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Q029 · Slowing and trapping atoms with light

Laser Cooling & MOT

Can light slow an atom down and also hold it in place? It can do both. Tune the beams slightly below resonance, and the Doppler shift makes a moving atom absorb more from the beam it is heading into, so its motion is damped. A magnetic field gradient adds a Zeeman shift that grows away from the center, pushing stray atoms back. The random photon recoils also heat the cloud.

Compare three ways light cools atoms: Doppler cooling, Sisyphus cooling by optical pumping, and coherent dark states in momentum. Release a cloud, take camera frames with finite pixels, and work out the velocity spread, starting size and drift from the detected photons.

Interactive modelLaser Cooling & MOT
Camera frames—\text{—}
Inferred kinetic variance—\text{—}
Predict the photograph

01 / Before acquisition

Predict first, then record.

Acquire frames to compare this prediction with the observed count profile.

An ideal beam splitter routes the axial cooling input away from the camera; detected-photon gain includes collection losses. Stage dots show the release ensemble. Cooling light is off during flight; the selected later image is shown below.

Save, restore and export

05 / Save an unfinished run

Pause, save, restore, continue.

Up to six snapshots retain prepared atoms, partial frames, random generator state and the next flight time. Restoring and resuming reproduces the remaining photon records exactly. CSV labels model-density rows separately and never uses model velocities as observed camera data.

Physical models, calibration and primary sources

Coordinates: counterpropagating cooling waves are along horizontal x. The camera views the x–y plane along z. All cooling fields are off during ballistic expansion; a uniform release kick changes the center without changing the kinetic variance. Gravity, collisions, optical depth, photon recoil during imaging, loss between frames and saturation of the camera are omitted. The imaging is explicitly ideal and nondestructive. The finite field selects detected photons; edge contamination above 2.5 percent withholds a temperature rather than silently treating lost tails as cold atoms.

U±(x)=U02[1±sin⁡(2kx)]U_\pm(x)=\frac{U_0}{2}[1\pm\sin(2kx)]
γ±→∓=γp2[1±sin⁡(2kx)]\gamma_{\pm\to\mp}=\frac{\gamma_p}{2}[1\pm\sin(2kx)]

Sisyphus mode propagates classical positions and momenta on two periodic ground-state potentials. Position-dependent optical pumping switches the state and applies recoil. The excited manifold is eliminated; the rates are a bounded qualitative reduction of the low-saturation lin-perpendicular-lin mechanism, with rubidium mass and recoil scale, not a fitted rubidium hyperfine calculation. No imposed cooling temperature or friction term appears. It cannot justify semiclassical predictions at or below one recoil.

∣Dq⟩=∣g−,q−1⟩−∣g+,q+1⟩2|D_q\rangle=\frac{|g_-,q-1\rangle-|g_+,q+1\rangle}{\sqrt2}
Hq/ℏ=−ωr2(4q+δ2/ωr)σzH_q/\hbar=-\frac{\omega_r}{2}(4q+\delta_2/\omega_r)\sigma_z

The coherent mode evolves positive two-by-two ground density blocks. Kinetic phase mixes dark and bright components away from two-photon resonance; only the bright component scatters. Completely positive no-jump, recoil-jump and dephasing maps preserve trace. Equal ground branching and 21-node isotropic axial emission redistribute momentum. Inter-block coherence and explicit excited-state dynamics are omitted. The grid spans 24 recoil units on either side with 0.1 recoil spacing and reflecting edges; cumulative reflected probability is reported. A narrow central quasi-momentum dark packet produces two physical momentum peaks separated by two recoils. Its narrow width does not make the total kinetic variance subrecoil; a numerical central-bin population is not a historical temperature measurement.

The Doppler and MOT protocols use the model of six independent traveling waves with recoil, a common saturation denominator and ideal Zeeman branches. That model leaves out multilevel ground structure and realistic loading. Each protocol is a separate physical reduction; the set is not a continuous temperature slider.

Dalibard & Cohen-Tannoudji (1989) · polarization-gradient models
Aspect et al. (1988) · velocity-selective coherent population trapping
Aspect et al. (1989) · theoretical VSCPT analysis
Barker et al. · time-of-flight imaging and temperature fits
Steck · rubidium-87 D-line constants

Physics tutorial

Laser cooling, dark states and the camera

BackgroundThree cooling mechanisms trade momentum between light and atoms in different ways. The camera, with its finite field and pixels, sees only photons from the expanding cloud; it does not read the simulated velocities.

Why it mattersDraw a conclusion from what the camera frames show, then test it by changing the cooling mechanism or the calibration.

