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arXiv:2503.03477 · Physical Review Letters

Dual Spectroscopy of Quantum Simulated Fermi-Hubbard Systems

K. Knakkergaard Nielsen, Martin W. Zwierlein, Georg M. Bruun

Published Jul 2, 2025• 4 citations
arXivHTMLPDF

Abstract

Quantum gas microscopy with atoms in optical lattices provides remarkable insights into the real space properties of many-body systems, but does not directly reveal the nature of their fundamental excitation spectrum. Here, we demonstrate that radio-frequency spectroscopy can reveal the quasiparticle nature of doped quantum many-body systems, crucial for our understanding of, e.g., high-temperature superconductors. In particular, we showcase how the existence and energy of magnetic polaron quasiparticles in doped Fermi-Hubbard systems may be probed, revealed by hallmark peaks in the spectroscopic spectrum. In combination with fundamental dualities of the Fermi-Hubbard model, we describe how these findings may be tested using several experimental platforms.

DOI
10.1103/yfqr-y9ks

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Quantum gas microscopy with atoms in optical lattices provides remarkable insights into the real space properties of many-body systems, but does not directly reveal the nature of their fundamental excitation spectrum. Here, we demonstrate that radio-frequency spectroscopy can reveal the quasiparticle nature of doped quantum many-body systems, crucial for our understanding of, e.g., high-temperature superconductors. In particular, we showcase how the existence and energy of magnetic polaron quasiparticles in doped Fermi-Hubbard systems may be probed, revealed by hallmark peaks in the spectroscopic spectrum. In combination with fundamental dualities of the Fermi-Hubbard model, we describe how these findings may be tested using several experimental platforms.
These lecture notes review recent progress in studying the Fermi-Hubbard model using ultracold gases in optical lattices. We focus on results from quantum gas microscope experiments that have allowed site-resolved measurements of charge and spin correlations in half-filled and doped Hubbard systems, as well as direct imaging of various types of polaronic quasiparticles. We also review experiments exploring dynamical properties of the Hubbard model through transport and spectroscopy. Moving beyond the plain-vanilla square-lattice Hubbard model, we present more recent work exploring Hubbard systems with novel lattice geometries and long-range interactions that stabilize new phases. Finally, we discuss the realization of entropy distribution protocols to cool these systems to ultralow temperatures where comparison to unbiased numerics is no longer possible.
Ultracold neutral atoms in optical lattices have become a powerful platform for the simulation of complex quantum systems. With our quantum gas microscope, we measure snapshots of the quantum many-body wavefunction by fully resolving the position and spin of each atom. I will present the application of this method to two quantum phases: The Haldane spin-1 phase is the prototype of a symmetry-protected topological phase, whose spin order is hidden in conventional two-point correlation functions. On our images, we can evaluate the characteristic string-correlator of this state and directly see the associated edge states of the system. In an antiferromagnetic background, holes get dressed by a surrounding cloud of ferromagnetic correlations. We study these magnetic polarons, which are a building block of the intricate physics of cuprates, by mapping out the spatial structure of the spin environment of individual holes. Upon increased doping, we observe the transition from this unusual polaronic metal to a Fermi Liquid and provide quantum-simulated results of the Fermi-Hubbard model as a benchmark for different theoretical approaches.
Recent realization of well-controlled quantum simulators of the triangular-lattice Fermi-Hubbard model, including the triangular optical lattices loaded with ultracold Fermions and the heterostructures of the transition-metal dichalcogenides, as well as the more advanced techniques to probe them, pave the way for studying frustrated Fermi-Hubbard physics. Here, we theoretically predict asymmetric photoemission and tunneling spectroscopies for a lightly hole-doped and electron-doped triangular Mott antiferromagnet, and reveal two distinct types of magnetic polarons: a lightly renormalized quasiparticle with the same momentum as the spin background and a heavily renormalized quasiparticle with a shifted momentum and a nearly flat band, using both analytical and unbiased numerical methods. We propose these theoretical findings to be verified in frustrated optical lattices and Moir\'e superlattices by probing various observables including the spectral function, the density of states, the energy dispersion, and the quasiparticle weight. Moreover, we reveal the asymmetric response of the spin background against charge doping, demonstrating that the interplay between the local spin and charge degrees of freedom plays a vital role in doped triangular Mott antiferromagnets.
The physics of strongly correlated fermions described by Hubbard or t − J models in the underdoped regime—relevant for high-temperature superconductivity in cuprate compounds—remains a subject of ongoing debate. In particular, the nature of charge carriers in this regime is poorly understood, in part due to the unusual properties of their spectral function. In this Letter, we present unbiased numerical results for the one-hole spectral function in a t − J model at finite temperatures. Our study provides valuable insights into the underlying physics of magnetic (or spin-) polaron formation in a doped antiferromagnet (AFM). For example, we find how the suppression of spectral weight outside the magnetic Brillouin zone—a precursor of Fermi arc formation–disappears with increasing temperature, revealing nearly-deconfined spinon excitations of the undoped AFM. The pristine setting we consider can be directly explored using quantum simulators. Our calculations demonstrate that coherent quasiparticle peaks associated with magnetic polarons can be observed up to temperatures T > J above the spin-exchange J , routinely obtained in such experiments. This paves the way for future studies of the fate of magnetic polarons in the pseudogap phase.
Quasiparticles are emergent excitations of matter that underlie much of our understanding of quantum many-body systems. Therefore, the prospect of controlling their properties has both fundamental and practical implications. However, in solid-state materials, it is often challenging to understand how quasiparticles are modified by external fields due to their complex interplay with other collective excitations. Here we demonstrate the manipulation of Fermi polarons—quasiparticles formed by impurities interacting with a Fermi gas—in a homogeneous atomic gas using fast radio-frequency control. Exploiting two internal states of the impurity species, we develop a steady-state spectroscopy, from which we extract the energy of the driven polaron. By varying the drive Rabi frequency, we measure the decay rate and the quasiparticle residue of the polaron in the weak-drive limit. At large Rabi frequencies, we observe signs that the drive causes a hybridization of the driven polaron with an incoherent background, leading to the breakdown of a description in terms of textbook quasiparticles. Our experiment establishes the driven Fermi polaron as a promising platform for studying controllable quasiparticles in strongly driven quantum matter and calls for a controlled theoretical framework to describe the dynamics of this strongly interacting quantum system. Fermi polarons are quasiparticles formed by impurities immersed in a Fermi gas. An experiment in an ultracold fermionic gas now shows how to control their properties with a tunable radio-frequency field.
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/tU/tU/t, magnetism is enhanced by doping away from n=1n=1n=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.