= Sub-Doppler cooling
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. <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]{ref}.
<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. <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]{ref}.
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