Skip to main content
Sandbox Physics

QUANTUM TIME / A KICKED ROTOR

Molecular Alignment Revivals

Kick an ideal molecular rotor with a short laser pulse. Rotate the three-dimensional axis distribution, find alignment revivals and slide a second pulse through the sequence. Collect independent axis readouts and compare their alignment with the model.

Interactive modelMolecular Alignment Revivals
AXIS PROBABILITY
PULSE 01DRAG PULSE 02
POLARIZATION AXIS

Radius: square root of axis density. Schematic, not an orbit.

t/Trev=0t/T_{\mathrm{rev}}=0

Preparing the spectrum…

FREEZE A MOMENT. BUILD THE EVIDENCE.

Which way did the axes point?

Each ideal readout uses a fresh identical preparation. Collecting pauses time.

Recorded trials00
Return probability · model11
Alignment · records—\text{—}
Total probability · model11

MODEL / RECORDS / PINNED

Horizontal coordinate u=cos⁡θu=\cos\theta

Teal: model. Gold: recorded frequency density. Dashed: pinned model. Equal-width bins.

ALIGNMENT / AFTER THE PULSES

The dashed baseline is one third for an isotropic ensemble. Parallel and antiparallel axes are equivalent; this is alignment, not orientation.

00
Model, units and what the picture means

Initially an isotropic rotational ground state. Two optional, collinear kicks add a phase proportional to the squared projection on the polarization axis. Free evolution includes angular momenta zero through 48. Pulse strength is dimensionless, not laser power.

EJ=BJ(J+1),Trev=πℏBE_J=BJ(J+1),\quad T_{\mathrm{rev}}=\frac{\pi\hbar}{B}

All time labels use the revival period. Records sample the displayed 384-bin density, normalized for the ideal detector. No finite resolution, thermal ensemble or instrument response is modeled. Display brightness uses a fixed square-root gain.

Original research：Seideman (1999)

Physics tutorial

Molecular Alignment Revivals

BackgroundKick an ideal molecular rotor with a short laser pulse. Rotate the three-dimensional axis distribution, find alignment revivals and slide a second pulse through the sequence. Collect independent axis readouts and compare their alignment with the model.

Why it mattersMake coherent time evolution visible, then test it with finite records.

Start with the essentials

Focus question
The pulse is gone. The molecules remember.
One-sentence intuition
A short pulse changes phase first. The resulting rotational states interfere later, when the light is already gone.

Core mathematical model

The energy spectrum

EJ=BJ(J+1),Trev=πℏBE_J=BJ(J+1),\quad T_{\mathrm{rev}}=\frac{\pi\hbar}{B}

Time is displayed as a fraction of this exact revival period. The rotor rotational constant is an energy.

The impulsive kick

UP=exp⁡(iPcos⁡2θ),P=Δα4ℏ∫E2(t) dtU_P=\exp(iP\cos^2\theta),\quad P=\frac{\Delta\alpha}{4\hbar}\int\mathcal E^2(t)\,dt

A nonresonant pulse with positive polarizability anisotropy. The electric field is the envelope of the rapidly oscillating real field; both pulses share a polarization axis.

What the records estimate

A=⟨cos⁡2θ⟩,Aisotropic=13A=\langle\cos^2\theta\rangle,\quad A_{\mathrm{isotropic}}=\frac13

The sample mean of the squared axial projection estimates alignment. Head and tail remain equivalent; mean direction stays zero.

Common difficulties

What the image is

Typical misconceptionAn isolated linear rigid rotor initially in its rotational ground state. Collinear, instantaneous nonresonant kicks; no thermal mixture, centrifugal distortion, ionization or detector calibration. The surface shows axis probability, not a molecule or orbit.

Better mental modelThe radius encodes the square root of angular probability density. It is neither a molecule outline nor a trajectory. Thermal populations and a real probe require a different model.

Run the experiment

  1. 01

    Predict, then jump

    Compare the instant of the pulse, a short time afterward and one full period.

    What to observe: The pulse alone does not instantly align axes. Free evolution turns its phase imprint into a visible distribution.
  2. 02

    Change one cause

    Enable the second pulse and drag its arrival time. Pin one sequence before changing it.

    What to observe: Compare the entire time trace, not a single attractive frame.
  3. 03

    Acquire and audit

    Collect 500 independent readouts. Pin the sample, change time, restore it and export the raw CSV.

    What to observe: Counts fluctuate. The standard error describes sampling only; the teal reference comes from the model.