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We theoretically investigate the ground state of trapped neutral fermionswith population imbalance in the BCS-BEC crossover regime. On the basis of thesingle-channel Hamiltonian, we perform full numerical calculations of theBogoliubov-de Gennes equation coupled with the regularized gap and numberequations. The zero-temperature phase diagram in the crossover regime ispresented, where the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing stategoverns the weak-coupling BCS region of a resonance. It is found that the FFLOoscillation vanishes in the BEC side, in which the system under populationimbalance turns into a phase separation (PS) between locally binding superfluidand fully polarized spin domains. We also demonstrate numerical calculationswith a large particle number O(10^5), comparable to that observed in recentexperiments. The resulting density profile on a resonance yields the PS, whichis in good agreement with the recent experiments, while the FFLO modulationexists in the pairing field. It is also proposed that the most favorablelocation for the detection of the FFLO oscillation is in the vicinity of thecritical population imbalance in the weak coupling BCS regime, where theoscillation periodicity becomes much larger than the interparticle spacing.Finally, we analyze the radio-frequency (RF) spectroscopy in the imbalancedsystem. The clear difference in the RF spectroscopy between BCS and BEC sidesreveals the structure of the pairing field and local ``magnetization''.

Imbalanced Superfluid Phase of a Trapped Fermi Gas in the BCS-BEC Crossover Regime