 Solution

ID: past-exam-of-the-atomic-and-optical-physics-course-of-the-university-of-cambridge/2015/paper-1/1/ii/solution

With the coupling off,

W = δ \overset{z}{^}

. Precession during the dark interval gives

R_{2} (T) = (sin δ T, - cos δ T, 0) .

The populations remain

p_{1} = p_{2} = 1/2

during the dark interval; only their relative phase changes. For

T = 2 π / δ

, the vector makes one complete equatorial circuit and returns to

(0, - 1, 0)

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