Equal brightness can hide a changing landscape
Imagine an atom repeatedly climbing a hill, then finding itself at the foot of another. Each climb takes some of its speed away. The next hill arrives before the atom has recovered that energy. This is the picture behind Sisyphus cooling, named after the figure condemned to push a stone uphill again and again.
The hills are made by light. Two equal beams traveling in opposite directions can maintain constant total intensity and still change how their electric fields turn or vibrate from one position to the next. That pattern is a polarization gradient. An atom with several internal orientations responds differently to different parts of the pattern.
Read the evidence: J. Dalibard and C. Cohen-Tannoudji (1989), Laser cooling below the Doppler limit by polarization gradients: simple theoretical models, JOSA B 6, 2023–2045
The atom has more than one kind of ground state
A ground-state atom can have several magnetic sublevels: states with different projections of its internal angular momentum. Light changes their energies by different amounts. That change is called a light shift. As the polarization varies along the beam, the energy of a given sublevel can rise and fall, forming a sequence of hills and valleys.
A second sublevel can have its valleys near the first one’s crests. The same place is then uphill for one internal state and downhill for another. These landscapes depend on the atomic transition and polarization. A drawing with two alternating hills is a useful simplification of a more detailed atomic calculation.
An atom moving up its current hill trades kinetic energy for potential energy. On a fixed hill it would recover the lost speed when it rolled down. Sustained cooling needs a way to move it onto the other landscape at a favorable moment.
Read the evidence: J. Dalibard and C. Cohen-Tannoudji (1989), Laser cooling below the Doppler limit by polarization gradients: simple theoretical models, JOSA B 6, 2023–2045
Absorbing and emitting light changes the hill
Repeated absorption and spontaneous emission can transfer an atom between sublevels. This redistribution is optical pumping. Its rate depends on position because the polarization depends on position. In the cooling cycle, a transfer near the top of one hill can put the atom near the bottom of the other.
The atom now has another uphill journey ahead of it. Energy transferred to the light during the change is carried away, so successive climbs can keep reducing the atom’s motion. The useful ingredient is the repeated combination of motion on one landscape and a change of internal state.
The populations take time to adjust as atoms cross the changing polarization. That delay favors energy-losing cycles over energy-gaining ones. Atoms moving too quickly cross many hills before their state responds, and the simple climb-and-switch picture becomes less effective.
Read the evidence: J. Dalibard and C. Cohen-Tannoudji (1989), Laser cooling below the Doppler limit by polarization gradients: simple theoretical models, JOSA B 6, 2023–2045
The same photons also give random kicks
Every emitted photon gives a recoil kick. A series of random kicks broadens the distribution of atomic momenta and adds heating. The final motion reflects both the energy lost in the hill-climbing cycles and the heating from these kicks.
Turning down the light makes the hills shallower and changes the pumping time. It also changes which velocities can take part effectively. Near the energy associated with one photon recoil, momentum must be treated quantum mechanically; a classical picture of a particle moving over smooth hills has reached its boundary.
Read the evidence: J. Dalibard and C. Cohen-Tannoudji (1989), Laser cooling below the Doppler limit by polarization gradients: simple theoretical models, JOSA B 6, 2023–2045A. Aspect et al. (1988), Laser Cooling below the One-Photon Recoil Energy by Velocity-Selective Coherent Population Trapping, PRL 61, 826–829J. Dalibard and C. Cohen-Tannoudji, Laser cooling and trapping of neutral atoms — author-hosted review, Sections 3–5
A missing piece in the early cooling theory
Dalibard and Cohen-Tannoudji’s 1989 account showed how polarization gradients and several ground-state sublevels could cool atoms below the simple Doppler prediction. The two-level description had left out both the changing landscapes and the redistribution between them. Those internal details became essential once experiments found unexpectedly low temperatures.
Their treatment distinguished opposing beams with perpendicular linear polarizations from another arrangement with opposite circular polarizations. Both could produce cooling beyond the simple benchmark, through different mechanisms. The uphill energy cycle explains the first arrangement and gives a concrete reason why an atom’s internal state matters to its motion.
Read the evidence: J. Dalibard and C. Cohen-Tannoudji (1989), Laser cooling below the Doppler limit by polarization gradients: simple theoretical models, JOSA B 6, 2023–2045J. Dalibard and C. Cohen-Tannoudji, Laser cooling and trapping of neutral atoms — author-hosted review, Sections 3–5