We study attractively interacting binary mixtures of fermionic particles confined in one-dimensional harmonic traps. The properties of balanced and unbalanced systems are systematically investigated using an exact diagonalization approach, focusing on finite temperature effects. Specific non-classical pairing correlations are analyzed in terms of noise correlations using single-particle and two-particle density distributions. This quantity is directly accessible in state-of-the-art experiments with ultracold atoms. With increasing temperature, the unbalanced system hosting the Fulde-Ferrel-Larkin-Ovchinnikov pair crosses to the standard his Bardeen-Cooper-Schrieffer pair characterized by zero net momentum of the resulting pair. shown to be over. By performing calculations for systems with different imbalances, the approximate boundary between two phases on the phase diagram is determined.
