Imaging magnetic polarons in the doped Fermi-Hubbard model

Polarons are among the most fundamental quasiparticles emerging in interacting many-body systems, forming already at the level of a single mobile dopant. In the context of the two-dimensional Fermi-Hubbard model, such polarons are predicted to form around charged dopants in an antiferromagnetic background in the low doping regime close to the Mott insulating state. Macroscopic transport and spectroscopy measurements related to high $T_{c}$ materials have yielded strong evidence for the existence of such quasiparticles in these systems. Here we report the first microscopic observation of magnetic polarons in a doped Fermi-Hubbard system, harnessing the full single-site spin and density resolution of our ultracold-atom quantum simulator. We reveal the dressing of mobile doublons by a local reduction and even sign reversal of magnetic correlations, originating from the competition between kinetic and magnetic energy in the system. The experimentally observed polaron signatures are found to be consistent with an effective string model at finite temperature. We demonstrate that delocalization of the doublon is a necessary condition for polaron formation by contrasting this mobile setting to a scenario where the doublon is pinned to a lattice site. Our work paves the way towards probing interactions between polarons, which may lead to stripe formation, as well as microscopically exploring the fate of polarons in the pseudogap and bad metal phase

Can Three-Body Recombination Purify a Quantum Gas?

Three-body recombination in quantum gases is traditionally associated with heating, but it was recently found that it can also cool the gas. We show that in a partially condensed three-dimensional homogeneous Bose gas three-body loss could even purify the sample, that is, reduce the entropy per particle and increase the condensed fraction η. We predict that the evolution of η under continuous three-body loss can, depending on small changes in the initial conditions, exhibit two qualitatively different behaviors-if it is initially above a certain critical value, η increases further, whereas clouds with lower initial η evolve towards a thermal gas. These dynamical effects should be observable under realistic experimental conditions

Ultracold field-linked tetratomic molecules

Ultracold polyatomic molecules offer intriguing new opportunities in cold chemistry, precision measurements, and quantum information processing, thanks to their rich internal structure. However, their increased complexity compared to diatomic molecules presents a formidable challenge to employ conventional cooling techniques. Here, we demonstrate a new approach to create ultracold polyatomic molecules by electroassociation in a degenerate Fermi gas of microwave-dressed polar molecules through a field-linked resonance. Starting from ground state NaK molecules, we create around $1.1\times 10^3$ tetratomic (NaK)$_2$ molecules, with a phase space density of $0.040(3)$ at a temperature of $134(3)\,\text{nK}$, more than $3000$ times colder than previously realized tetratomic molecules. We observe a maximum tetramer lifetime of $8(2)\,\text{ms}$ in free space without a notable change in the presence of an optical dipole trap, indicating these tetramers are collisionally stable. The measured binding energy and lifetime agree well with parameter-free calculations, which outlines pathways to further increase the lifetime of the tetramers. Moreover, we directly image the dissociated tetramers through microwave-field modulation to probe the anisotropy of their wave function in momentum space. Our result demonstrates a universal tool for assembling ultracold polyatomic molecules from smaller polar molecules, which is a crucial step towards Bose--Einstein condensation (BEC) of polyatomic molecules and towards a new crossover from a dipolar Bardeen-Cooper-Schrieffer (BCS) superfluid to a BEC of tetramers. Additionally, the long-lived FL state provides an ideal starting point for deterministic optical transfer to deeply bound tetramer states

Many-Body Decay of the Gapped Lowest Excitation of a Bose-Einstein Condensate.

We study the decay mechanism of the gapped lowest-lying axial excitation of a quasipure atomic Bose-Einstein condensate confined in a cylindrical box trap. Owing to the absence of accessible lower-energy modes, or direct coupling to an external bath, this excitation is protected against one-body (linear) decay, and the damping mechanism is exclusively nonlinear. We develop a universal theoretical model that explains this fundamentally nonlinear damping as a process whereby two quanta of the gapped lowest excitation mode couple to a higher-energy mode, which subsequently decays into a continuum. We find quantitative agreement between our experiments and the predictions of this model. Finally, by strongly driving the system below its (lowest) resonant frequency, we observe third-harmonic generation, a hallmark of nonlinear behavior

Direct observation of incommensurate magnetism in Hubbard chains

The interplay between magnetism and doping is at the origin of exotic strongly correlated electronic phases and can lead to novel forms of magnetic ordering. One example is the emergence of incommensurate spin-density waves with a wave vector that does not match the reciprocal lattice. In one dimension this effect is a hallmark of Luttinger liquid theory, which also describes the low energy physics of the Hubbard model. Here we use a quantum simulator based on ultracold fermions in an optical lattice to directly observe such incommensurate spin correlations in doped and spin-imbalanced Hubbard chains using fully spin and density resolved quantum gas microscopy. Doping is found to induce a linear change of the spin-density wave vector in excellent agreement with Luttinger theory predictions. For non-zero polarization we observe a decrease of the wave vector with magnetization as expected from the Heisenberg model in a magnetic field. We trace the microscopic origin of these incommensurate correlations to holes, doublons and excess spins which act as delocalized domain walls for the antiferromagnetic order. Finally, when inducing interchain coupling we observe fundamentally different spin correlations around doublons indicating the formation of a magnetic polaron

Can Three-Body Recombination Purify a Quantum Gas?

