Universal pairing-gap measurement proposal by dynamical excitations in a two-dimensional doped attractive Fermi-Hubbard model with spin-orbit coupling

By calculating the dynamical structure factor of the two-dimensional doped attractive Fermi-Hubbard model with Rashba spin-orbit coupling (SOC), we not only investigate collective modes and single-particle excitations of the system during the phase transition between the Bardeen-Cooper-Schrieffer superfluid and topological superfluid, but also propose a universal method to measure the pairing gap in an optical lattice system. Our numerical results show that the area of the molecular excitation peak at the transferred momentum $\mathbf{q}=[\ensuremath{\pi},\ensuremath{\pi}]$ is proportional to the square of the pairing gap in the system with Rashba SOC. In particular, this method is very sensitive to the pairing gap. We verify that this method is universal to measure the pairing gap in a doped optical lattice with Rashba SOC. These theoretical results are important for experimentally measuring the pairing gap and studying the topological superfluid in an optical lattice.