Davies theory for reservoir-induced entanglement in a bipartite system

Abstract

Two mutually noninteracting qubits with identical modest coupling to one and the same reservoir are considered. For a given Hamiltonian and uncorrelated initial state, the mathematically rigorous Davies theory of the weak-coupling and van Hove limit provides a unique Markovian quantum master equation where absolutely none of the usually made additional assumptions and further approximations are introduced. Due to completely positive time evolution also no artificial correlations can arise. Numerical solution of the Markovian master equation shows that the qubits become entangled. In a first short time-interval containing one single maximum of entanglement for reservoir temperature T = 0, different choices of uncorrelated initial states give rise to a remarkable emergence of entanglement of different degree. The quantitative evaluation is analysed in terms of a measure derived from Wootters concurrence. Selected results show that there are even states that acquire the possible maximum. Particularly those states will show a periodic type of ‘collapse and revival’ behaviour with exponentially decaying envelope at longer times. This has never been reported so far for noninteracting qubits as mediated by simultaneous coupling to an uncontrollable reservoir. Moreover, even selected uncorrelated mixed states of modest degree of mixture may show a similar behaviour, although less pronounced. For T > 0 states with high degree of entanglement at T = 0 in the first time-interval still show a gradually reduced value up to a few tenth of Kelvin but for T ⩾ 33 K no effects can be observed. Finally, initially entangled states will slowly lose their oscillatory degree, again with exponential envelope, as the bipartite system approaches its stationary final state.