---
title: "Sisyphus cooling: where the energy leaves the hill"
description: "How can spatially changing polarization remove kinetic energy even when the total light intensity stays constant?"
canonical_url: "https://sandboxphysics.com/stories/quantum-evidence/sisyphus-cooling-polarization-energy/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/quantum-evidence/sisyphus-cooling-polarization-energy/"
last_modified: "2026-10-18"
---

[Quantum physics: reading the evidence](https://sandboxphysics.com/stories/quantum-evidence/)

Nobel A · Evidence and control

# Sisyphus cooling: where the energy leaves the hill

Sandbox Physics · 2026-10-18

How can spatially changing polarization remove kinetic energy even when the total light intensity stays constant?

## 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.

$$
\begin{aligned}U_1(z)&=U_0\sin^2(kz)\\U_2(z)&=U_0\cos^2(kz),\qquad U_0>0\end{aligned}
$$

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, 2023–2045 J. 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, 2023–2045 A. Aspect et al. (1988), Laser Cooling below the One-Photon Recoil Energy by Velocity-Selective Coherent Population Trapping, PRL 61, 826–829 J. 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, 2023–2045 J. Dalibard and C. Cohen-Tannoudji, Laser cooling and trapping of neutral atoms — author-hosted review, Sections 3–5

## Continue with the models

These are existing teaching Labs. Their simulated records are separate from the historical observations discussed above.

- [Compare the declared Doppler force model](https://sandboxphysics.com/labs/laser-cooling-magneto-optical-trap/)
- [Inspect population transfer and relaxation](https://sandboxphysics.com/labs/optical-pumping-relaxation/)

## Sources and reading notes

We consulted Sections 1–3 and the model boundaries of Dalibard and Cohen-Tannoudji’s 1989 JOSA B paper in the author-hosted PDF. The sinusoidal potentials below are a deliberately simplified energy ledger, not its exact Clebsch–Gordan light shifts or a sodium-temperature prediction.

1. [J. Dalibard and C. Cohen-Tannoudji (1989), Laser cooling below the Doppler limit by polarization gradients: simple theoretical models, JOSA B 6, 2023–2045](https://www.phys.ens.psl.eu/~dalibard/publi2/josaB_89.pdf)
2. [A. Aspect et al. (1988), Laser Cooling below the One-Photon Recoil Energy by Velocity-Selective Coherent Population Trapping, PRL 61, 826–829](https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.61.826)
3. [J. Dalibard and C. Cohen-Tannoudji, Laser cooling and trapping of neutral atoms — author-hosted review, Sections 3–5](https://pro.college-de-france.fr/jean.dalibard/publi2/laser_cooling.pdf)

