---
title: "Subrecoil cooling: two narrow peaks are not zero motion"
description: "Which width becomes small when coherent population trapping selects a dark velocity class?"
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language: "en"
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last_modified: "2026-10-18"
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[Quantum physics: reading the evidence](https://sandboxphysics.com/stories/quantum-evidence/)

Nobel A · Evidence and control

# Subrecoil cooling: two narrow peaks are not zero motion

Sandbox Physics · 2026-10-18

Which width becomes small when coherent population trapping selects a dark velocity class?

## Begin with the measured profile

Aspect and colleagues reported one-dimensional transverse cooling of a metastable helium beam in 1988. A downstream detector scan resolved two narrow velocity peaks on a broader background. The reported temperature scale near 2 microkelvin characterized the narrow structure, not thermal equilibrium of every direction of the beam.

This distinction changes the reading question. Ask for the peak centers, each peak’s width, the cooled fraction and the detector resolution separately. A narrow component can be scientifically decisive even when a wide background remains and the beam still has substantial forward motion.

Read the evidence: A. Aspect et al. (1988), Laser Cooling below the One-Photon Recoil Energy by Velocity-Selective Coherent Population Trapping, PRL 61, 826–829

## Keep internal state and momentum together

Two counterpropagating optical couplings can connect distinct ground sublevels to one excited state while transferring opposite momenta. Choose the phases so that the two absorption amplitudes are equal and positive. For the zero-centered momentum family, the antisymmetric combination below then has canceling excitation amplitudes.

The ground labels identify internal states; the second entries are actual momenta along the cooling axis. The wave number is that of the light. The two components have equal kinetic energies, so the ideal dark superposition can remain stationary in the rotating description when other splittings and decoherence are absent.

$$
|D\rangle=\frac{|g_1,-\hbar k\rangle-|g_2,+\hbar k\rangle}{\sqrt{2}}
$$

Read the evidence: A. Aspect et al. (1988), Laser Cooling below the One-Photon Recoil Energy by Velocity-Selective Coherent Population Trapping, PRL 61, 826–829

## Darkness is velocity selective

A shifted momentum family gives the two components unequal kinetic energies. Their relative phase then evolves, spoiling the cancellation that made the zero-centered family dark. Spontaneous emission redistributes population between families, while sufficiently dark components scatter less and remain longer.

This is accumulation through selective scattering and residence time, rather than every atom experiencing a smooth friction force toward rest. Longer coherent interaction can select a narrower range, but magnetic splittings, phase instability, finite transit time and imperfect level isolation can limit that protection.

Read the evidence: 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

## Separate the peak width from the total variance

Even the ideal displayed state has zero mean momentum but nonzero momentum variance. Half the outcomes lie at each of two opposite recoil momenta. Measuring zero average motion would therefore miss the kinetic energy stored in the separation of those outcomes.

For an invented equal-weight mixture of peaks centered at opposite recoil momenta, give each peak a standard deviation equal to one tenth of a recoil momentum. The total variance is 1.01 times the squared recoil momentum: one part comes from the centers, and 0.01 from the within-peak widths. Extremely narrow peaks do not remove the first part.

Read the evidence: A. Aspect et al. (1988), Laser Cooling below the One-Photon Recoil Energy by Velocity-Selective Coherent Population Trapping, PRL 61, 826–829

## A momentum histogram does not measure every coherence

The paper compared polarization configurations and also disturbed the beam overlap, producing changes in the two-peak pattern. Such interventions test the proposed mechanism more specifically than one cold-looking profile. Its calculated distribution and detector scan must still be identified as different kinds of evidence.

A coherent superposition and an incoherent mixture can share the same momentum populations. The histogram alone cannot distinguish them; phase-sensitive recombination would ask an additional question. Likewise, a narrow fitted peak does not establish the temperature of a whole nonthermal distribution.

Read the evidence: A. Aspect et al. (1988), Laser Cooling below the One-Photon Recoil Energy by Velocity-Selective Coherent Population Trapping, PRL 61, 826–829

## Use the models for separate comparisons

The qubit Lab helps compare coherence and mixtures of internal states. It does not include the linked internal and translational momentum families of this helium experiment. The existing cooling Lab instead provides a Doppler force and diffusion comparison under its stated assumptions.

Carry three separate statements between them: which states stop absorbing, which measured momentum features narrow, and which energy or temperature definition is being reported. Keeping those statements distinct makes the subrecoil result more informative without turning it into a claim of motionless atoms.

Read the evidence: 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

## Continue with the models

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

- [Compare coherence with a population mixture](https://sandboxphysics.com/labs/qubit-state/)
- [Contrast with Doppler cooling](https://sandboxphysics.com/labs/laser-cooling-magneto-optical-trap/)

## Sources and reading notes

We read the 1988 Aspect et al. PRL paper through the APS PDF text, including the momentum families and Figures 2–4. Direct local PDF retrieval returned 403. The dark-state sign below uses equal positive optical couplings by a basis-phase convention. Our two-peak variance example is not a reconstruction of the helium profile.

1. [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)
2. [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)

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