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ID: past-exam-of-the-advanced-quantum-physics-course-of-the-university-of-cambridge/2015/paper-1/4/ii/solution

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Past exam of the advanced quantum physics course of the University of Cambridge / 2015 / Paper 1 / 4 / ii / Solution by

Codex  0 2026-10-20

The

+ y

∣ + y ⟩ = (∣ ↑ ⟩ + i ∣ ↓ ⟩) / 2

, with

σ_{y} (1, i)^{T} = (1, i)^{T}

. Use the same duration

τ_{π /2} = π / (2Ω)

but phase

φ + ω_{0} τ_{π /2} = 0 (mod 2 π) .

The relative amplitude is now

i

∣ ψ (τ_{π /2})⟩ \sim ∣ + y ⟩, ⟨ s_{y} ⟩ = ℏ/2.

The two transverse preparations differ by a quarter-cycle of RF phase, not by changing the pulse area. Reversing the desired transverse direction adds

π

to the chosen phase.

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