Coherent tunnelling in a double well — Model & Constraints

QPE preset #12

Values below come from the v7.9.4/Step 56 guided preset; live values may differ after user edits.

Numerical model actually used

Scalar Schrödinger split-step FFT

QPE evolves a complex scalar 2D wavefunction. The ordinary kinetic step is performed in Fourier space and the scalar potential in position space with Strang-type splitting; special events such as measurements, kicks or pulse recipes are layered on top without changing the rendering/physics separation.

Guided preset defaults

Domain	16 × 16
Grid	256 × 256
Boundary	Periodic / closed numerical box
Initial packet	centre=(-1.2, 0), σ=0.8, p=(0, 0), m=1
Base geometry	Rectangle
Geometry parameters	V₀=0, centre=(0, 0), size=(0, 0)
Preparation	coherent bound-state superposition
Bound-state default	nA=1, nB=2, relative phase=0°

For special modules (Ramsey, LZ, gauge, Dirac, kicks, measurement, etc.), complete authoritative parameters for the current run are exposed by Help → Current Experiment → Current Parameters.

Common assumptions

Dimensionless simulation units with ħ=1 unless explicitly stated otherwise.
Rendering, palettes, bloom and post-processing never modify ψ, V, observables or probabilities.
The grid is finite: structures below a few cells/pixels do not carry reliable physical meaning.

Experiment-specific assumptions and simplifications

Isolated coherent single-particle double well.
No dissipative tunnelling, thermal activation or many-body Josephson nonlinearity.
Left/right population is a coarse observable; the full field remains coherent.

How not to over-interpret the result

A visually convincing result is not a substitute for a numerical check. Inspect the relevant norms, populations, fluxes or Analysis curves; if the packet reaches the CAP or a numerical wall, always separate the physical effect from finite-domain behaviour.

Real-world mapping

Representative platform	ultracold Rb-87 atom / trapped matter wave
Mapping basis	Rb-87 kinetic-unit mapping
1 QPE length unit	1 µm
1 QPE time unit	1.37 ms
Note	Representative cold-atom mapping. Trap frequencies, optical geometries and internal-state protocols set the actual laboratory scale; this mapping is intentionally order-of-magnitude.

This mapping is representative only. The model remains the one described above: changing units does not add missing degrees of freedom.

Model references

Numerical methods · Conventions and units · General bibliography