Polarization supplies a spatial structure
Two counterpropagating beams with equal intensity and perpendicular linear polarizations can have constant total intensity while their combined polarization changes with position. An atom with several ground-state magnetic sublevels can therefore see different position-dependent light shifts and pumping probabilities.
Dalibard and Cohen-Tannoudji’s 1989 treatment distinguished this configuration from counterpropagating opposite circular polarizations. The mechanisms are not interchangeable merely because both can cool below the Doppler benchmark. Here the question is the energy cycle associated with spatially modulated sublevel potentials.
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
Build a deliberately simple pair of hills
Let the positive energy scale be the height of each hill, the wave number refer to the light, and position increase along the beam axis. The two potentials below have complementary minima and maxima. They illustrate two state-dependent landscapes; they are not the exact atomic potentials in the published calculation.
Choose an atom initially at a minimum of the first potential. It moves to that potential’s maximum while remaining in the same internal sublevel. With no scattering during this leg, conservation of mechanical energy says the kinetic energy lost equals the potential energy gained.
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 reset prevents the energy coming back
If the atom simply rolls down the same hill, it recovers its kinetic energy. Cooling requires an irreversible part of the cycle. Optical pumping can change the internal sublevel near a crest, placing the atom near the bottom of the other potential; exchanged light carries energy away.
In our idealized cycle, one quarter-wavelength climb costs one hill height in kinetic energy, followed by a state change at fixed position. Repeating two such legs removes twice that height over half a wavelength before recoil heating is counted. Real jumps have distributed locations, branching probabilities and momentum kicks.
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
A delay matters more than a decorative hill
A static landscape alone cannot explain sustained cooling. The state populations take time to respond as an atom moves through changing polarization. Their lag creates a statistical preference for energy-losing cycles rather than equal numbers of cooling and heating cycles.
This also explains why lowering intensity cannot be extrapolated into unlimited cooling. Shallower light shifts and slower optical pumping change both the energy removed and the velocity range that can participate. A particle traversing many polarization periods before its state changes does not follow our crest-reset cartoon.
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
Diffusion closes the ledger
Spontaneous emission makes the reset dissipative but also gives random recoil. An energy ledger must retain both the systematic loss associated with state-dependent motion and the random growth of momentum variance. Counting only uphill trajectories selects the favorable part of the process.
Near a single-photon recoil scale, continuous classical momentum and simple diffusion approximations require re-examination. Our pair of hills specifies neither an equilibrium distribution nor a final temperature. A measured narrow velocity feature also needs its own thermometry and resolution analysis.
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
Ask which mechanism the Lab contains
The existing cooling Lab provides a useful Doppler force and diffusion comparison. The pumping Lab resolves a different population-preparation problem. Linking them does not combine them into a quantitative polarization-gradient cooling simulation.
To test the hill mechanism numerically would require consistent sublevel light shifts, position-dependent transitions, recoil and motion. Read the published model against that checklist of quantities, then compare the separate subrecoil article: a velocity-selective dark state protects a narrow class by a different route.
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