Quantum non-Markovian reservoirs of atomic condensates engineered via dipolar interactions

We investigate the quantum dephasing dynamics of an impurity qubit immersed in a quasi-two-dimensional dipolar Bose-Einstein condensate whose collective excitations act as a reservoir for the qubit. We show that the properties of the environment are highly engineerable through the relative strength of the dipolar and contact interactions such that qubit's dephasing dynamics could be Markovian, weak non-Markovian, or even highly non-Markovian. It is also revealed that the appearance of the roton excitation is responsible for the highly non-Markovian dephasing dynamics. Since rotonlike dispersions also appear in condensates placed in cavities or with spin-orbit couplings, our results pave the way for searching for systems that are suitable environment engineering.