Three-body recombination in quantum gases is traditionally associated with heating, but it was recently found that it can also cool the gas. We show that in a partially condensed three-dimensional homogeneous Bose gas three-body loss could even purify the sample, that is, reduce the entropy per particle and increase the condensed fraction $\eta$. We predict that the evolution of $\eta$ under continuous three-body loss can, depending on small changes in the initial conditions, exhibit two qualitatively different behaviours - if it is initially above a certain critical value, $\eta$ increases further, whereas clouds with lower initial $\eta$ evolve towards a thermal gas. These dynamical effects should be observable under realistic experimental conditions

Quantifying hole-motion-induced frustration in doped antiferromagnets by Hamiltonian reconstruction

Abstract Unveiling the microscopic origins of quantum phases dominated by the interplay of spin and motional degrees of freedom constitutes one of the central challenges in strongly correlated many-body physics. When holes move through an antiferromagnetic spin background, they displace the positions of spins, which induces effective frustration in the magnetic environment. However, a concrete characterization of this effect in a quantum many-body system is still an unsolved problem. Here we present a Hamiltonian reconstruction scheme that allows for a precise quantification of hole-motion-induced frustration. We access non-local correlation functions through projective measurements of the many-body state, from which effective spin-Hamiltonians can be recovered after detaching the magnetic background from dominant charge fluctuations. The scheme is applied to systems of mixed dimensionality, where holes are restricted to move in one dimension, but SU(2) superexchange is two-dimensional. We demonstrate that hole motion drives the spin background into a highly frustrated regime, which can quantitatively be described by an effective J 1–J 2-type spin model. We exemplify the applicability of the reconstruction scheme to ultracold atom experiments by recovering effective spin-Hamiltonians of experimentally obtained 1D Fermi-Hubbard snapshots. Our method can be generalized to fully 2D systems, enabling promising microscopic perspectives on the doped Hubbard model

Quantifying hole-motion-induced frustration in doped antiferromagnets by Hamiltonian reconstruction

Unveiling the microscopic origins of quantum phases dominated by the interplay of spin and motional degrees of freedom constitutes one of the central challenges in strongly correlated many-body physics. When holes move through an antiferromagnetic spin background, they displace the positions of spins, which induces effective frustration in the magnetic environment. However, a concrete characterization of this effect in a quantum many-body system is still an unsolved problem. Here we present a Hamiltonian reconstruction scheme that allows for a precise quantification of hole-motion-induced frustration. We access non-local correlation functions through projective measurements of the many-body state, from which effective spin-Hamiltonians can be recovered after detaching the magnetic background from dominant charge fluctuations. The scheme is applied to systems of mixed dimensionality, where holes are restricted to move in one dimension, but SU(2) superexchange is two-dimensional. We demonstrate that hole motion drives the spin background into a highly frustrated regime, which can quantitatively be described by an effective J1–J2-type spin model. We exemplify the applicability of the reconstruction scheme to ultracold atom experiments by recovering effective spin-Hamiltonians of experimentally obtained 1D Fermi-Hubbard snapshots. Our method can be generalized to fully 2D systems, enabling promising microscopic perspectives on the doped Hubbard model

First and second sound in a compressible 3D Bose fluid

The two-fluid model is fundamental for the description of superfluidity. In the nearly-incompressible-liquid regime, it successfully describes first and second sound, corresponding, respectively, to density and entropy waves, in both liquid helium and unitary Fermi gases. Here, we study the two sounds in the opposite regime of a highly compressible fluid, using an ultracold $^{39}$K Bose gas in a three-dimensional box trap. We excite the longest-wavelength mode of our homogeneous gas, and observe two distinct resonant oscillations below the critical temperature, of which only one persists above it. In a microscopic mode-structure analysis, we find agreement with the hydrodynamic theory, where first and second sound involve density oscillations dominated by, respectively, thermal and condensed atoms. Varying the interaction strength, we explore the crossover from hydrodynamic to collisionless behavior in a normal gas.Comment: Main text (5 pages, 4 figures), Supplemental Material (14 pages, 8 figures

Research data supporting "First and Second Sound in a Compressible 3D Bose Fluid"

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