Enhancement of the entanglement generation via randomly perturbed series of external pulses in a nonlinear Bose-Hubbard dimer

We discuss a model of a short Bose-Hubbard dimer involving two anharmonic quantum oscillators mutually coupled with the use of the linear interaction and additionally driven by a series of ultra-short external pulses. We show that under some conditions the system behaves as a two-qubit one, and contrary to its continuously driven counterpart can be a source of maximally entangled states (MES). We discuss the cases when the system is excited only in one mode and in both ones, and additionally when the cross-Kerr-type interaction is present or omitted. We show that the generation of maximally (or almost maximally) entangled states depends on the time of free evolution of oscillators and hence, the proper steering of the changes of the time between subsequent pulses can increase the effectiveness of MES generation. Moreover, we show the influence of the timing between two series of pulses (corresponding to the two modes) on such a process. What is relevant, thanks to the presence of additional randomness in the timings, the states with stronger entanglement can be achieved than for the situation when the time between consecutive pulses remains ideally fixed.