Quantum many-body problems are ubiquitous in modern physics across a wide range of research fields. One of the most important challenges is the elucidation of dense matter properties relevant to neutron star physics. While numerous attempts have been made to address this problem within nuclear many-body theories, we pursue an alternative approach by exploiting an analogy with ultracold atomic systems. In this talk, we discuss a microscopic mechanism of the hadron-quark crossover that occurs in dense matter, drawing an analogy with the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover established in ultracold atomic experiments. Moreover, we present our recent theoretical progress on a tunable three-body force in ultracold atoms, in analogy with the Fujita Miyazawa three-nucleon force.