---
title: "Can One Particle Interfere? Interactive Lab | Sandbox Physics"
description: "How do unpredictable hits accumulate into stable fringes?"
canonical_url: "https://sandboxphysics.com/labs/single-particle-interference/"
language: "en"
page_type: "lab"
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  zh-CN: "https://sandboxphysics.com/zh/labs/single-particle-interference/"
last_modified: "2026-10-27"
---

Quantum Lab 03 · path amplitudes

# Single-Particle Interference

**How do unpredictable hits accumulate into stable fringes?** Each particle lands at one random spot, but the chance of each spot comes from adding the amplitudes for both paths and squaring the sum. Many independent hits sample that pattern and slowly build up steady fringes. Reduce the coherence and the fringes fade.

Each particle lands at a single spot, but where it is likely to land depends on the complex amplitudes from both paths together. Send many particles and the unpredictable hits build up a stable interference pattern. Lower the coherence and the fringes wash out.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Here the amplitudes of the two paths add, not the probabilities of a particle secretly taking one slit. Which-path information reduces coherence: if the paths can be told apart, fringe visibility drops even when nobody reads the result.

Physics tutorial

## Single-particle interference: one at a time, still fringes

**Background** A detector records one localized hit at a time, but the probability amplitude for that hit can include two indistinguishable paths.

**Why it matters** This is the most direct way to see that quantum theory adds probability amplitudes, not a classical wave made of many particles.

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 hit lands at random according to the squared magnitude of the sum of two path amplitudes, and many independent hits trace out that probability distribution.

### Core mathematical model

#### Path-amplitude superposition

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

The cross term contains the relative phase of the two paths and produces the bright and dark fringes.

#### 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 misconception** Many particles must pass simultaneously for interference to occur.

**Better mental model** Even when hits arrive far apart in time, each one still shows interference between its own two path amplitudes.

#### Path detection is not merely a mechanical kick

**Typical misconception** Fringes vanish only because the detector knocks particles aside.

**Better mental model** If the path could in principle be identified, the particle becomes entangled with its environment, and that entanglement suppresses the cross term.

### Run the experiment

1. 01

   #### Build a distribution hit by hit

   Emit fully coherent particles at a low rate.

   **What to observe:** Each hit is unpredictable, but the accumulated pattern settles into stable fringes.

2. 02

   #### Reduce coherence

   Move $\mathcal V$ slowly from 1 to 0.

   **What to observe:** Hits keep arriving, but the contrast between bright and dark fades.

3. 03

   #### Change the geometry

   Vary $\lambda$ and $d$ separately.

   **What to observe:** Larger $\lambda$ spreads fringes; larger $d$ compresses them.

Physical conclusion

Quantum interference is built into the probability rule for each event, not into interactions between particles.

Quantum & fields · Starter path

## Start from a single measurement

Predict an outcome, then count what the measurements actually give. The path starts with one qubit and moves on to wave packets, bound states and two-photon interference.

[Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare your prediction with the measured frequency over many shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/)

1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/)
2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/)
3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/)
4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/)
5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/)
6. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/)

[View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)