We present a novel theoretical approach for computing and analyzing two-dimensional spectroscopy of bosonic collective excitations in disordered many-body systems. Specifically, we employ the Keldysh formalism to derive, within a non-pertubative treatment of disorder effects, the third-order nonlinear response and obtain two-dimensional spectroscopy maps. In the weak nonlinear regime of our formalism, we demonstrate the ability of the echo peak to distinguish between elastic and inelastic scattering processes, in perfect agreement with the intuition developed in isolated two-level systems. Furthermore, we discuss unique many-body effects on the echo peak signature arising from interaction induced quantum fluctuations. In particular, we show that these quantum fluctuations induce a finite nonrephasable broadening and examine how the echo peak is influenced by the attractive or repulsive nature of the collective excitations.

The interplay of magnetic excitations and itinerant charge carriers is a ubiquitous phenomenon in strongly correlated electron systems. In the vicinity of magnetically ordered phases, strong interactions between itinerant quasiparticles and magnetic excitations can result in the dramatic renormalization of both. A key theoretical question is understanding the renormalization of the magnon quasiparticle, a collective spin excitation, upon doping a magnetic insulator. Here, we report the observation of a new type of quasiparticle arising from the dressing of a magnon with the doped holes of a cold atom Fermi-Hubbard system, i.e. a magnon-Fermi-polaron. Utilizing Raman excitation with controlled momentum in a doped, spin-polarized band insulator, we address the spectroscopic properties of the magnon-polaron. In an undoped system with strong interactions, photoexcitation produces magnons, whose properties are accurately described by spin wave theory. We measure the evolution of the photoexcitation spectra as we move away from this limit to produce magnon-polarons due to dressing of the magnons by charge excitations. We observe a shift in the polaron energy with doping that is strongly dependent on the injected momentum, accompanied by a reduction of spectral weight in the probed energy window. We anticipate that the technique introduced here, which is the analog of inelastic neutron scattering, will provide atomic quantum simulators access to the dynamics of a wide variety of excitations in strongly correlated phases.

Quantum interference can deeply alter the nature of many-body phases of matter. In the paradigmatic case of the Hubbard model, Nagaoka famously proved that introducing a single itinerant charge can transform a paramagnetic insulator into a ferromagnet through path interference. However, a microscopic observation of such kinetic magnetism induced by individually imaged dopants has been so far elusive. Here we demonstrate the emergence of Nagaoka polarons in a Hubbard system realized with strongly interacting fermions in a triangular optical lattice. Using quantum gas microscopy, we reveal these polarons as extended ferromagnetic bubbles around particle dopants arising from the local interplay of coherent dopant motion and spin exchange. In contrast, kinetic frustration due to the triangular geometry promotes antiferromagnetic polarons around hole dopants, as proposed by Haerter and Shastry. Our work augurs the exploration of exotic quantum phases driven by charge motion in strongly correlated systems and over sizes that are challenging for numerical simulation.

The emergence of quasiparticles in quantum many-body systems underlies the rich phenomenology in many strongly interacting materials. In the context of doped Mott insulators, magnetic polarons are quasiparticles that usually arise from an interplay between the kinetic energy of doped charge carriers and superexchange spin interactions. However, in kinetically frustrated lattices, itinerant spin polarons - bound states of a dopant and a spin-flip - have been theoretically predicted even in the absence of superexchange coupling. Despite their important role in the theory of kinetic magnetism, a microscopic observation of these polarons is lacking. Here we directly image itinerant spin polarons in a triangular lattice Hubbard system realised with ultracold atoms, revealing enhanced antiferromagnetic correlations in the local environment of a hole dopant. In contrast, around a charge dopant, we find ferromagnetic correlations, a manifestation of the elusive Nagaoka effect. We study the evolution of these correlations with interactions and doping, and use higher-order correlation functions to further elucidate the relative contributions of superexchange and kinetic mechanisms. The robustness of itinerant spin polarons at high temperature paves the way for exploring potential mechanisms for hole pairing and superconductivity in frustrated systems. Furthermore, our work provides microscopic insights into related phenomena in triangular lattice moiré materials.

