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Pairing sizes in attractively interacting Fermi gases with Spin-orbit Couplings

Extensive research has been lavished on effects of spin-orbit couplings (SOC) in attractively interacting Fermi systems in both neutral cold atom systems and condensed matter systems. Recently, it was suggested that a SOC drives a new class of BCS to BEC crossover which is different than the conventional one without a SOC. Here, we explore what are the most relevant physical quantities to describe such a new BCS to BEC crossover and their experimental detections. We extend the concepts of the pairing length and "Cooper-pair size" in the absence of SOC to Fermi systems with SOC. We investigate the dependence of chemical potential, pairing length, "Cooper-pair size" on the SOC strength and the scattering length at $ 3d $ (the bound state energy at $ 2d $) for three attractively interacting Fermi gases with 3 dimensional (3d) Rashba, 3d Weyl and 2d Rashba SOC respectively. We show that only the pairing length can be used to characterize this new BCS to BEC crossover. Furthermore, it is the only length which can be directly measured by radio-frequency dissociation spectra type of experiments. We stress crucial differences among the pairing length, "Cooper-pair size " and the two-body bound state size. Our results provide the fundamental and global picture of the new BCS to BEC crossover and its experimental detections in various cold atom and condensed matter systems.