 Solution

ID: past-exam-of-the-laser-science-and-quantum-information-processing-course-of-the-university-of-oxford/2019/1/c/iv/solution

Extracting 95 percent of the maximum available inversion energy means

η = 0.95/ β

, or

x = β η = 0.95

. Substitution in ii gives

r = \frac{- ln ( 0.05 )}{0.95} = 3.1534 \dots .

The degeneracy factor cancels because the target is a fraction of the maximum energy

N_{i}^{*} V_{g} ℏ ω_{L} / β

, rather than a fraction of

N_{i}^{*} V_{g} ℏ ω_{L}

without that factor.

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