We analyze the formation of multiparticle bound states in ladders with frustrated kinetic energy in two-component bosonic and two-component fermionic systems. We focus on the regime of light doping relative to insulating states at half-filling, spin polarization close to 100%, and strong repulsive interactions. A special feature of these systems is that the binding energy scales with single-particle tunneling t rather than exchange interactions, since effective attraction arises from alleviating kinetic frustration. For two-component Fermi systems on a zigzag ladder we find a bound state between a hole and a flipped spin (magnon) with a binding energy that can be as large as 0.6t. We demonstrate that magnon-hole attraction leads to formation of clusters comprising several holes and magnons, and we expound on antiferromagentic correlations for the transverse spin components inside the clusters. We identify several many-body states that result from self-organization of multiparticle bound states, including a Luttinger liquid of hole-magnon pairs and a density wave state of two-hole–three-magnon composites. We establish a symmetry between the spectra of Bose and Fermi systems and use it to establish the existence of antibound states in two-component Bose mixtures with SU(2) symmetric repulsion on a zigzag ladder. We also consider Bose and Fermi systems on a square ladder with flux and demonstrate that both systems support bound states. We discuss experimental signatures of multiparticle bound states in both equilibrium and dynamical experiments. We point out intriguing connections between these systems and the quark bag model in QCD. Published by the American Physical Society 2024

Quantum simulations with ultracold fermions in triangular optical lattices have recently emerged as a new platform for studying magnetism in frustrated systems. Experimental realizations of the Fermi Hubbard model revealed striking contrast between magnetism in bipartite and triangular lattices. In bipartite lattices magnetism peaks at half filling, and doped charge carriers tend to suppress magnetic correlations. In triangular lattices for large $U/t$, magnetism is enhanced by doping away from $n=1$ because kinetic energy of dopants can be lowered through developing magnetic correlations. This corresponds to formation of magnetic polarons, with hole and doublon doping resulting in antiferro- and ferromagnetic polarons respectively. Snapshots obtained with quantum gas microscopes revealed formation of magnetic polarons around dopants at temperatures exceeding the superexchange energy scale. In this work we discuss theoretically that additional insight into properties of magnetic polarons can be achieved using spectroscopic experiments with ultracold atoms. We consider starting from a spin polarized state with small hole doping and applying a two-photon Raman photoexcitation, which transfers atoms into a different spin state. We show that such magnon injection spectra exhibit a separate peak corresponding to formation of a bound state between a hole and a magnon. This polaron peak is separated from the simple magnon spectrum by energy proportional to single particle tunneling and can be easily resolved with currently available experimental techniques. For some momentum transfer there is an additional peak corresponding to photoexciting a bound state between two holes and a magnon. We point out that in two component Bose mixtures in triangular lattices one can also create dynamical magnetic polarons, with one hole and one magnon forming a repulsive bound state.

We use density matrix renormalization group to investigate the phase diagram of the Fermi Hubbard model on a triangular lattice with densities above half-filling, 1 ≤ n < 2. We discuss the important role of kinetic magnetism and magnetic polarons. For strong interactions and low doublon dopings, attractive interaction between polarons results in phase separation between the fully polarized state at finite doping and the commensurate spin-density wave state at half-filling. For intermediate interaction strength and small doping, competition between antiferromagnetic superexchange and kinetic magnetism gives rise to the incommensurate spin density wave (I-SDW) phase. Fully polarized ferromagnetic (FPF) phase for weak interactions is limited to dopings close to the van Hove singularity in the density of states. With increasing interactions the FPF phase expands to lower dopings. For strong interactions it reaches the low doping regime and is better understood as arising from proliferation of Nagaoka-type ferromagnetic polarons. Other phases that we find include a partially polarized phase, another type of I-SDW at high densities, and Müller-Hartmann ferromagnetism close to the band insulating regime.

We study the formation of particle-imbalanced quantum droplets in a one-dimensional optical lattice containing a binary bosonic mixture at zero temperature. To understand the effects of the imbalance from both the few- and many-body perspectives, we employ density matrix renormalization group (DMRG) simulations and perform the extrapolation to the thermodynamic limit. In contrast to the particle-balanced case, not all bosons are paired, resulting in an interplay between bound states and individual atoms that leads to intriguing phenomena. Quantum droplets manage to sustain a small particle imbalance, resulting in an effective magnetization. However, as the imbalance is further increased, a critical point is eventually crossed, and the droplets start to expel the excess particles while the magnetization in the bulk remains constant. Remarkably, the unpaired particles on top of the quantum droplet effectively form a super Tonks-Girardeau (hard-rod) gas. The expulsion point coincides with the critical density at which the size of the super Tonks-Girardeau gas matches the size of the droplet.

