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
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
We study two-component (or pseudospin-1/2) bosons with pair hopping interactions in synthetic dimension, for which a feasible experimental scheme on a square optical lattice is also presented. Previous studies have shown that two-component bosons with on-site interspecies interaction can only generate nontrivial interspecies paired superfluid (super-counter-fluidity or pair-superfluid) states. In contrast, apart from interspecies paired superfluid, we reveal two new phases by considering this additional pair hopping interaction. These novel phases are intraspecies paired superfluid (molecular superfluid) and an exotic noninteger Mott insulator which shows a noninteger atom number at each site for each species, but an integer for total atom number.
Inspired by the recent experimental advances in cold atom quantum simulators, we explore the experimentally implemented bosonic t-t^{'}-J model on the square lattice using large-scale density matrix renormalization group simulations. By tuning the doping level δ and hopping ratio t^{'}/t, we uncover six distinct quantum phases, several of which go far beyond the conventional paradigm of phase-coherent superfluidity (SF) expected for bosonic systems. In particular, in the presence of antiferromagnetic (AFM) order, doped holes are tightly bound into pairs, giving rise to a pair density wave phase at low doping and small |t^{'}/t|, which is suppressed on the t^{'}<0 side, resulting in a disordered pair density wave state that lacks coherence of either individual bosons or pairs. Upon further doping, bosons can regain phase coherence and form an SF* state, characterized by condensation at emergent incommensurate momenta concurrent with an incommensurate magnetic order. On the t^{'}>0 side, the sign-induced kinetic frustration inherently disfavors local AFM correlations, leading to a phase separation in which doped holes cluster into ferromagnetic (FM) domains spatially separated by undoped AFM regions. Upon further doping, this inhomogeneous state evolves into a uniform SF+xy-FM phase. Finally, we propose a concrete experimental scheme to realize both signs of t^{'}/t in Rydberg tweezer arrays, with an explicit mapping between model parameters and experimentally accessible regimes. Our results reveal competing and intertwined orders in doped antiferromagnets, which are relevant to central issues in high-T_{c} superconductivity, reflecting the frustrated interplay between doped holes and spin background.
Fermionic many-body systems provide an unrivaled arena to investigate how interactions drive the emergence of collective quantum behavior, such as macroscopic coherence and superfluidity. Central to these phenomena is the formation of Cooper pairs, correlated states of two fermions that behave as composite bosons and condense below a critical temperature. However, unlike elementary bosons, these pairs retain their internal structure set by underlying fermionic correlations, essential for understanding superfluid properties throughout the so-called Bose-Einstein condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover -- a cornerstone of strongly correlated fermionic matter. Here, we harness a sonic analog of the optical Sagnac effect to disclose the composite nature of fermionic condensates across the BEC-BCS crossover. We realize an in-situ loop interferometer by coherently exciting two counter-propagating long-wavelength phonons of an annular fermionic superfluid with tuneable interparticle interactions. The frequency degeneracy between clock- and anticlock-wise sound modes is lifted upon controllably injecting a quantized supercurrent in the superfluid ring, resulting in a measurable Doppler shift that enables us to probe the elementary quantum of circulation and the angular momentum carried by each particle in the fermionic fluid. Our observations directly reveal that the superflow circulation is quantized in terms of h/2m, where m is the mass of the constituents, in striking contrast to bosonic condensates where h/m is the relevant circulation quantum. Further, by operating our interferometer at tunable temperature, we measure the thermal depletion of the superfluid in the unitary Fermi gas, demonstrating phonon interferometry as a powerful technique for probing fundamental properties of strongly-correlated quantum systems.
The study of strongly correlated quantum matter has revealed numerous exotic phases beyond the conventional Landau Fermi liquid paradigm. Non-Fermi liquid (NFL) behavior, characterized by the breakdown of the quasiparticle concept and anomalous scaling laws for thermodynamic and transport properties, is a central theme in this field. While extensively investigated near quantum critical points in condensed matter systems, the emergence of NFL states in non-equilibrium, driven quantum systems, particularly in synthetic quantum matter platforms such as ultracold atomic Bose-Fermi mixtures, remains a frontier of research. This paper explores the theoretical framework and potential mechanisms for the emergence of NFL behavior in Bose-Fermi mixtures subjected to periodic driving (Floquet engineering) or quantum quenches. We review the fundamental properties of Fermi liquids and NFLs, delve into the intricacies of Bose-Fermi mixtures and non-equilibrium dynamics, and propose a methodology for investigating such emergent phenomena. We discuss expected experimental signatures, including anomalous spectral functions, power-law resistivity, and altered entanglement properties, providing a comprehensive perspective on how driving can sculpt novel quantum phases. The findings suggest a rich interplay between bosonic and fermionic degrees of freedom under non-equilibrium conditions, potentially leading to new avenues for quantum control and the discovery of universal NFL physics.
Fermionic condensation typically occurs via pairing. In recent decades, however, a fundamental question has emerged: whether alternative forms of order exist, such as condensates of fermion quadruplets. These states--including ``charge-4e" superconductors and ``charge-0" counterflow condensates--lie beyond the standard Bardeen-Cooper-Schrieffer framework, and require strong fluctuations and correlation effects that invalidate the BCS mean-field description. This makes the problem notoriously difficult to study numerically at a microscopic level, as it involves both strong interactions and the fermionic sign problem. Here, we present a microscopic fermionic model featuring correlated hopping that significantly mitigates the sign problem, enabling rigorous Monte-Carlo-based analysis. Using large-scale simulations, we demonstrate the existence of a fermion-quadrupling condensate with a transition temperature comparable to the hopping energy scale. These results provide direct numerical evidence for quartic fermionic order in a microscopic system and suggest that these exotic states are also experimentally accessible in ultracold atomic gases.
We study possible many body phenomena in the Quantum Anomalous Hall system of weakly interacting spinor bosons in a square lattice. There are various novel spin-bond correlated superfluids (SF) and quantum or topological phase transitions among these SF phases. One transition is a first order one driven by roton droppings ( but with non-zero gaps $ Δ_R $ ) tuned by the Zeeman field $ h $. Another is a second order bosonic Lifshitz transition with the dynamic exponents $ z_x=z_y=2 $ and an accompanying $ [C_4 \times C_4]_D $ symmetry breaking. It is driven by the softening of the superfluid Goldstone mode tuned by the ratio of spin-orbit coupled (SOC) strength over the hopping strength. The two phase boundaries meet at a topological tri-critical (TT) point which separates the $ h=0 $ line into two SF phases with $ N=2 $ and $ N=4 $ condensation momenta respectively. At the $ h=0 $ line where the system has an anti-unitary $ Z_2 $ Reflection symmetry, there are infinite number of classically degenerate family of states on both sides. We perform a systematic order from quantum disorder analysis to find the quantum ground states, also calculate the roton gaps $ Δ_R $ generated by the order from disorder mechanism on both sides of the TT point. The $ N=2 $ and $ N=4 $ SF phases have the same spin-orbital XY-AFM spin structure, respect the anti-unitary symmetry and break the $ [C_4 \times C_4]_D $ symmetry, so they be distinguished only by the different topology of the BEC condensation momenta instead of by any differences in the symmetry breaking patterns. All these novel quantum or topological phenomena can be probed in the recent experimentally realized weakly interacting Quantum Anomalous Hall (QAH) model of $ ^87 Rb $ by Wu, {\sl et.al}, Science 354, 83-88 (2016).