  Pseudogap is a ubiquitous phenomenon in strongly correlated systems such as
high-$T_{\rm c}$ superconductors, ultracold atoms and nuclear physics. While
pairing fluctuations inducing the pseudogap are known to be enhanced in
low-dimensional systems, such effects have not been explored well in one of the
most fundamental 1D models, that is, Gaudin-Yang model. In this work, we show
that the pseudogap effect can be visible in the single-particle excitation in
this system using a diagrammatic approach. Fermionic single-particle spectra
exhibit a unique crossover from the double-particle dispersion to pseudogap
state with increasing the attractive interaction and the number density at
finite temperature. Surprisingly, our results of thermodynamic quantities in
unpolarized and polarized gases show an excellent agreement with the recent
quantum Monte Carlo and complex Langevin results, even in the region where the
pseudogap appears.
