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Quantum correlations can be used as a resource for quantum computing, eg forquantum state manipulation, and for quantum sensing, eg for creatingnon-classical states which allow to achieve the quantum advantage regime. Thisreview collects the predictions coming from a family of exact solutions whichallows to describe the many-body wavefunction of strongly correlated quantumfluids confined by a tight waveguide and subjected to any form of longitudinalconfinement. It directly describes the experiments with trapped ultracold atomswhere the strongly correlated regime in one dimension has been achieved. Theexact solution applies to bosons, fermions and mixtures. It allows to obtainexperimental observables such as the density profiles and momentum distributionat all momentum scales, beyond the Luttinger liquid approach. It also predictsthe exact quantum dynamics at all the times, including the small oscillationsregime yielding the collective modes of the system and the large quench regimewhere the system parameters are changed considerably. The solution can beextended to describe finite-temperature conditions, spin and magnetizationeffects. The review illustrates the idea of the solution, presents the keytheoretical achievements and the main experiments on strongly correlatedone-dimensional quantum gases.

Strongly interacting trapped one-dimensional quantum gases: an exact solution