Coherent State Calculator
Enter the complex amplitude α. The Coherent State Calculator instantly computes mean photon number, uncertainty, Mandel Q, and all key properties of Glauber coherent states.
About the Coherent State Calculator
The Coherent State Calculator is a precise, scientifically accurate tool that computes all properties of quantum coherent states |α⟩ — the closest quantum states to classical light. This Coherent State Calculator implements the exact formulas from quantum optics for mean photon number, uncertainty, Mandel Q parameter, and photon number distribution. Proudly supported by Agri Care Hub.
Scientific Definition
⟨n⟩ = |α|²
Δn = √|α|²
Q = (⟨n²⟩ - ⟨n⟩²)/⟨n⟩ - 1 = 0 (Poissonian)
g²(0) = 1
Why This Calculator Is Essential
Coherent states are the quantum description of laser light and are crucial in: • Quantum optics and laser physics • Optical communication • Quantum information processing • Interferometry and precision measurement • Squeezed and displaced states They have minimum uncertainty Δx Δp = ħ/2 and Poissonian photon statistics.
How to Use
- Enter real and imaginary parts of complex amplitude α.
- Magnitude |α| determines mean photon number ⟨n⟩ = |α|².
- Click “Calculate Coherent State”.
- See all quantum properties.
When Should You Use This Tool?
- Quantum optics research
- Laser physics and coherence
- Quantum information theory
- Optical communication systems
- Teaching Glauber states and quantum light
- Comparing to thermal or Fock states
Scientific Foundation
Coherent states were introduced by Roy Glauber in 1963 (Nobel Prize 2005) as eigenstates of the annihilation operator a|α⟩ = α|α⟩. They are minimum uncertainty states and have Poissonian photon statistics. Full theory at Coherent State on Wikipedia and Glauber’s original papers.
Conclusion
The Coherent State Calculator brings the quantum states of classical light to your browser — with perfect accuracy and beautiful design. Whether you’re a student learning quantum optics, a researcher studying laser coherence, or an engineer working with optical systems, this tool delivers precise results every time. For more quantum tools, visit Agri Care Hub.