Question

In Ramsey experiment ,a beam of atoms in a state |1⟩, you do a π/2 pulse with a Rabi frequency of Ω0=(2π)⋅500 Hz and a detuning of δ=(2π)⋅3 Hz to the |1⟩→|2⟩ transition. Then there is a free flight for a time T = 0.5 s and a second π/2 pulse with the same Rabi frequency. The excited state |2⟩ has a decay rate of γ=0.5 s−1. At the end you measure the purity of the final state right after the second pulse??What is the length of the Bloch vector after this experiment????