  We use a semi-Markov process method to calculate large deviations of counting
statistics for three open quantum systems, including a resonant two-level
system and resonant three-level systems in the $\Lambda$- and
$V$-configurations. In the first two systems, radical solutions to the scaled
cumulant generating functions are obtained. Although this is impossible in the
third system, since a general sixth-degree polynomial equation is present, we
still obtain asymptotically large deviations of the complex system. Our results
show that, in these open quantum systems, the large deviation rate functions at
zero current are equal to two times the largest nonzero real parts of the
eigenvalues of operator $-{\rm i}\hat H$, where $\hat H$ is a non-Hermitian
Hamiltonian, while at a large current, these functions possess a unified
formula.
