Stern-Gerlach Experiment Simulator

An interactive educational tool for exploring quantum mechanics through the Stern-Gerlach experiment, based on McIntyre's approach.

Overview

This simulator provides an interactive learning experience that allows students to explore quantum mechanics concepts through hands-on experimentation with the Stern-Gerlach apparatus. The implementation follows the pedagogical approach outlined in McIntyre's "Quantum Mechanics: A Paradigms Approach" which uses the SG experiment as a foundational teaching tool.

The tool has two main modes:

1. Simulation mode: A web-based interactive simulator that allows students to manipulate SG apparatus parameters and observe outcomes
2. Real quantum mode: Integration with IBM Quantum systems to run actual quantum experiments (requires API key)

Features

Multi-Stage Experiments

The enhanced simulator now supports multi-stage Stern-Gerlach experiments with the following capabilities:

1. Multiple Apparatuses: Configure sequences of up to 10 Stern-Gerlach apparatuses with different magnetic field orientations
2. Experiment Types:
   • Simple: Single apparatus measurement
   • Cascade: Particles pass through multiple apparatuses in sequence
   • Disturbance: Measurement at each stage collapses the quantum state
   • Recombination: Quantum paths can interfere when recombined
3. Particle Tracking: Visualize individual particle paths through all stages
4. Blocking/Recombination: Simulate blocking of specific paths and recombination of others

3D Visualization

• Interactive 3D visualization of Stern-Gerlach apparatuses using Three.js
• Particle path visualization through multiple stages
• Real-time animation of beam splitting and particle movement
• Orbit controls for viewing from any angle

Quantum State Simulation

• Accurate quantum state evolution through multiple measurements
• Probability calculations based on quantum mechanics principles
• Support for different initial spin states (|+⟩, |-⟩, |+x⟩, |-x⟩)

Usage

Web Interface

1. Open src/index.html in a web browser
2. Select the operating mode:
   • Simulation Mode: Instant results with theoretical predictions
   • Real Quantum Mode: Execute on actual quantum hardware (requires IBM Quantum account)
3. Configure the experiment:
   • Select experiment type from the dropdown
   • For single apparatus: Set the magnetic field angle
   • For multiple apparatuses: Add apparatuses and set their angles
   • Set the number of particles to simulate (1-10,000)
4. Click "Run Experiment" to execute

Experiment Types

1. Simple Experiment:

   • Single Stern-Gerlach apparatus
   • Measures probability of spin states
   • Compares experimental results with theoretical predictions

2. Cascade Experiment:

   • Multiple apparatuses in sequence
   • Particles pass through all apparatuses
   • Demonstrates quantum state evolution

3. Disturbance Experiment:

   • Measurement at each stage affects subsequent stages
   • Shows the effect of observation on quantum systems
   • Demonstrates wave function collapse

4. Recombination Experiment:

   • Paths are recombined after splitting
   • Shows quantum interference effects
   • Demonstrates the principle of superposition

Programmatic Usage

The simulator can also be used programmatically:

// Import the required classes
import { SpinState, SGApparatus, SGExperimentSimulator } from './src/js/sg-simulator.js';

// Create initial state
const initialState = SpinState.plusState(); // |+⟩ state

// Create apparatus sequence
const apparatusSequence = [
    new SGApparatus(0),    // First apparatus at 0°
    new SGApparatus(90),   // Second apparatus at 90°
    new SGApparatus(45)    // Third apparatus at 45°
];

// Run simulation
const results = SGExperimentSimulator.simulate(
    initialState,
    apparatusSequence,
    1000, // Number of particles
    { experimentType: 'cascade' }
);

// Access results
console.log('Stage results:', results.stageResults);
console.log('Particle paths:', results.particlePaths);
console.log('Final counts:', { plus: results.plusCount, minus: results.minusCount });

File Structure

src/
├── index.html              # Main HTML file
├── css/
│   └── styles.css          # Styling for the UI
├── js/
│   ├── main.js             # Main application logic
│   ├── sg-simulator.js     # Core simulation logic
│   ├── quantum-backend.js  # Quantum computing backends
│   ├── visualization.js    # 3D visualization components
│   └── utils.js            # Utility functions
└── python/
    └── quantum_backend.py  # Python quantum backend (for future expansion)

tests/
├── js-tests.html           # JavaScript unit tests
├── test-multistage.html    # Multi-stage experiment tests
└── run_tests.py            # Python test runner

Dependencies

• Three.js - 3D graphics library
• Chart.js - Data visualization
• Qiskit - Quantum computing framework (Python)

Testing

Run the test suite by opening the following files in a browser:

• tests/js-tests.html - Unit tests for JavaScript components
• tests/test-multistage.html - Tests for multi-stage experiments

Educational Value

This simulator helps students understand:

• Quantum state measurement and collapse
• The probabilistic nature of quantum mechanics
• Wave-particle duality
• The effect of measurement on quantum systems
• Quantum interference and superposition
• Non-classical correlations in quantum systems

Future Enhancements

Planned improvements include:

• More sophisticated particle blocking/recombination
• Additional quantum state initialization options
• Enhanced visualization with particle animations
• More experiment types (e.g., Bell's theorem demonstrations)
• Integration with more quantum computing platforms
• Mobile-responsive design