We propose a mechanism for liquid formation in strongly correlated lattice systems. The mechanism is based on an interplay between long-range attraction and superexchange processes. As an example, we study dipolar bosons in one-dimensional optical lattices. We present a perturbative theory and validate it in comparison with full density-matrix renormalization group simulations for the energetic and structural properties of different phases of the system, i.e., self-bound Mott insulator, liquid, and gas. We analyze the nonequilibrium properties and calculate the dynamic structure factor. Its structure differs in compressible and insulating phases. In particular, the low-energy excitations in compressible phases are linear phonons. We extract the speed of sound and analyze its dependence on dipolar interaction and density. We show that it exhibits a nontrivial behavior owing to the breaking of Galilean invariance. We argue that an experimental detection of this previously unknown quantum liquid could provide a fingerprint of the superexchange process and open intriguing possibilities for investigating non-Galilean invariant liquids.

Magnetic properties of materials ranging from conventional ferromagnetic metals to strongly correlated materials such as cuprates originate from Coulomb exchange interactions. The existence of alternate mechanisms for magnetism that could naturally facilitate electrical control has been discussed theoretically 1 – 7 , but an experimental demonstration 8 in an extended system has been missing. Here we investigate MoSe 2 /WS 2 van der Waals heterostructures in the vicinity of Mott insulator states of electrons forming a frustrated triangular lattice and observe direct evidence of magnetic correlations originating from a kinetic mechanism. By directly measuring electronic magnetization through the strength of the polarization-selective attractive polaron resonance 9 , 10 , we find that when the Mott state is electron-doped, the system exhibits ferromagnetic correlations in agreement with the Nagaoka mechanism.

We study kinetic magnetism for the Fermi-Hubbard models in triangular type lattices, including a zigzag ladder, four- and six-legged triangular cylinders and a full two- dimensional triangular lattice. We focus on the regime of strong interactions, $U\gg t$ and filling factors around one electron per site. For temperatures well above the hopping strength, the Curie-Weiss form of the magnetic susceptibility suggests effective antiferromagnetic correlations for systems that are hole doped with respect to $\nu=1$, and ferromagnetic correlations for systems with electron dopings. We show that these correlations arise from magnetic polaron dressing of charge carrier propagating in a spin incoherent Mott insulator. Effective interactions corresponding to these correlations can strongly exceed the magnetic super-exchange energy. In the case of hole doping, antiferromagnetic polarons originate from kinetic frustration of individual holes in a triangular lattice. In the case of electron doping, Nagaoka type ferromagnetic correlations are induced by propagating doublons. These results provide a theoretical explanation of recent experimental results in moire TMDC materials. To understand many-body states arising from antiferromagentic polarons at low temperatures, we study hole doped systems in finite magnetic fields. At low dopings and intermediate magnetic fields we find a magnetic polaron phase, separated from the fully polarized state by a metamagnetic transition. With decreasing magnetic field the system shows a tendency to phase separate, with hole rich regions forming antiferromagnetic spinbags. We demonstrate that direct observations of magnetic polarons in triangular lattices can be achieved in experiments with ultracold atoms, which allow measurements of three point hole-spin-spin correlations.

We provide a detailed presentation of the functional renormalisation group (FRG) approach for weakly-interacting Bose–Bose mixtures, including a complete discussion on the RG equations. To test this approach, we examine thermodynamic properties of balanced three-dimensional Bose–Bose gases at zero and finite temperatures and find a good agreement with related works. We also study ground-state energies of repulsive Bose polarons by examining mixtures in the limit of infinite population imbalance. Finally, we discuss future applications of the FRG to novel problems in Bose–Bose mixtures and related systems.

We consider interacting one-dimensional bosons in the universal low-energy regime. The interactions consist of a combination of attractive and repulsive parts that can stabilize quantum gases, droplets, and liquids. In particular, we study the role of effective three-body repulsion, in systems with weak attractive pairwise interactions. Its low-energy description is often argued to be equivalent to a model including only two-body interactions with nonzero range. Here, we show that, at zero temperature, the equations of state in both theories agree quantitatively at low densities for overall repulsion, in the gas phase. However, this agreement is absent in the attractive regime, where universality only occurs in the long-distance properties of quantum droplets. We develop analytical tools to investigate the properties of the theory and obtain astounding agreement with exact numerical calculations using the density-matrix renormalization group.

