  We investigate the effect of counter-rotating-wave terms on the
non-Markovianity in quantum open systems by employing the hierarchical
equations of motion in the framework of the non-Markovian quantum state
diffusion approach. As illustrative examples, the non-Markovian memory effect
of a qubit embedded in a bosonic and a fermionic environment at zero
temperature are analyzed. It is found that the counter-rotating-wave terms are
able to enhance the observed non-Markovianity no matter the environment is
composed of bosons or fermions. This result suggests that the rotating-wave
approximation may inevitably reduce the non-Markovianity in quantum open
systems. Moreover, we find that the modification of the non-Markovianity due to
the different statistical properties of environmental modes becomes larger with
the increase of the system-environment coupling strength.
