  In the preceding Comment [1] it was claimed that the third-order Hamiltonian
obtained in our original paper [2] is not Hermitian for general situations when
considering time-dependence and the way of deriving the effective third-order
expansion is not very rigorous. To reply the comment we should emphasize the
following three points: first of all, the third-order Hamiltonian given in our
paper is exactly Hermitian under the conditions mentioned there. Secondly, the
iterative method adopted in our paper to derive the generalized effective
Hamiltonian is equivalent to the Dyson series, and its correctness can thus be
guaranteed. Thirdly, although the truncated effective Hamiltonian is indeed
non-Hermitian under the time-dependent situation as presented in the Comment,
it corresponds exactly to the non-unitary truncated Dyson series. Considering
the truncated Dyson series has been extensively utilized in the time-dependent
perturbation theory, in our opinion, the non-Hermitian truncated effective
Hamiltonian can still be treated as an approximation of the effective
Hamiltonian.
