We study quantum information flow in a model comprised of a trapped impurity qubit immersed in a BoseEinstein-condensed reservoir. We demonstrate how information flux between the qubit and the condensate can be manipulated by engineering the ultracold reservoir within experimentally realistic limits. We show that this system undergoes a transition from Markovian to non-Markovian dynamics, which can be controlled by changing key parameters such as the condensate scattering length. In this way, one can realize a quantum simulator of both Markovian and non-Markovian open quantum systems, the latter ones being characterized by a reverse flow of information from the background gas (reservoir) to the impurity (system). More recently, hybrid systems composed of quantum dots, single trapped ions, and optical lattices coupled to Bose-Einstein condensates (BECs) have been studied both theoretically and experimentally [5]. These systems are studied in the framework of open quantum systems [6], effectively described as one or more two-level systems (qubits) interacting with a reservoir consisting of the ultracold gas. The possibility of manipulating crucial parameters of the reservoir, such as the scattering length [7], combined with the continuous improvements in quantum control of qubits, highlights the enormous potential of hybrid systems as quantum simulators of both condensed-matter models and open quantum systems.In this Rapid Communication, we study a qubit system composed of an impurity atom trapped in a double-well potential, interacting with a BEC environment. This model has been shown to describe an effective pure-dephasing model [8]. Our focus is on the dynamics of quantum information between the qubit system and the ultracold reservoir. We show how information flux can be manipulated by experimentally achievable means, such as changing the scattering length, the effective dimension of the background gas, or the trapping geometry of the qubit.Recently, dynamics of information flow has been an active area of research in the open quantum systems community due to several proposals to link it to the division of quantum processes into Markovian and non-Markovian ones [9][10][11][12]. The latter ones have been defined as processes where an

A simple relationship between recently proposed measures of non-Markovianity and the Loschmidt echo is established, holding for a two-level system (qubit) undergoing pure dephasing due to a coupling with a many-body environment. We show that the Loschmidt echo is intimately related to the information flowing out from and occasionally back into the system. This, in turn, determines the non-Markovianity of the reduced dynamics. In particular, we consider a central qubit coupled to a quantum Ising ring in the transverse field. In this context, the information flux between system and environment is strongly affected by the environmental criticality; the qubit dynamics is shown to be Markovian exactly and only at the critical point. Therefore non-Markovianity is an indicator of criticality in the model considered here.

We present a detailed investigation of the dynamics of two physically different qubit models, dephasing under the effect of an ultracold atomic gas in a Bose-Einstein condensed (BEC) state. We study the robustness of each qubit probe against environmental noise; even though the two models appear very similar at a first glance, we demonstrate that they decohere in a strikingly different way. This result holds significance for studies of reservoir engineering as well as for using the qubits as quantum probes of the ultracold gas. For each model we study whether and when, upon suitable manipulation of the BEC, the dynamics of the qubit can be described by a (non-)Markovian process and consider the the effect of thermal fluctuations on the qubit dynamics. Finally, we provide an intuitive explanation for the phenomena we observe in terms of the spectral density function of the environment.Comment: 6 pages, 4 figure