 Solution

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

The conditional probability of the atomic ground state is the squared ground-state amplitude divided by the five-photon event probability:

P (g ∣ 5) = \frac{∣ c _{4} ∣ ^{2} sin ^{2} ( g 5 t )}{∣ c _{5} ∣ ^{2} cos ^{2} ( g 6 t ) + ∣ c _{4} ∣ ^{2} sin ^{2} ( g 5 t )} .

For

z \neq = 0

∣ c_{5} ∣^{2} = ∣ z ∣^{2} ∣ c_{4} ∣^{2} /5

, giving the equivalent expression

P (g ∣ 5) = \frac{5 sin ^{2} ( g 5 t )}{∣ z ∣ ^{2} cos ^{2} ( g 6 t ) + 5 sin ^{2} ( g 5 t )} .

It applies only when the conditioning denominator is nonzero. The distinct

5

and

6

factors reflect the two different initial photon-number blocks.

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