In particular, for a box-confined medium repulsive impurity-medium couplings lead, due to attractive induced interactions, to the localization of the impurities around the trap center. Accordingly the impurities dynamical response, triggered by ramping down the central potential barrier, is affected by the medium's trapping geometry. The interval of existence of these phases depends strongly on the impurity-impurity interactions and external confinement of the medium. Specifically, bound impurity structures reminiscent of bipolarons for strong attractive couplings as well as configurations with two clustered or separated impurities in the repulsive case are identified. We determine the ground state phase diagram of the system according to the impurity-medium entanglement and the impurities two-body correlations. The counterflow many-body dynamics of two impurities in a double-well coupled to an one-dimensional bosonic medium is explored. We conclude by giving an outlook on possible future directions that are interesting to explore in these correlated systems. Besides describing the fundamental physical phenomena arising in these systems, we also provide an overview of the tools and methods that are commonly used, thus delivering a balanced and comprehensive overview of the field. We mainly focus on bosonic systems in one dimension and provide an introduction to the well-known static properties before we discuss the state-of-the-art quantum dynamical processes stimulated by the presence of correlations. In this review, we discuss recent advances in few-body cold atom systems confined in low dimensions from a theoretical viewpoint. In particular, it is possible to operate in lower dimensions and drive atomic systems in the strongly correlated regime.
The accelerating developments in the field have led to a highly advanced set of engineering techniques that, among others, can tune interactions, shape the external geometry, select among a large set of atomic species with different properties, as well as control the number of atoms. Cold atomic gases have become a paradigmatic system for exploring fundamental physics, while at the same time allowing to explore applications in quantum technologies.
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