Start with the essentials

Focus question
Can one camera tell apart real cooling, a drifting cloud, a coherent dark packet and velocity tails lost from view?
One-sentence intuition
Doppler damping, Sisyphus dissipation driven by optical pumping and coherent population trapping each need a different model of the atomic states. A smaller image on the camera is not enough to prove any one of them.

Core mathematical model

Photon counts in each camera frame

nij∼Poisson⁡(b+g∑aPij[ra(t)])n_{ij}\sim\operatorname{Poisson}(b+g\sum_a P_{ij}[\mathbf r_a(t)])

Each square pixel collects light over its own area, blurred by a calibrated Gaussian point-spread function. The same frozen set of released atoms flies ballistically to every exposure time.

Cloud width over time, with the correlation term

σx2(t)=σx,02+2Cov⁡(x,vx)t+σvx2t2\sigma_x^2(t)=\sigma_{x,0}^2+2\operatorname{Cov}(x,v_x)t+\sigma_{v_x}^2t^2

The initial size, the position–velocity correlation and the velocity variance are fitted to the corrected moments of the frames. The mean position gives the drift separately.

Temperature from the fitted velocity spread

Tx=mσvx2kBT_x=\frac{m\sigma_{v_x}^2}{k_B}

This temperature uses only a second moment and does not assume a thermal Maxwell distribution. If the field of view clips the cloud noticeably or the signal is weak, no estimate is given.

A coherent superposition that does not absorb

∣D0⟩=(∣g−,−1⟩−∣g+,1⟩)/2|D_0\rangle=(|g_-,-1\rangle-|g_+,1\rangle)/\sqrt2

On resonance, the relative phase of the two components cancels their coupling to the light. Dephasing destroys this cancellation. The two components carry opposite recoil momenta.

Common difficulties

One image cannot give a temperature

Typical misconceptionIf the spot on the camera is smaller, the atoms must be colder.

Better mental modelThe initial size, drift, position–velocity correlations, point spread and the camera's finite acceptance all change the image too. You need images at several calibrated flight times.

Three separate reduced models

Typical misconceptionThe three protocols are the same rubidium model, just aimed at a lower target temperature.

Better mental modelRecoil from traveling waves, optical pumping among many levels and coherent momentum blocks each follow their own evolution law. No final temperature is set in advance.

Run the experiment

  1. 01

    Predict and image

    Choose MOT and acquire five frames. Then add a uniform kick at release and compare the fitted width and drift.

    What to observe: The center moves, but that does not mean the velocity variance grew.
  2. 02

    Remove the step that takes energy away

    Save a Sisyphus run, then set the optical pumping to zero. At the same exposure, compare the jumps in potential energy and the camera images.

    What to observe: When atoms switch internal state at different positions, potential energy is removed. A static potential by itself does not give the same cooling cycle.
  3. 03

    Destroy the phase

    Record a run of the coherent protocol, then increase the ground-state dephasing. Look at the populations of both ground-state momentum components and at the negative coherence that forms the dark packet.

    What to observe: The narrowing of the dark packet in quasi-momentum is not the same as the variance of the total real momentum. The model does not reproduce any historical helium temperature.
  4. 04

    Try to fool the camera

    Reduce the field width or the photon gain. Pause partway through a frame sequence, then save, restore and resume.

    What to observe: When the images cannot support an estimate, no temperature is given. Restoring the saved random state reproduces the later photon records exactly.

Related experiments and articles

Quantum evidence · Reading path

Clocks, traps and single-quantum control

Articles on this path that use this experiment, followed by the other experiments they suggest.

  1. ArticleWhen sodium atoms came out colder than expected
  2. ArticleKeeping a slowing atomic beam in tune with one laser
  3. LabZeeman Atomic-beam SlowerAcquire an exit velocity spectrum in a synthetic slower
  4. ArticleHow six laser beams slowed Chu’s atoms
  5. ArticleReading a cold-atom thermometer from the flight of the cloud
  6. ArticleHow an atom loses energy climbing hills made of light
  7. LabOptical Pumping and RelaxationPump atoms between states with light, then watch them relax
  8. ArticleHow helium atoms escaped the light and formed two narrow peaks
  9. LabSTIRAP Dark-State TransferMove an atom through a dark state with STIRAP
  10. LabQuantum State & Born MeasurementCompare a coherent superposition with a plain mixture

Probes and measurement · Reading path

Molecules, forces and ultrafast dynamics

Articles on this path that use this experiment, followed by the other experiments they suggest.

  1. ArticleOptical tweezers: from holding a bead to measuring force
  2. LabOptical Tweezers: Brownian CalibrationCalibrate a bead trap from thermal motion
  3. LabCompound Optics WorkbenchWiden a laser beam with two lenses
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