Effects of counter-rotating-wave terms on the non-Markovianity in quantum open systems

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 or a fermionic environment with a detuned Lorentz spectrum at
zero temperature is 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 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.