 Solution

ID: past-exam-of-the-laser-science-and-quantum-information-processing-course-of-the-university-of-oxford/2019/3/d/solution

There is at most one field photon in b. Projection onto its one-photon sector gives

P (n = 1; t) = sin^{2} (g t), ρ_{atom ∣ n = 1} = ∣ g ⟩ ⟨ g ∣.

Before detector absorption, the normalized conditional joint state is

∣ g, 1 ⟩

up to an overall phase. A destructive photon count changes the field to its vacuum but leaves the atom in

∣ g ⟩

. This conditional state is meaningful whenever the one-photon outcome has nonzero probability.

 New to topics? Read the docs here!