Kristian Knakkergaard Nielsen

The motion of dopants in magnetic spin lattices has received tremendous attention for at least four decades due to its connection to high-temperature superconductivity. Despite these efforts, we lack a complete understanding of their behavior, especially out of the equilibrium and at nonzero temperatures. In this paper, we take a significant step towards a much deeper understanding based on state-of-the-art matrix-product-state calculations. In particular, we investigate the nonequilibrium dynamics of a dopant in two-leg t − J ladders with antiferromagnetic XXZ spin interactions. In the Ising limit, we find that the dopant is for all investigated temperatures due to an emergent disordered potential, with a localization length controlled by the underlying correlation length of the spin lattice, which increases exponentially with decreasing temperature. The dopant, hereby, only delocalizes asymptotically in the zero temperature limit. This greatly generalizes the localization effect discovered recently in Hilbert space fragmented models [, ]. In the presence of spin-exchange processes at rate α , the dopant diffuses with a diffusion coefficient, D h , depending nonmonotonically on α . It initially increases linearly as D h ∝ α for α ≪ 1 before dropping off as α − 1 for α > 1 . Moreover, we show that the underlying spin dynamics at infinite temperature behaves qualitatively the same, albeit with important quantitative differences. We substantiate these findings by showing that the dynamics features self-similar scaling behavior, which strongly deviates from the Gaussian behavior of regular diffusion, especially for weak spin exchange. Finally, we show that the diffusion coefficient D h follows an Arrhenius relation at high temperatures, whereby it is exponentially suppressed upon cooling.

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.

The physics of impurities in a bosonic quantum environment is a paradigmatic and challenging many-body problem. Here, this problem is investigated for impurities with strong repulsive interactions based on Ramsey interferometry in a quantum degenerate gas of K 39 atoms. We observe revivals in the amplitude of the interferometric signal and identify them as beat signals between two coexisting quasiparticle branches, the attractive and repulsive polarons. The interferometric signal allows for an extraction of their energies for a wide range of interaction strengths, thus resolving outstanding discrepancies in earlier spectroscopic measurements. Furthermore, we identify several dynamical regimes in the formation of the repulsive Bose polaron. Our results improve the understanding of quantum impurities interacting strongly with a bosonic environment and show how short-lived nonequilibrium many-body states can be probed using quantum beat spectroscopy.

I demonstrate a pairing mechanism of dopants in a magnetic lattice, emerging from the underlying of the spins. The effect is demonstrated in a mixed-dimensional model, where dopants travel along a two-leg ladder, while the spins feature Ising interactions along the rungs and the legs of the ladder. The dynamics following the sudden immersion of two nearest neighbor dopants in an infinite temperature spin lattice shows that thermal spin disorder frustrates the relative motion of the dopants and enforces them to copropagate. The predictions are shown to be realistically testable in quantum simulation experiments.

I investigate the motion of a single hole in 2D spin lattices with square and triangular geometries. While the spins have nearest neighbor Ising spin couplings J J , the hole is allowed to move only in 1D along a single line in the 2D lattice with nearest neighbor hopping amplitude t t . The non-equilibrium hole dynamics is initialized by suddenly removing a single spin from the thermal Ising spin lattice. I find that for any nonzero spin coupling and temperature, the hole is localized. This is an extension of the thermally induced localization phenomenon [Phys. Rev. Res. 6, 023325 (2024)] to the case, where there is a phase transition to a long-range ordered ferromagnetic phase. The dynamics depends only on the ratio of the temperature to the spin coupling, k_BT / |J| k B T / | J | , and on the ratio of the spin coupling to the hopping J/t J / t . I characterize these dependencies in great detail. In particular, I find universal behavior at high temperatures, common features for the square and triangular lattices across the Curie temperatures for ferromagnetic interactions, and highly distinct behaviors for the two geometries in the presence of antiferromagnetic interactions due geometric frustration in the triangular lattice.

Adding a dopant to an antiferromagnetic spin background disturbs the magnetic order and leads to the formation of a quasiparticle coined the magnetic polaron, which plays a central role in understanding strongly correlated materials. Recently, remarkably detailed insights into the spatial properties of such polarons have been obtained using atoms in optical lattices. Motivated by this we develop a nonperturbative scheme for calculating the wave function of the magnetic polaron in a bilayer antiferromagnet using the self-consistent Born approximation. The scheme includes an infinite number of spin waves, which is crucial for an accurate description of the most interesting regime of strong correlations. Utilizing the developed wave function, we explore the spatial structure of the polaron dressing cloud consisting of magnetically frustrated spins surrounding the hole. Mimicking the nonmonotonic behavior of the antiferromagnetic order, we find that the dressing cloud first decreases and then increases in size with increasing interlayer hopping. The increase reflects the decrease in the magnetic order as a quantum phase transition to a disordered state is approached for large interlayer hopping. We, furthermore, find that the symmetry of the ground state dressing cloud changes as the interlayer coupling increases. Our results should be experimentally accessible using quantum simulation with optical lattices.