We analyze the formation of multi-particle bound states in ladders with frustrated kinetic energy in two component bosonic and two component fermionic systems. We focus on the regime of light doping relative to insulating states at half-filling, spin polarization close to 100 percent, and strong repulsive interactions. A special feature of these systems is that the binding energy scales with single particle tunneling $t$ rather than exchange interactions, since effective attraction arises from alleviating kinetic frustration. For two component Fermi systems on a zigzag ladder we find a bound state between a hole and a flipped spin (magnon) with a binding energy that can be as large as $0.6t$. We demonstrate that magnon-hole attraction leads to formation of clusters comprised of several holes and magnons and expound on antiferromagentic correlations for the transverse spin components inside the clusters. We identify several many-body states that result from self-organization of multi-particle bound states, including a Luttinger liquid of hole-magnon pairs and a density wave state of two hole - three magnon composites. We establish a symmetry between the spectra of Bose and Fermi systems and use it to establish the existence of antibound states in two component Bose mixtures with SU(2) symmetric repulsion on a zigzag ladder. We also consider Bose and Fermi systems on a square ladder with flux and demonstrate that both systems support bound states. We discuss experimental signatures of multi-particle bound states in both equilibrium and dynamical experiments. We point out intriguing connections between these systems and the quark bag model in QCD.

We study weakly-repulsive Bose-Bose mixtures in two and three dimensions at zero temperature using the functional renormalization group (FRG). We examine the RG flows and the role of density and spin fluctuations. We study the condition for phase separation and find that this occurs at the mean-field point within the range of parameters explored. Finally, we examine the energy per particle and condensation depletion. We obtain that our FRG calculations compare favorably with known results from perturbative approaches for macroscopic properties.

We consider interacting one-dimensional bosons in the universal low-energy regime. The interactions consist of a combination of attractive and repulsive parts that can stabilize quantum gases, droplets and liquids. In particular, we study the role of effective three-body repulsion, in systems with weak attractive pairwise interactions. Its low-energy description is often argued to be equivalent to a model including only two-body interactions with non-zero range. Here, we show that, at zero temperature, the equations of state in both theories agree quantitatively at low densities for overall repulsion, in the gas phase, as can be inferred from the $S$-matrix formulation of statistical mechanics. However, this agreement is absent in the attractive regime, where universality only occurs in the long-distance properties of quantum droplets. We develop analytical tools to investigate the properties of the theory, and obtain astounding agreement with exact numerical calculations using the density-matrix renormalization group.

The ground-state properties of two-component bosonic mixtures in a one-dimensional optical lattice are studied both from few- and many-body perspectives. We rely directly on a microscopic Hamiltonian with attractive inter-component and repulsive intra-component interactions to demonstrate the formation of a quantum liquid. We reveal that its formation and stability can be interpreted in terms of finite-range interactions between dimers. We derive an effective model of composite bosons (dimers) which correctly captures both the few- and many-body properties and validate it against exact results obtained by DMRG method for the full Hamiltonian. The threshold for the formation of the liquid coincides with the appearance of a bound state in the dimer-dimer problem and possesses a universality in terms of the two-body parameters of the dimer-dimer interaction, namely scattering length and effective range. For sufficiently strong effective dimer-dimer repulsion we observe fermionization of the dimers which form an effective Tonks-Girardeau state. Finally, we identify conditions for the formation of a solitonic solution.

Ivan Morera, 2, 3 Annabelle Bohrdt, 4, 5, 6 Wen Wei Ho, 7, 8 and Eugene Demler 9 Departament de F́ısica Quàntica i Astrof́ısica, Facultat de F́ısica, Universitat de Barcelona, E-08028 Barcelona, Spain Institut de Ciències del Cosmos, Universitat de Barcelona, ICCUB, Mart́ı i Franquès 1, E-08028 Barcelona, Spain Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA∗ Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA MIT-Harvard Center for Ultracold Atoms, Cambridge, MA, USA Department of Physics, Stanford University, Stanford, CA 94305, USA Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland (Dated: June 18, 2021)

We study the properties of a single impurity in a dilute Bose gas, a Bose polaron, using the functional renormalization group. We use an ansatz for the effective action motivated by a derivative expansion, and we compute the energies of the attractive and repulsive branches of excitations in both two and three spatial dimensions. Three-body correlations play an important role in the attractive branch, and we account for those by including three-body couplings between two bath bosons and the impurity. Our calculations compare very favorably with state-of-the-art experimental measurements and numerical simulations.