Quantum-field treatment of the EM field — Fock states, coherent and squeezed states, cavity QED, Jaynes-Cummings dynamics, non-classical photon statistics (antibunching, HOM interference). Distinct from laser physics in that the field…
quantum-optics
Photon Fock state
Eigenstate |n⟩ of the photon-number operator with definite photon count. Forms an orthonormal basis of the single-mode Hilbert space; phase…
Photon number operator
n̂ = â†â acting on Fock space; commutes with the free Hamiltonian. Bose commutators [â,â†] = 1 generate the full ladder structure.
Glauber coherent state
Eigenstate of the annihilation operator â|α⟩ = α|α⟩, α∈C. Photon-number distribution is Poissonian with ⟨n⟩ = |α|², and quadrature…
Squeezed state of light
Minimum-uncertainty state with one quadrature variance below the vacuum value (Δx)² < ½, the conjugate quadrature correspondingly enlarged.…
Squeezing operator
Unitary Ŝ(ξ) = exp[½(ξ*â² − ξ↲)] generated by two-photon processes. Acting on the vacuum produces the squeezed vacuum |0,ξ⟩; combined…
Cavity quantum electrodynamics
Single-atom-single-mode regime where coherent atom-photon coupling g exceeds atomic decay γ and cavity loss κ — the strong-coupling regime.…
Jaynes–Cummings model
Exactly-solvable two-level-atom + single-cavity-mode Hamiltonian under the rotating-wave approximation: H = ℏω(â†â + ½σ_z) + ℏg(âσ⁺ +…
Spontaneous parametric down-conversion (SPDC)
Pump photon (frequency ω_p) splitting in a χ⁽²⁾ nonlinear crystal into signal and idler photons (ω_p = ω_s + ω_i, k_p = k_s + k_i).…
Photon antibunching
Second-order intensity correlation g⁽²⁾(0) < 1, achievable only by genuinely non-classical light (cannot be reproduced by classical noise…
Hong–Ou–Mandel effect
Two indistinguishable single photons entering opposite ports of a 50:50 beamsplitter bunch into the same output port — coincidence…
Shot-noise (standard quantum) limit
Phase-measurement uncertainty Δφ ≥ 1/√N for N independent photons in a coherent state — the noise floor of classical interferometry.…
Quantum vacuum fluctuation
Non-zero variance of the EM field in the |0⟩ state, ⟨E²⟩ ≠ 0, even though ⟨E⟩ = 0. Drives spontaneous emission, the Casimir force, the Lamb…