Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.
Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.
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.
Quantum Simulation
Strongly interacting chains of fermions are predicted to exhibit two types of collective excitations: spinons, which carry only spin, and holons, which carry only charge. These excitations move at different velocities. Signatures of this so-called spin-charge separation have been observed in solid-state systems, but obtaining direct dynamical evidence is tricky. With this goal in mind, Vijayan et al. perturbed a chain of ultracold interacting fermions housed in a one-dimensional optical lattice by removing one of the atoms. This gave rise to two independent excitations, which the researchers identified as spinons and holons using a quantum gas microscope.
Science , this issue p. [186][1]
[1]: /lookup/doi/10.1126/science.aay2354
The complex interplay between charge and spin dynamics lies at the heart of strongly correlated quantum materials, and it is a fundamental topic in basic research with far-reaching technological perspectives. We explore in this paper the dynamics of holes in a single-band, extended t - J model where the background spins form a Z 2 quantum spin liquid. Using a field theory approach based on a parton construction, we show that while the electrons for most momenta fractionalize into uncorrelated charge-carrying holons and spin-carrying spinons as generally expected for a quantum spin liquid, the spinon-holon scattering cross section diverges for certain momenta, signaling strong correlations. By deriving an effective low-energy Hamiltonian describing this dynamics, we demonstrate that these divergences are due to the formation of long-lived spinon-holon bound states. Since the wave function of these bound states is localized over a few lattice sites, they correspond to well-defined fermions with the same charge and spin as the underlying electrons. We then show that quantum gas microscopy with atoms in optical lattices provides an excellent platform for verifying and probing the internal spatial structure of these emerging fermions. The fermions will furthermore show up as clear quasiparticle peaks in angle-resolved photoemission spectroscopy with an intensity determined by their internal structure. For a nonzero hole concentration, the fermions form hole pockets with qualitatively the same location, shape, and intensity variation in the Brillouin zone as the so-called Fermi arcs observed in the pseudogap phase. Such agreement is remarkable since the Fermi arcs arise from the delicate interplay between the symmetry of the quantum spin liquid and the internal structure of the emerging fermions in a minimal single-band model with no extra degrees of freedom added. Our results, therefore, provide a microscopic mechanism for the conjectured fractionalized Fermi liquid and open up new pathways for exploring the pseudogap phase and high-temperature superconductivity as arising from a quantum spin liquid.
Due to the mechanism of confinement, as known from quantum chromodynamics, it is difficult to observe individual particles carrying fractional quantum number (e.g., quark with fractional electric charge). A condensed-matter example of fractionalized particles is spinons in quasi-one-dimensional spin systems, which are domain walls in the background of N\'eel configurations carrying spin-21. Using the time-evolving block decimation algorithm, we visualize the nontrivial spinon dynamics induced by the confine mechanism in a two-leg spin-21 ladder. It can be illustrated by a simple single-particle picture of Bloch oscillation, not only qualitatively but also quantitatively. We propose the experimental realization and the real time detection of the spinon dynamics in the ultracold boson systems of 87Rb.
Fractionalization remains one of the most fascinating manifestations of strong interactions in quantum many-body systems. In quantum magnetism, the existence of spinons—collective magnetic excitations that behave as quasiparticles with fractional quantum numbers—is proven in spin chains, but the criteria for their appearance in higher dimensions remain disputed. Motivated by experiments reporting the observation of spinons at high energies in the square-lattice Heisenberg antiferromagnet, we adopt the approach of extrapolating from where spinons are well defined. We study the dynamical properties of a Gutzwiller-projected wave function, the staggered-flux state, on a rectangular spin-1/2 Heisenberg lattice as a function of the spatial coupling ratio, γ = J y / J x . By studying the spectrum and the spinon separation distribution we show how, as the system evolves from one-dimensional (1D) towards 2D, the spinons become progressively more confined over most of reciprocal space, but remain deconfined at specific wave vectors.
This thesis reports on the microscopic investigation of antiferromagnetic order in Hubbard chains, realized with ultracold repulsively interacting fermions in an optical lattice. Extending a quantum gas microscope on spin resolution opened the possibility to Access the full charge and spin statistics of a strongly correlated fermionic many body system. Using this technique, we measured antiferromagnetic correlations over distances up to three lattice sites. Starting with a repulsive degenerate two component mixture of 6Li atoms trapped in a single plane of a vertical lattice, we loaded the Atoms into one-dimensional tubes of a transverse optical superlattice. By adiabatically ramping up the lattice potential along the tubes, we isentropically entered the strongly correlated regime of the one-dimensional Fermi-Hubbard Hamiltonian. We spatially separated the two spin states into opposite sites of local double wells orthogonal to the direction of the lattice before single atom and site sensitive imaging. In this way we extracted the spin information of every single lattice site and were able to evaluate spin-spin correlations. The two component degenerate gases were produced with sub-Poissonian atom number fluctuations by magnetically driven evaporative cooling in vicinity of a Feshbach resonance, used to set the scattering length. The dependence of antiferromagnetic correlations on the driving superexchange coupling was experimentally investigated by varying the interparticle scattering length before loading the atoms into the optical lattice. Taking advantage of the underlying trapping potential of the optical lattice, which shaped the filling and the entropy of the gases, the influence of density excitations and different entropies on spin correlations was observed. By post-selecting the Hubbard chains based on their average filling and local atom number fluctuations, spin correlations corresponding to 58% of the zero temperature predictions in the Heisenberg regime were measured. By comparing the obtained antiferromagnetic correlations to Quantum-Monte-Carlo predictions for our System the lowest measured entropy per particle could be stated as s = 0.51(4)kB, clearly below the critical value of s = ln(2)kB, which is required to form longer ranged correlations. Below this critical entropy, in contrast to local density fluctuations, these spin correlations strongly depend on the entropy of the system. In the future, such a spin thermometer can be used to benchmark novel cooling techniques, which are required to enter the temperature regime of d-wave superconducting states. The access to the full particle and spin statistics will enable us to read out multi-point correlation functions, which characterize such exotic states of matter.