QUANTUM FLUID / INTERFERENCE

Matter-Wave Collision

Launch two coherent condensate clouds toward one another. Slide their relative phase, turn on repulsion, and watch interference ridges emerge from the evolving wave field. Freeze a moment and build its density from independent position measurements.

Effective two-dimensional, dilute, low-depletion mean-field model with a prescribed coherent initial state. The height is density, not a physical surface. Finite periodic numerical box; no thermal gas, imaging calibration or many-body correlations.

EVOLVING MODEL FIELD

Dark → bright: low → high density

\tau=0

Scrub timePlayback

Preparing the wave field…

PAUSE. COLLECT. COMPARE.

From a wave to recorded positions.

One ideal position from each fresh, identical preparation. Sampling pauses the film.

Recorded positions

0

Peak model density

0

Integrated density

1

Relative energy drift

0

RECORDED / POSITION COUNTS

No positions acquired. The model field is shown above.

What is being solved?

Two phase-coherent Gaussian packets with equal and opposite launch momenta. A fixed initial phase is prescribed, not inferred from independent number states.

Two-dimensional Gross–Pitaevskii mean field, a 64 by 64 Fourier grid on a periodic square of side 24, time step 0.015. No dissipation or real-time renormalization. Brightness uses a fixed square-root display gain; height remains proportional to density. Phase is hidden at very low density.

i\partial_\tau\psi=\left[-\frac12\nabla^2+V+g|\psi|^2\right]\psi

Primary sources and model limits：Dalfovo et al. (1999) · Bao et al. (2003) · Andrews et al. (1997)

Start with the essentials

Focus question: Two clouds of atoms. A landscape of interference.
One-sentence intuition: Phase shifts move interference minima. Repulsive interactions change the evolution itself.

Core mathematical model

The evolving field

i\partial_\tau\psi=\left[-\frac12\nabla^2+V+g|\psi|^2\right]\psi

Length is measured in a fixed unit; energy and time follow from mass and Planck’s constant. The field has unit integrated density.

Units and density

E_0=\frac{\hbar^2}{m\ell^2},\quad t_0=\frac{m\ell^2}{\hbar},\quad\int |\psi|^2\,d^2r=1

The interaction includes the effective atom-number factor. No specific atomic species or trap calibration is assumed.

Interference cross term

|\psi_1+\psi_2|^2=|\psi_1|^2+|\psi_2|^2+2\operatorname{Re}(\psi_1^*\psi_2)

The sum is exact for noninteracting coherent fields. With repulsion, the combined field must be evolved as a whole.

Common difficulties

Simulation boundaries

Typical misconceptionEffective two-dimensional, dilute, low-depletion mean-field model with a prescribed coherent initial state. The height is density, not a physical surface. Finite periodic numerical box; no thermal gas, imaging calibration or many-body correlations.

Better mental modelReal-time evolution preserves norm without renormalization. Boundary occupation, high-frequency weight and energy drift warn about numerical limitations.

Run the experiment

01
Watch one controlled contrast
Start with no interaction, then flip the relative phase.
What to observe: The central bright ridge becomes a dark seam.
02
Introduce an obstacle
Raise the obstacle and drag its ring before releasing a new preparation.
What to observe: The potential changes the computed field; dragging restarts the experiment rather than stirring it mid-flight.
03
Collect and compare
Pause, collect positions, and pin the result. Change a setting and compare at the same time.
What to observe: Counts fluctuate. The reference line is the integrated model density, not a fit to the points.