Two-channel physics in a lightly doped antiferromagnetic Mott insulator revealed by two-hole spectroscopy

Understanding pairing in the strong-coupling regime of doped Mott insulators remains an open problem in the context of cuprate superconductors. We perform ultra-high resolution numerical simulations of spectral functions in the highly underdoped $t-J$ model and discover two coupled branches of hole pairs emerging at low energies in the largely unexplored two-particle spectrum. As spin anisotropy is tuned from the Ising limit to the $SU(2)$-symmetric Heisenberg regime, the lowest $d$-wave pair evolves from a single bipolaronic branch into two hybridized branches separated by an avoided crossing. We explain this behaviour using an effective two-channel model involving a tightly bound bipolaronic state and a second channel associated with two magnetic polarons. The model reproduces the qualitative low-energy spectra and implies near-resonant $d$-wave interactions in the $SU(2)$-symmetric $t-J$ model, consistent with proximity to an emergent Feshbach-type resonance. To probe these predictions experimentally, we propose a Raman spectroscopy scheme for the attractive Hubbard model that can be directly implemented using ultracold atoms in optical lattices. Our work establishes two-particle spectroscopy, beyond single-particle Green's functions, as a powerful tool for revealing the microscopic origins of unconventional superconductivity.