Quantum Lab 03 · path amplitudes

Single-Particle Interference

Each particle leaves one localized hit, yet its landing distribution is set by complex amplitudes from both paths. Over many emissions, unpredictable events accumulate into a stable interference pattern. Reduce coherence and the fringes wash out.

Detected particles0

Fringe visibility100%

Fringe spacing0.100 L

RegimeCoherent

Start with the essentials

Focus question: If particles are emitted one at a time and never collide, where does the fringe pattern come from?
One-sentence intuition: Each event samples the squared sum of two path amplitudes; many independent events reveal that probability distribution.

Core mathematical model

Path-amplitude superposition

P(x)=|\psi_1(x)+\psi_2(x)|^2

The cross term carries relative phase and creates bright-dark modulation.

Fringe visibility

\mathcal V=\frac{I_{\max}-I_{\min}}{I_{\max}+I_{\min}}

As $\mathcal V$ falls from 1 to 0, coherent interference disappears.

Common difficulties

Particles do not need to collide

Typical misconceptionMany particles must pass simultaneously for interference to occur.

Better mental modelEven widely separated events can show self-interference between path amplitudes.

Path detection is not merely a mechanical kick

Typical misconceptionFringes vanish only because the detector knocks particles aside.

Better mental modelIf paths become distinguishable in principle, entanglement with the environment suppresses the cross term.

Run the experiment

01
Build a distribution hit by hit
Emit fully coherent particles at a low rate.
What to observe: Individual hits are unpredictable while the accumulated pattern becomes stable.
02
Reduce coherence
Move $\mathcal V$ slowly from 1 to 0.
What to observe: Hits continue while bright-dark contrast fades.
03
Change geometric scales
Vary $\lambda$ and $d$ separately.
What to observe: Larger $\lambda$ spreads fringes; larger $d$ compresses them.