Session P10: Hubbard Simulators

06.09 FOCUS SESSION: Hubbard SimulatorsHubbard Quantum Simulations - from Dipolar Quantum Solids to Kinetic Magnetism

Quantum simulations with ultracold atoms in optical lattices enter the next phase, in which we can extend bosonic and fermionic Hubbard models in a wide range of ways. Using magnetic long-ragne interacations we realize strongly correlated dipolar quantum gases in a Hubbard lattice and observe quantum-phase transitions to stripe and checkerboard phases. In our Fermi-Hubbard system we are making progress on lowering temperatures and observe Nagaoka Ferromagnetism, a surprising realization of kinetic magnetism, emerging as we introduce geometric spin frustration in a triangular Fermi-Hubbard lattice. We use floquet engineering to further extend the programmability of Hubbard simulators.   

Observation of Magnetic Polarons in a Triangular Hubbard Model with Kinetic Frustration

Itinerant spin polarons - bound quasiparticle states of magnons and charge dopants - have been predicted to emerge in two-dimensional Fermi-Hubbard models with frustration. These polarons are expected to be robust even at high temperatures since their binding energy is on the tunneling rather than the superexchange energy scale. I present results from the Princeton group's atomic triangular Fermi-Hubbard quantum simulator, which incorporates a bilayer imaging technique that allows us to access arbitrary n-point spin and charge correlation functions. Over a wide range of interactions, we observe the enhancement of antiferromagnetic ordering in the local environment of a hole dopant. Around a charge dopant, we witness enhanced ferromagnetic correlations, constituting a direct observation of Nagaoka polarons in an extended system. Additionally, higher order 4-point correlations allow us to directly compare the strengths of kinetic and superexchange magnetism in our system. Our results pave the path to studying more complex multi-particle bound states that can lead to hole pairing at high temperatures in frustrated systems.   

Frustration and Kinetic Magnetism in a Fermi-Hubbard Quantum Simulator

We report on recent experimental quantum simulations of strongly correlated materials with ultracold fermions, revealing emergent magnetic states in a Hubbard model with tunable geometric frustration and doping. Using an optical lattice that transitions from a square to a triangular geometry, we observe the transformation of a Néel antiferromagnet into a short-range 120° spiral state at half-filling due to frustration. Beyond half-filling, antiferromagnetic correlations strengthen with hole dopants but intriguingly reverse to ferromagnetic with particle dopants. By measuring three-point dopant-spin-spin correlations, we uncover the emergence of ferromagnetic polarons, offering the first cold-atom observation of Nagaoka ferromagnetism. Our work provides insights into kinetic magnetism, akin to observations in twisted TMD bilayers, and opens new avenues for exploring dopant pairing mediated by frustration.   

Kinetic magnetism in a frustrated Fermi-Hubbard system

Nagaoka famously proved that introducing a single itinerant charge to the half-filled Fermi-Hubbard model can transform a paramagnetic insulator into a ferromagnet through path interference. Such kinetic magnetism has recently been realized with strongly interacting fermions in a triangular optical lattice [1,2]. In this talk, I will give a quick summary of the experimental findings, including the emergence of Nagaoka polarons as extended ferromagnetic bubbles around particle dopants, and present theory results based on simulations of the model using the numerical linked-cluster expansions in support of these observations on both the square and triangular lattices. [1] Lebrat et al., arXiv:2308.12269 [2] Prichard et al., arXiv:2308.12951   

Observation of antiferromagnetic phase transition in the fermionic Hubbard model

The repulsive fermionic Hubbard model (FHM) is rather simple but captures essential features of electron behaviors in strongly correlated materials. At half filling, its ground state is characterized by an antiferromagnetic phase, which is reminiscent of the parent state in high-temperature cuprate superconductors. Introducing dopants into the antiferro-magnet, the fermionic Hubbard (FH) system is believed to give rise to various exotic quantum phases, including stripe order, pseudogap, and d-wave superconductivity. However, despite significant advances in quantum simulation of the FHM, realizing the low-temperature antiferromagnetic phase transition in a large-scale quantum simulator remains elusive. In this talk, I will present our recent progress on the realization of a low-temperature repulsive FH system in three dimensions, consisting of lithium-6 atoms in a uniform optical lattice with approximately 800,000 sites. Using spin-sensitive Bragg diffraction of light, we measure the spin structure factor (SSF) of the system. We observe divergences in the SSF by finely tuning the interaction strength, temperature, and doping concentration to approach their respective critical values for the phase transition, which are consistent with a power-law scaling in the Heisenberg universality class. Our results successfully demonstrate the antiferromagnetic phase transition in the FHM, paving the way for exploring the low-temperature phase diagram of the FHM.   

A strontium quantum-gas microscope for Bose- and Fermi-Hubbard quantum simulation

Alkaline-earth atoms offer exciting opportunities for quantum science in optical-lattice experiments. Atomic strontium, in particular, has many desirable properties for quantum simulation, such as its ultra-narrow clock transition, and the fact that it exhibits both bosonic and fermionic isotopes.

Here we present a quantum-gas microscope for ultracold strontium [1]. In our experiment we routinely prepare quantum gases of strontium, and load them into a clock-magic potential consisting of a 2D optical lattice and a light sheet. We successfully perform site-resolved fluorescence imaging using the blue 461-nm transition and simultaneous attractive Sisyphus cooling on the narrow 689-nm transition.

Our system allows us to operate with the bosonic isotope ⁸⁴Sr and realize the Bose-Hubbard model. We can also work with fermionic ⁸⁷Sr, and simulate the SU(N) Fermi-Hubbard model, with N =10, which displays exotic quantum-magnetism states. In this talk I will discuss the status of our setup and our current efforts to introduce an “clock” laser module.

[1] S. Buob et al., “A strontium quantum-gas microscope” arXiv: 2312.14818 (2023)   

Revealing fermion pair density waves via interaction quench

The 2D Fermi-Hubbard model with attractive interactions hosts a plethora of phases from the BEC-BCS crossover to charge density wave ordering. Such a gas with balanced spin populations is fully paired at low temperatures. However, in the strongly correlated regime where the kinetic and interaction energies are comparable, the pair size is similar to the pair-pair distance. This large pair size obscures the underlying pair ordering. A quench of the interaction energy associates the long range pairs to tightly bound, local pairs without creating new ones. This reveals the underlying spin and charge ordering previously hidden by the non-local nature of pairs. This was confirmed by comparing total spatial correlations with and without this rapid ramp using our quantum gas microscope with spin and charge resolved readout. We found that the charge density wave correlations of the gas are strongly enhanced with the rapid interaction quench and they persist at weak attractive interactions where the large pair size makes it harder to observe the ordering of pairs. The number of unpaired atoms also provide a tool for directly measuring pairing in a strongly correlated gas. In the case of complete pairing all the atoms form local pairs on doubly occupied sites after the rapid ramp. This opens the door for measuring polaronic correlations in many body paired systems.