  This work strives to better understand how the entanglement in an open
quantum system, here represented by two coupled Brownian oscillators, is
affected by a nonMarkovian environment (with memories), here represented by two
independent baths each oscillator separately interacts with. We consider two
settings, a `symmetric' configuration wherein the parameters of both
oscillators and their baths are identical, and an `asymmetric' configuration
wherein they are different, in particular, a `hybrid' configuration, where one
of the two coupled oscillators interacts with a nonMarkovian bath and the other
with a Markovian bath. We ask two groups of questions: Q1) Which time regime
does the bath's nonMarkovianity benefit the system's entanglement most? The
answers we get from detailed numerical studies suggest that A1) For an
initially entangled pair of oscillators, we see that in the intermediate time
range, the duration of entanglement is proportional to the memory time, and it
lasts a fraction of the relaxation time, but at late times when the dynamics
reaches a steady state, the value of the symplectic eigenvalue of the partially
transposed covariance matrix barely benefit from the bath nonMarkovianity. For
the second group of questions: Q2)Can the memory of one nonMarkovian bath be
passed on to another Markovian bath? And if so, does this memory transfer help
to sustain the system's entanglement dynamics? Our results from numerical
studies of the asymmetric hybrid configuration indicate that A2) A system with
a short memory time can acquire improvement when it is coupled to another
system with a long memory time, but, at a cost of the latter. The
sustainability of the bipartite entanglement is determined by the party which
breaks off entanglement most easily.