[Blackbody radiation: a whole curve, not one quantum](https://sandboxphysics.com/stories/quantum-evidence/blackbody-spectrum-planck-wien/) [Photoelectric evidence: the voltage is not yet the energy](https://sandboxphysics.com/stories/quantum-evidence/photoelectric-stopping-potential-contact/) [Oil drops: finding a charge unit in falling times](https://sandboxphysics.com/stories/quantum-evidence/millikan-oil-drop-charge-inference/) [Atomic spectra: evidence for states, not photographs of orbits](https://sandboxphysics.com/stories/quantum-evidence/atomic-spectra-stationary-states/) [Franck–Hertz: what a falling current can establish](https://sandboxphysics.com/stories/quantum-evidence/franck-hertz-discrete-excitation/) [Compton scattering: light must balance momentum too](https://sandboxphysics.com/stories/quantum-evidence/compton-scattering-energy-momentum/) [de Broglie: a wavelength for matter, a speed for the packet](https://sandboxphysics.com/stories/quantum-evidence/de-broglie-matter-waves-phase-packets/) [Matrices and waves: two routes to the same predictions](https://sandboxphysics.com/stories/quantum-evidence/matrix-wave-mechanics-observables/) [Born: how a scattering direction became a probability](https://sandboxphysics.com/stories/quantum-evidence/born-scattering-probability/) [Pauli: count the states before filling the shells](https://sandboxphysics.com/stories/quantum-evidence/pauli-spectra-exclusion-principle/) [Dirac’s electron: a successful equation with an unfinished story](https://sandboxphysics.com/stories/quantum-evidence/dirac-electron-spin-relativity/) [Zeeman lines: polarization belongs to the evidence](https://sandboxphysics.com/stories/quantum-evidence/zeeman-lines-polarization-lorentz/) [The Stark effect: an electric field changes the spectrum](https://sandboxphysics.com/stories/quantum-evidence/stark-effect-electric-field-spectra/) [Canal rays: moving light does not identify the emitter by itself](https://sandboxphysics.com/stories/quantum-evidence/stark-canal-rays-doppler-emitters/) [Stern–Gerlach: two traces, then a new interpretation](https://sandboxphysics.com/stories/quantum-evidence/stern-gerlach-silver-beam-spin/) [Stern’s proton moment: a small deflection with a large consequence](https://sandboxphysics.com/stories/quantum-evidence/stern-proton-moment-molecular-hydrogen/) [Magnetic resonance: three ways to notice a transition](https://sandboxphysics.com/stories/quantum-evidence/magnetic-resonance-beams-absorption-induction/) [Optical pumping: make a population difference visible](https://sandboxphysics.com/stories/quantum-evidence/optical-pumping-populations-double-resonance/) [The Lamb shift: a missing signal reveals a missing correction](https://sandboxphysics.com/stories/quantum-evidence/lamb-shift-microwave-evidence/) [Kusch and Foley: a small mismatch between magnetic factors](https://sandboxphysics.com/stories/quantum-evidence/kusch-foley-electron-magnetic-moment/) [Mössbauer resonance: recoil has not disappeared](https://sandboxphysics.com/stories/quantum-evidence/mossbauer-recoil-free-resonance/) [Ramsey and ion traps: make time to measure](https://sandboxphysics.com/stories/quantum-evidence/ramsey-ion-traps-measurement/) [Ramsey clocks: a stable fringe can carry a phase bias](https://sandboxphysics.com/stories/quantum-evidence/ramsey-cavity-phase-frequency-bias/) [Quantum projection noise: better detection still leaves a random count](https://sandboxphysics.com/stories/quantum-evidence/quantum-projection-noise-population-counts/) [Fountain clocks: the density ratio is part of the correction](https://sandboxphysics.com/stories/quantum-evidence/fountain-clock-collision-density-extrapolation/) [Paul’s trap: stability comes from the changing field](https://sandboxphysics.com/stories/quantum-evidence/paul-trap-dynamic-stability-micromotion/) [Dehmelt’s single electron: spin appears as an axial frequency shift](https://sandboxphysics.com/stories/quantum-evidence/dehmelt-single-electron-penning-spin-readout/) [Laser cooling: when the temperature contradicted the model](https://sandboxphysics.com/stories/quantum-evidence/laser-cooling-below-doppler-limit/) [Zeeman slowing: keep a moving atom within reach of the light](https://sandboxphysics.com/stories/quantum-evidence/zeeman-slowing-neutral-atom-beam/) [Chu’s optical molasses: slowing motion while atoms still escape](https://sandboxphysics.com/stories/quantum-evidence/chu-optical-molasses-diffusion-escape/) [Cold-atom thermometry: read the flight, then infer the temperature](https://sandboxphysics.com/stories/quantum-evidence/cold-atom-ballistic-thermometry/) [Subrecoil cooling: two narrow peaks are not zero motion](https://sandboxphysics.com/stories/quantum-evidence/subrecoil-cooling-dark-state-momentum/) [A dark interval from one ion: reading electron shelving](https://sandboxphysics.com/stories/quantum-evidence/electron-shelving-single-ion-jumps/) [Unequal sidebands: how cold is a trapped ion?](https://sandboxphysics.com/stories/quantum-evidence/sideband-asymmetry-ground-state-cooling/) [Quantum logic spectroscopy: let another ion report the answer](https://sandboxphysics.com/stories/quantum-evidence/quantum-logic-spectroscopy-shared-motion/) [Single quantum systems: what survives a measurement?](https://sandboxphysics.com/stories/quantum-evidence/single-quantum-measurement-backaction/) [A cavity cat loses coherence before it loses its energy](https://sandboxphysics.com/stories/quantum-evidence/cavity-cat-coherence-energy-decay/) [Counting stored light: one atom gives a clue](https://sandboxphysics.com/stories/quantum-evidence/qnd-photon-counting-atomic-records/) [Quantum feedback: a target needs more than an estimate](https://sandboxphysics.com/stories/quantum-evidence/quantum-feedback-photon-number-verification/) [Bell tests: correlations need an experimental contract](https://sandboxphysics.com/stories/quantum-evidence/bell-tests-correlations-loopholes/) [Freedman–Clauser: the denominator belongs to the experiment](https://sandboxphysics.com/stories/quantum-evidence/freedman-clauser-coincidence-normalization/) [Aspect’s switches: read the spacetime before the slogan](https://sandboxphysics.com/stories/quantum-evidence/aspect-switching-spacetime-records/) [An event-ready Bell test: count the trials before the wins](https://sandboxphysics.com/stories/quantum-evidence/event-ready-bell-trials-finite-statistics/) [Photon Bell tests: the trials with no clicks still count](https://sandboxphysics.com/stories/quantum-evidence/photon-bell-losses-optical-trials/) [GHZ correlations: four settings, no consistent instruction table](https://sandboxphysics.com/stories/quantum-evidence/ghz-parity-three-photon-records/) [Teleportation: read the conditions before the coincidence](https://sandboxphysics.com/stories/quantum-evidence/quantum-teleportation-conditional-records/) [Heralded photons: the missing coincidences need a denominator](https://sandboxphysics.com/stories/quantum-evidence/heralded-photon-anticorrelation-gates/) [The Hong–Ou–Mandel dip: which alternatives became indistinguishable?](https://sandboxphysics.com/stories/quantum-evidence/hong-ou-mandel-dip-mode-overlap/) [Entanglement swapping: four clicks define the selected pair](https://sandboxphysics.com/stories/quantum-evidence/entanglement-swapping-fourfold-records/) [Delayed-choice swapping: later labels, earlier records](https://sandboxphysics.com/stories/quantum-evidence/delayed-choice-swapping-sorted-records/) [Dense coding: three messages and a resource ledger](https://sandboxphysics.com/stories/quantum-evidence/dense-coding-three-messages-resources/) [Photon tomography: a physical matrix still needs calibrated counts](https://sandboxphysics.com/stories/quantum-evidence/photon-tomography-counts-physical-states/)