Q029 · Recoil / cooling / confinement

Laser Cooling & MOT

Prepare a displaced warm cloud. Turn on six cooling beams, record individual final positions and velocities, then switch off the coils. Separate a colder cloud from a confined cloud.

Recorded particles $\text{—}$

Recorded temperature $\text{—}$

01 / FOLLOW THE ENERGY

Slower does not always mean trapped.

Record the displaced cloud. Save, switch off the coils, and repeat. Compare the velocity spread and the cloud center separately.

Six counterpropagating beams · opposing-current coils · dots are recorded atoms, not a camera image · uniform schematic magnification · beam colors distinguish direction

Exposure duration

t/\mathrm{ms}

4

Each scan time uses a newly prepared cloud of 64 atoms; these are independent endpoints.

TRY A CONTRAST

Laser detuning

\delta/\Gamma

-0.5

Intensity per beam

s=I/I_{\rm sat}

0.04

Radial field gradient

b/(\mathrm{G/cm})

12

Beam helicities

Preparation & sampling

Initial cloud offset

x_0/\mathrm{mm}

1.2

Initial temperature

T_0/\mathrm{\mu K}

1000

Sampling seed

s_0

7261

The probe only selects an exposure or voltage. Other changes start a fresh sample; save first. Nothing runs by itself.

Semiclassical six-beam Doppler model with idealized Zeeman branches, isotropic recoil and rubidium-87 D2 scales. Independent Poisson scattering in 5 microsecond steps. Simulated particle readout, not a fluorescence-camera reconstruction. No sub-Doppler cooling, multilevel pumping, atom collisions or real loading dynamics.

02 / WHAT DID THE PARTICLES DO?

Measure speed and position separately.

$t/\mathrm{ms}$ · Blue: active sample. Amber: last other saved sample. Drag to select the probe.

AT THE SELECTED PROBE

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\text{—}

Temperature uses the surviving atoms’ sample velocity variance after subtracting drift. It is a kinetic statistic, not proof of thermal equilibrium. Escaped atoms are retained in CSV.

03 / THE SAME RECORDS, A DIFFERENT VIEW

A cold cloud can still be off-center.

$x/\mathrm{mm},\quad v_x/(\mathrm{m/s})$ · Each dot is one surviving recorded atom. Hollow dots show its preparation. Axes adapt to the samples.

\text{—}

Center and RMS radius are computed from the same surviving endpoints. A hard 10 mm radial boundary marks escape, not a real chamber wall or a measured capture rate.

$v_x/(\mathrm{m/s})$ · Final recorded velocities; bin counts.

MODEL INSPECTION · DISTINCT FROM THE READOUT

Drag changes the experiment, not the temperature.

$v_x/(\mathrm{m/s}),\quad a_x/(\mathrm{m/s^2})$ · Model force at the center. Red detuning damps small velocities; blue detuning amplifies them.

$x/\mathrm{mm},\quad a_x/(\mathrm{m/s^2})$ · Coils off: no restoring force. Reversing helicities reverses confinement.

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04 / KEEP THE EVIDENCE

Save before changing the experiment.

Eight frozen samples. Restoring preserves the original settings and records. Acquiring again starts a new run. CSV also contains simulated collision or recoil diagnostics.

Model, units & primary sources

R_{i,\pm}=\frac{\Gamma s/2}{1+6s+4[\delta\mp(kv_i+\zeta_i)]^2/\Gamma^2}

Angular-frequency detuning, with the control expressed in natural linewidths. Idealized Zeeman branches follow a divergence-free quadrupole field proportional to (x,y,−2z); helicities make the three restoring slopes agree. Six equal plane waves, constant intensity within a 10 mm sphere; effective magnetic moment one Bohr magneton. The atom mass, wavelength and linewidth use rubidium-87 D2 values. The approximate common saturation denominator does not solve multilevel optical Bloch equations.

\mathbf B=b(x,y,-2z),\quad\Delta\mathbf v=v_r(\mathbf e_{\rm abs}-\mathbf n_{\rm em})

Initial Gaussian cloud: 0.6 mm standard deviation per axis and Maxwell velocities. Finite-step independent Poisson absorption and isotropic spontaneous emission conserve the recorded recoil ledger. No gravity, beam attenuation, dipole forces, coherent standing waves, repump dynamics or detector noise. A kinetic temperature below the textbook limit in a small or selected sample is not evidence of sub-Doppler cooling.

Raab et al. · MOT · Steck · Rubidium 87 D line data · Phillips · Doppler and sub-Doppler cooling

Start with the essentials

Focus question: Can light slow an atom—and keep it there?
One-sentence intuition: Doppler shifts produce damping; position-dependent Zeeman shifts produce confinement. Recoil also heats.

Core mathematical model

One photon cycle

\Delta\mathbf p=\hbar k(\mathbf e_{\rm abs}-\mathbf n_{\rm em})

Absorption pushes along a selected beam. Isotropic spontaneous emission has zero mean but nonzero variance.

Damping and restoring force

F_i=\hbar k(R_{i,+}-R_{i,-})\simeq-\alpha v_i-\kappa_i x_i

The linear expansion applies near rest and the field zero. Turning off the gradient removes the restoring term while keeping velocity damping.

Temperature from recorded velocities

T_{\rm kin}=\frac{m}{3k_B(N-1)}\sum_{a=1}^{N}|\mathbf v_a-\bar{\mathbf v}|^2

Uses surviving atoms and subtracts center-of-mass drift. At least two records are required. Escape can bias the selected population.

Separate linear equilibrium reference

T_{\rm lin}=\frac{\hbar\Gamma}{8k_B}\frac{1+6s+4d^2}{|d|},\quad d=\delta/\Gamma<0

Zero field, six equal beams, low velocity and isotropic recoil in the declared model. In the weak-light optimum the rubidium scale is about 146 microkelvin. This is not a finite-time or real multilevel-atom guarantee.

Common difficulties

What was actually recorded?

Typical misconceptionThe cloud picture is a fluorescence-camera reconstruction.

Better mental modelThis is ideal simulated particle readout. Final positions and velocities feed both plots; no optical imaging system is reconstructed.

Scope of the model

Typical misconceptionA successful simulation calibrates a physical instrument.

Better mental modelSemiclassical six-beam Doppler model with idealized Zeeman branches, isotropic recoil and rubidium-87 D2 scales. Independent Poisson scattering in 5 microsecond steps. Simulated particle readout, not a fluorescence-camera reconstruction. No sub-Doppler cooling, multilevel pumping, atom collisions or real loading dynamics.

Run the experiment

01
Make a prediction
Predict which will change when the coils are off: speed spread, cloud center, or both.
What to observe: The data panel begins empty. Record a sample before interpreting it.
02
Record a contrast
Record 128 atoms with coils on. Save, choose molasses, and record another cloud at the same duration.
What to observe: Similar low temperatures can coexist with very different cloud sizes and centers.
03
Try to break the explanation
Change to blue detuning, then reverse helicities under red detuning. Compare the two force curves and the survival records.
What to observe: Heating and anti-confinement have different local force signatures. An empty survivor set has no reported temperature.