Floquet-Engineered Hybrid Topological Orders with Majorana Edge Modes in Number-Conserving Fermionic Quantum Simulators

We develop an experimental protocol based on Floquet-engineered ultracold fermions in optical lattices, enabling the emulation of pair-hopping and competing singlet/triplet pairing interactions. Through large-scale density matrix renormalization group (DMRG) simulations, we uncover three emergent topological phases: (i) A Majorana-enabled spin-density-wave (MS) phase featuring exponentially localized edge charges, non-local fermionic edge correlations, and doubly degenerate entanglement spectra; (ii) A z-axis polarized triplet superconducting (TS) phase exhibiting fractionalized edge spins (S=1/4 per edge), two-fold ground state degeneracy and a bulk single-particle gap; (iii) A hybrid x-directional triplet superconducting (XTS) phase that uniquely combines fractional spin textures and Majorana-type edge correlations, defining a new universality class of hybrid orders in number-conserving systems. These findings establish a universal framework for engineering non-Abelian topological matter, crucially bypassing the need for external pairing fields while maintaining experimental feasibility with current cold-atom techniques.