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Imaginary-coupled two-level Hamiltonian

For

H = (E_{-} iλ - iλ E_{+}), Δ = E_{+} - E_{-} > 0,

the exact energies are

E_{\pm}^{exact} = \frac{E _{-} + E _{+}}{2} \pm \frac{Δ ^{2}}{4} + λ^{2} .

The perturbation series around

λ = 0

has radius

Δ/2

, set by the branch points

λ = \pm i Δ/2

.

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Solution