(8521) Decay from an aymmetric double well

Consider a two level atom. The two levels have binding energies \( \varepsilon_0 \) and \(\varepsilon_1 \). The ground state is stable, while the excited state is metastable and has a decay rate \( \Gamma_0 \). The atom is resonantly driven by a laser. Consequently there is coupling \( c \) between the two levels.

(1) Write the effective non-hermitian Hamiltonian \( \mathcal{H} \).

(2) Find the eigenvalues of \( \mathcal{H} \).

(3) Specifically write results for degenerate atom with \(\varepsilon_1 = \varepsilon_0 = 0 \). Determine the critical value of \( c \) above which Rabi oscillations can be observed.

(4) Compare the results of the previous item with results that would be obtained if both levels were equally unstable with different decay channels.

(5) Compare the results of the previous item with results that would be obtained if both levels were equally coupled to the same decay channel.