Non-Markovian Dynamics and Entanglement in Quantum Brownian Motion

Dynamical aspects of quantum Brownian motion at low temperatures are investigated. Exact calculations of quantum entanglement among two Brownian oscillators are given without invoking the Born-Markov or Born approximation widely used for the study of open systems. Our approach is applicable for arbitrary time scale, in particular, suitable to probe short time regime at cold temperatures where many experiments on quantum information processing are performed. We study separability criteria based on the uncertainty relation, negativity, and entanglement of formation. We found a crossover behavior in a disentanglement process between quantum and thermal fluctuation dominated regimes. The fluctuationdissipation relation which holds for one-particle quantum Brownian particle in the long time limit does not hold for two particles interacting with common environment. The deviation from the relation is originated in the interaction mediated by environment which drives two particles into a steady oscillatory state preventing the system to thermalize. Consequently there is a residual entanglement at low temperatures for arbitrary coupling strength. This entanglement is generated from environment nonperturbatively even when two modes are not entangled initially. When a distance of two oscillators are varied, competition between entanglement induced from environment and modified decoherence due to finite separation leads to the characteristic distance where entanglement is minimized. ∗E-mail address: [email protected] 1