Entanglement Dynamics of Coupled Quantum Oscillators in Independent NonMarkovian Baths

Abstract

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. Upon finding the solutions to the Langevin equations governing the system dynamics and the evolution of the covariance matrix elements entering into its entanglement dynamics, 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.