Microscopy of spin-charge dynamics in Fermi-Hubbard chains

Obtaining a microscopic understanding of the dynamics in strongly correlated electronic systems has remained a challenge for many decades. The interplay between the spin and charge degrees of freedom in these materials at different temperatures and dopant concentrations is not well understood and is still an area of intense scientific research. Recently, quantum simulators based on ultracold atoms in optical lattices have emerged as a promising platform to probe strongly correlated fermionic systems. This thesis reports on the work carried out with a quantum gas microscope of ultracold fermionic Li-6, where Fermi-Hubbard systems are prepared and imaged with single site spin and density resolution. The main results of the thesis explore the microscopic dynamics underlying one-dimensional materials, where individual constituents such as the electron with charge e and spin-1/2 are not relevant to the description of the system anymore and are instead replaced by spin and charge excitations that can propagate independent of one another - a phenomenon called spin-charge separation. In our quantum simulator, we use analogous one-dimensional Fermi-Hubbard chains of Li-6, to perform time- and space-resolved microscopy of the spin and charge excitations following a local quench. By extracting their strikingly different velocities and showing an absence of binding between the excitations, we demonstrate spin-charge separation. Our microscopic technique also allows us to quantitatively extract the excess spin carried by the spin excitiation, connecting our results to the phenomenon of fractionalization. In another set of experiments, Fermi-Hubbard chains are probed at equilibrium and incommensurate spin correlations arising in the presence of both density doping and spin polarization are observed. The wavevector of these incommensurate correlations are found to have a linear dependence on doping and polarization. Finally, the effect of the spin-charge interplay is probed in the crossover from one to two dimensions. The spin correlations across dopants are seen to be dramatically different in two dimensions, and the strong antiferromagnetic correlations across dopants present in one dimension disappear. For a single dopant in a fully two dimensional system, the spin-charge interplay manifests as a distorted spin cloud surrounding the dopant, indicating the formation of a magnetic polaron. The experiments reported here demonstrate the power of a quantum simulator; by probing the physics of strongly correlated systems in real space with unprecedented resolution, we can zoom into emergent phenomena, validate theories and access regimes that are not possible in other experimental settings

Microscopy of spin-charge dynamics in Fermi-Hubbard chains

Obtaining a microscopic understanding of the dynamics in strongly correlated electronic systems has remained a challenge for many decades. The interplay between the spin and charge degrees of freedom in these materials at different temperatures and dopant concentrations is not well understood and is still an area of intense scientific research. Recently, quantum simulators based on ultracold atoms in optical lattices have emerged as a promising platform to probe strongly correlated fermionic systems. This thesis reports on the work carried out with a quantum gas microscope of ultracold fermionic Li-6, where Fermi-Hubbard systems are prepared and imaged with single site spin and density resolution. The main results of the thesis explore the microscopic dynamics underlying one-dimensional materials, where individual constituents such as the electron with charge e and spin-1/2 are not relevant to the description of the system anymore and are instead replaced by spin and charge excitations that can propagate independent of one another - a phenomenon called spin-charge separation. In our quantum simulator, we use analogous one-dimensional Fermi-Hubbard chains of Li-6, to perform time- and space-resolved microscopy of the spin and charge excitations following a local quench. By extracting their strikingly different velocities and showing an absence of binding between the excitations, we demonstrate spin-charge separation. Our microscopic technique also allows us to quantitatively extract the excess spin carried by the spin excitiation, connecting our results to the phenomenon of fractionalization. In another set of experiments, Fermi-Hubbard chains are probed at equilibrium and incommensurate spin correlations arising in the presence of both density doping and spin polarization are observed. The wavevector of these incommensurate correlations are found to have a linear dependence on doping and polarization. Finally, the effect of the spin-charge interplay is probed in the crossover from one to two dimensions. The spin correlations across dopants are seen to be dramatically different in two dimensions, and the strong antiferromagnetic correlations across dopants present in one dimension disappear. For a single dopant in a fully two dimensional system, the spin-charge interplay manifests as a distorted spin cloud surrounding the dopant, indicating the formation of a magnetic polaron. The experiments reported here demonstrate the power of a quantum simulator; by probing the physics of strongly correlated systems in real space with unprecedented resolution, we can zoom into emergent phenomena, validate theories and access regimes that are not possible in other experimental settings

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

Robust Bilayer Charge-Pumping for Spin- and Density-Resolved Quantum Gas Microscopy

Quantum gas microscopy has emerged as a powerful new way to probe quantum many-body systems at the microscopic level. However, layered or efficient spin-resolved readout methods have remained scarce as they impose strong demands on the specific atomic species and constrain the simulated lattice geometry and size. Here we present a novel high-fidelity bilayer readout, which can be used for full spin- and density-resolved quantum gas microscopy of two-dimensional systems with arbitrary geometry. Our technique makes use of an initial Stern-Gerlach splitting into adjacent layers of a highly-stable vertical superlattice and subsequent charge pumping to separate the layers by $21\,\mu$m. This separation enables independent high-resolution images of each layer. We benchmark our method by spin- and density-resolving two-dimensional Fermi-Hubbard systems. Our technique furthermore enables the access to advanced entropy engineering schemes, spectroscopic methods or the realization of tunable bilayer systems

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

Learning-Based Quantum Control for Optimal Pure State Manipulation

In this paper, we propose an adaptive critic learning approach for two classes of optimal pure state transition problems for closed quantum systems: i) when the target state is an eigenstate, and ii) when the target state is a superposition pure state. First, we describe a finite-dimensional quantum system based on the Schrodinger equation with the action of control fields. Then, we consider the target state to be i) an eigenstate of the internal Hamiltonian and ii) an arbitrary pure state via a unitary transformation. Meanwhile, the quantum state manipulation is formulated as an optimal control problem for solving the complex partial differential Hamilton-Jacobi-Bellman (HJB) equation, of which the control solution is found using continuous-time Q-learning of an adaptive critic. Finally, numerical simulation for a spin-1/2 particle system demonstrates the effectiveness of the proposed approach

Sub-Kelvin Feedback Cooling and Heating Dynamics of an Optically Levitated Librator

Rotational optomechanics strives to gain quantum control over mechanical rotors by harnessing the interaction of light and matter. We optically trap a dielectric nanodumbbell in a linearly polarized laser field, where the dumbbell represents a nanomechanical librator. Using measurement-based parametric feedback control in high vacuum, we cool this librator from room temperature to 240 mK and investigate its heating dynamics when released from feedback. We exclude collisions with residual gas molecules as well as classical laser noise as sources of heating. Our findings indicate that we observe the torque fluctuations arising from the zero-point fluctuations of the electromagnetic field.ISSN:0031-9007ISSN:1079-711