Enhancement of non-Markovianity due to environment-induced indirect interaction

Non-Markovian effects are often significant when the system-environment coupling is not weak. Indeed, we find the non-Markovianity to be negligible for a single two-level system undergoing pure dephasing via interaction with a harmonic oscillator environment. In this paper, we examine a natural extension, namely a pure dephasing model where a collection of two-level systems interacts with a common environment. We obtain analytically the dynamics of the collection of the two-level systems, and then take a partial trace over all the two-level systems except one. This remaining single two-level system is shown to display markedly non-Markovian dynamics, even in the weak system-environment coupling regime. This is due to the indirect interaction between two-level systems induced by their interaction with the common environment. In fact, this indirect interaction can not only increase the non-Markovianity by orders of magnitude, but also display qualitatively different characteristics. For instance, for a single two-level system undergoing pure dephasing, the dynamics are Markovian for Ohmic and sub-Ohmic environments. This is markedly not the case when we consider multiple two-level systems. We also show that the non-Markovianity increases as we increase the number of two-level systems. These findings provide insights into controlling decoherence in multi-qubit quantum systems and have implications for quantum technologies where non-Markovianity can be a resource rather than a limitation.