7, Cavity Quantum ElectroDynamics (Cavity-QED) 1. Cavity Modes 2 ...

Two-time correlation function
the input and output fields,
let ĉ(t) be any system operator, then
with
√
γ 1
âIN(t) = â(t) − √
2 2π
√
γ 1
âOUT (t) = â(t) + √
2 2π
dω ˆ b(ω, t),
dω ˆ b(ω, t),
[ĉ(t), √ γâIN(t ′ )] = γ
2 [ĉ(t), â(t′ )], for t = t ′ ,
[ĉ(t), √ γâIN(t ′ )] = 0, for t ′ > t,
[ĉ(t), √ γâOUT (t ′ )] = 0, for t ′ < t,
[ĉ(t), √ γâIN(t ′ )] = γ[ĉ(t), â(t ′ )], for t ′ < t,
âO(t) + âI(t) = √ γâ(t),
IPT5340, Fall ’06 – p.18/23