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We present a full phase diagram for the one-dimensional (1D) tothree-dimensional (3D) crossover of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)state in an attractive Hubbard model of 3D-coupled chains in a har- monic trap.We employ real-space dynamical mean-field theory which describes full localquantum fluctuations beyond the usual mean-field and local densityapproximation. We find strong dimensionality effects on the shell structureundergoing a crossover between distinctive quasi-1D and quasi-3D regimes. Wepredict an optimal regime for the FFLO state that is considerably extended tointermediate interchain couplings and polarizations, directly realizable withultracold atomic gases. We find that the 1D-like FFLO feature is vulnerable tothermal fluctuations, while the FFLO state of mixed 1D-3D character can bestabilized at a higher temperature.

Fulde-Ferrell--Larkin-Ovchinnikov state in the dimensional crossover between one- and three-dimensional lattices