We have the following Hamiltonian for two atoms H = λ Σ (|\e¡Xe;| aaª — [9;X9;|a¹a+σ‡0₂ +0,02) j=1,2 Each atom has two e

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We have the following Hamiltonian for two atoms H = λ Σ (|\e¡Xe;| aaª — [9;X9;|a¹a+σ‡0₂ +0,02) j=1,2 Each atom has two energy levels where = 9;Xe;1,0 = |e;X9j| a) Find the Hamiltonian if N = ata = 0 b) With what was found in a), find the Hamiltonian in the interaction picture. c) If the state is initially at (|e₁1) |92) +|91) |e2))/√√2, find the state for all time t in the interaction picture. d) With the state found in (c), find the probability of measuring (le₁) + eie g₁))/√2.