Beyond Conventional Pairing: Bosonic Quartic Superfluidity, Exotic XY Magnetism, and Phase Criticality

We report two unprecedented bosonic quartic superfluid (BQSF) phases in binary boson mixtures with synthetic pair-hopping (SPH) interaction realizable through Floquet engineering, transcending the conventional bosonic superfluidity paradigm via high-order correlations. Through extensive numerical simulations, we demonstrate: (i) The paired super-counter-fluid (PSCF) phase that exhibits bosonic 'four-particle' correlations, directly mirroring fermionic 4e superconductivity; (ii) The symbiotic super-counter-fluid which is an anomalous quantum phase featuring intrinsically intertwined, non-zero PSCF and super-counter-fluid orders. Both phases further reveal unreported pseudo-spin-ordered XY ferromagnetic states with filling-dependent magnetization textures. Adjacent to BQSF phases, we uncover both a previously unreported quantum quadruple critical point induced by interexchange asymmetry and SPH-driven state-dependent criticality-the latter exhibiting distinct behavior from conventional two-component bosonic systems. We propose momentum-resolved noise correlation spectroscopy-building on established quantum gas microscopy techniques-as a direct probe for the characteristic signatures of these BQSF states. Our results establish a new paradigm in quantum matter, opening unprecedented avenues to explore (i) quartic quantum coherence, (ii) emergent collective phenomena, and (iii) extended XY magnetism-resolving a longstanding classification challenge while discove