Photon Statistics Calculator
Select light source type and mean photon number. The Photon Statistics Calculator instantly computes Mandel Q parameter, second-order coherence g²(0), variance, and photon number distribution type.
About the Photon Statistics Calculator
The Photon Statistics Calculator is a precise, scientifically accurate tool that computes key photon statistics — Mandel Q parameter, second-order coherence g²(0), variance-to-mean ratio, and distribution type — for common quantum states of light. This Photon Statistics Calculator implements the exact formulas from quantum optics used to distinguish classical and non-classical light. Proudly supported by Agri Care Hub.
Scientific Formulas
g²(0) = ⟨n(n-1)⟩ / ⟨n⟩²
Coherent: Q = 0, g²(0) = 1 (Poisson)
Thermal: Q = ⟨n⟩, g²(0) = 2 (super-Poissonian)
Fock: Q = -1, g²(0) = 0 (sub-Poissonian)
Why This Calculator Is Essential
Photon statistics reveal the quantum nature of light: • g²(0) < 1 → antibunching (single-photon sources) • g²(0) = 1 → coherent (lasers) • g²(0) > 1 → bunching (thermal light) • Q < 0 → non-classical (sub-Poissonian) Used in quantum optics, single-photon sources, quantum cryptography, and Hanbury Brown-Twiss experiments.
How to Use
- Select light source type (coherent, thermal, Fock).
- Enter mean photon number ⟨n⟩.
- Click “Calculate Photon Statistics”.
- See Q, g²(0), variance, and classification.
When Should You Use This Tool?
- Quantum optics research
- Single-photon source characterization
- Hanbury Brown-Twiss experiments
- Non-classical light studies
- Quantum information processing
- Teaching quantum statistics of light
Scientific Foundation
Photon statistics were pioneered by Hanbury Brown and Twiss (1956) and formalized in quantum optics. The Mandel Q and g²(0) are standard measures of non-classicality. Values g²(0) < 1 prove quantum behavior. Full theory at Photon Statistics on Wikipedia and Mandel & Wolf’s *Optical Coherence and Quantum Optics*.
Conclusion
The Photon Statistics Calculator brings the quantum nature of light — bunching, antibunching, and non-classical statistics — to your browser with perfect accuracy and beautiful design. Whether you’re a student learning quantum optics, a researcher characterizing single-photon sources, or an engineer working on quantum technologies, this tool delivers precise results every time. For more quantum tools, visit Agri Care Hub.