance — red-detuned. An atom at rest scatters weakly; an atom moving towards a beam sees it blue-shifted, closer to resonance, and scatters more; an atom moving away sees it shifted further off and scatters less. Now add a second beam facing the first. Whichever way the atom moves, it preferentially absorbs from the beam it is moving into, so the force always opposes the velocity.

That is the feedback loop, and notice what makes it a loop rather than a push: the atom's own motion selects how hard it is pushed. The light was never aimed at the fast atoms. The fast atoms tune themselves into the light.

How fast must an atom be for the shift to matter? The Doppler shift kv, with k = 2π/λ = 1.07 × 10⁷ per metre, rivals the linewidth when kv ≈ Γ, at v ≈ 6 m/s. So the scheme discriminates over a window a few metres per second wide, which is why atoms must be slowed by other means before six beams can hold them.

And where does the energy go? Each cycle absorbs a red-detuned photon and re-emits, on average, a slightly bluer one at the atom's own resonance. The difference, ħ*kv*, comes out of the atom's kinetic energy and leaves in the scattered light — the light field is not heating the cloud but carrying energy out.

That gives us a test. The claim is that cooling depends on the sign of the detuning, not the intensity. Tune the lasers to the blue side of resonance, changing nothing else, and the feedback should run backwards — an atom moving away now scatters more, so the cloud should heat and explode. It does, immediately. If red- and blue-detuned beam pairs cooled alike, the Doppler mechanism would be dead.

Three refinements, and the last is the important one.

First, on the second law. The cloud's entropy plainly falls — a broad velocity spread has become a narrow one, precisely the sorting Maxwell's demon was forbidden. The escape is that this is not a closed system: the scattered photons leave in every direction and across a spread of frequencies, into an enormous number of empty modes, carrying away far more entropy than the atoms lost. The bill is paid in light.

Second, cooling is not trapping. Six beams make an "optical molasses", but a drag force has no position dependence, so nothing holds the cloud; a magnetic field gradient is what converts molasses into a trap.

Third, and most instructive: this Doppler picture predicts its own floor and gets it wrong. Cooling competes with the random walk of recoils from spontaneous emission, and balancing the two gives a limiting temperature k*B*T = ħΓ/2 — for sodium, 1.055 × 10⁻³⁴ × 6.3 × 10⁷ / (2 × 1.38 × 10⁻²³) ≈ 2.4 × 10⁻⁴ K, about 240 microkelvin. When this was measured in the late 1980s the clouds came out several times colder than the theory's floor. The theory was not refined; it was found to be missing something. Real atoms have several ground-state sublevels, and in the interference pattern of counter-propagating polarized beams an atom repeatedly climbs a potential hill and is optically pumped back to the bottom — Sisyphus cooling, which a two-level model cannot contain. Take the Doppler account as an honest mechanism for how the force arises, and a demonstrably wrong account of how cold you can get.

• How evaporative cooling takes over below the laser-cooling floor to reach Bose-Einstein condensation.

Every term the collection defines is gathered in the glossary.