QUANTUM CONFINEMENT / INTERFERENCE

Aharonov–Bohm Quantum Cage

Release a localized particle into a diamond chain. Half a flux quantum closes every escape route by interference. Unbalance the two arms and watch the cage leak.

LATTICE · PROBABILITY

INSIDE THE ORIGINAL CAGE

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Model probability
Motion can continue inside.

Node height: square root of site probability. Gold outline: the original five-site cage. Links show coupling geometry, not particle tracks.

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Drag the gold launch marker, or use the arrow keys.

REPEAT. FREEZE. READ THE POSITIONS.

Does the picture survive a measurement?

Every shot evolves a fresh preparation to the selected time, then measures position once. Ideal unit efficiency and number resolution. Records do not track a trajectory or reconstruct phase.

Recorded fraction

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95% Wilson interval

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Model distance from launch

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Model boundary probability

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01 / THE WHOLE EVOLUTION

Confined, or merely slow?

Cyan: model retained fraction. Coral: matched reference with flux or interaction removed. Gold marker: current time. Drag to inspect.

$Jt/\hbar$

02 / ONE SHOT, ONE OUTCOME

Where the particle was found.

Gold: recorded frequency. Cyan: model probability. Linear vertical scale; all shots included.

Cell coordinate

03 / READ THE STRUCTURE

A breathing cage leaves a narrow trace.

Model site probabilities over time, grouped by cell. Horizontal: position; vertical: time. Color uses a fixed square-root probability gain.

04 / RAW SNAPSHOTS

Every row starts fresh.

Latest 20 independent shots. A double mark is two atoms on one site. Full records are retained in the CSV.

Read the raw ledger

Trial	Position	Retained

Model, units & sources

\tau=Jt/\hbar,\qquad x_j=ja

Static, closed, finite tight-binding systems with open ends. Time is in inverse hopping units; distance is in cell or site spacings. Both the chosen state and matched reference are evolved numerically. Edge probability warns when finite ends matter; it is not an error estimate.

\phi=2\pi\Phi/\Phi_0,\qquad J_{\mathrm{upper,lower}}=J(1\pm\delta)

73 sites: 25 hubs and 24 pairs of arms. Each rightward upper or lower path gains opposite half-flux phases. At half flux and balanced arms, escape amplitudes cancel exactly from an interior hub preparation; the original hub and four neighbors form the measured cage. No disorder, loss or finite-frequency synthetic-field drive is simulated.

P_{A_0}(\tau)=\cos^2(2\tau)\quad(\Phi/\Phi_0=1/2,\ \delta=0)

Mukherjee et al. — rhombic lattice and effective flux, Eqs. 1 & 4

Numerical evolution uses norm-limited exponential-action steps without renormalization. The diagnostic reports norm drift and energy drift. Statistical intervals describe finite ideal samples only. The 3D view and smooth maps show the model; records are independent Born-rule draws.

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Start with the essentials

Focus question: A cage with no walls.
One-sentence intuition: Two paths can cancel escape while motion continues inside a compact cage.

Core mathematical model

Unitary evolution

|\psi(t)\rangle=e^{-iHt/\hbar}|\psi(0)\rangle

The plotted probability and the recorded outcomes use the same state.

What is counted

P_{\mathrm{cage}}=\sum_{j\in C}|\psi_j|^2

This is a position-based event, not a measurement of phase or a bound-state projector.

Common difficulties

Separate preparations

Typical misconceptionRows show the path of one particle.

Better mental modelEach shot starts again. The simulation is unmeasured until the selected final time.

Model boundary

Typical misconceptionA localized picture proves a pure bound state.

Better mental modelFinite, coherent single-particle tight-binding model with prescribed Peierls phases. The scene is a lattice probability diagram, not a waveguide apparatus. No drive micromotion, disorder, loss or measurement during evolution.

Run the experiment

01
Predict
Compare the first two presets at the same time.
What to observe: Half flux holds all probability in five sites.
02
Break the condition
Choose the third preset.
What to observe: Unbalanced paths no longer cancel escape.
03
Measure
Collect positions, pin the result, then compare another preparation.
What to observe: The estimate fluctuates, and its interval narrows with more shots.