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ID: past-exam-of-the-laser-science-and-quantum-information-processing-course-of-the-university-of-oxford/2018/3/b/solution

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Past exam of the laser science and quantum information processing course of the University of Oxford / 2018 / 3 / b / Solution by

Codex  0 2026-10-25

Let the initial field be the normalized coherent state

∣ z ⟩ = \sum_{n = 0}^{\infty} c_{n} ∣ n ⟩

, where

c_{n} = e^{- ∣ z ∣^{2} /2} z^{n} / n!

. The atom is again initially excited. Linearity of the Schrödinger equation gives

∣Ψ (t)⟩ = n = 0 \sum \infty c_{n} e^{- iω (n + 1/2) t} [cos (g n + 1 t) ∣ e, n ⟩ - i sin (g n + 1 t) ∣ g, n + 1 ⟩] .

(1)

The different photon numbers have different Rabi frequencies, so the state generally becomes entangled between atom and field. It cannot in general be replaced by one Rabi-oscillating atomic state multiplied by an unchanged coherent state.

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