Real atoms have multiple internal quantum states. Optical pumping and spatially varying electromagnetic polarization can remove kinetic energy by additional mechanisms, producing sub-Doppler cooling below the ideal Doppler cooling limit. In polarization-gradient cooling, state-dependent energy shifts from the Stark effect and delayed optical pumping make atoms repeatedly climb potential energy hills. This mechanism needs the internal-state structure omitted by the independent-beam two-level system above. [ref]
Nobel Lecture: Laser cooling and trapping of neutral atoms by William D. Phillips. William D. Phillips, Nobel Lecture: Laser cooling and trapping of neutral atoms, pp. 733–734 and Fig. 18: multilevel polarization-gradient cooling
.William D. Phillips's team tested unexpectedly cold sodium molasses with time-of-flight atom detection. A probe above the cloud initially saw no atoms; deliberately heating them verified that the detector worked. Moving the probe below the cloud produced arrival signals consistent with temperatures below the Doppler cooling limit. Independent release/recapture checks used sharply apertured beams and included gravity; uncertain cloud and probe geometry still limited the inferred temperature. These controls tested the thermometer as well as the cooling theory. [ref]
Nobel Lecture: Laser cooling and trapping of neutral atoms by William D. Phillips. William D. Phillips, Nobel Lecture: Laser cooling and trapping of neutral atoms, pp. 731–732, Figs. 15–16: probe reversal, deliberate heating, geometric uncertainties and independent thermometry
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