Abstract
The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display ...non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergodic behavior was established theoretically in certain limiting cases, there is no complete understanding of the complex thermalization properties of this model. In this work, we experimentally study the relaxation of an initial charge-density wave and find a remarkably long-lived initial-state memory over a wide range of parameters. Our observations are well reproduced by numerical simulations of a clean system. Using analytical calculations we further provide a detailed microscopic understanding of this behavior, which can be attributed to emergent kinetic constraints.
Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the band theory of solids. Here we report on the measurement of the geometric phase acquired by ...cold atoms moving in one-dimensional optical lattices. Using a combination of Bloch oscillations and Ramsey interferometry, we extract the Zak phase--the Berry phase gained during the adiabatic motion of a particle across the Brillouin zone--which can be viewed as an invariant characterizing the topological properties of the band. For a dimerized lattice, which models polyacetylene, we measure a difference of the Zak phase δstraight phiZak = 0.97(2)π for the two possible polyacetylene phases with different dimerization. The two dimerized phases therefore belong to different topological classes, such that for a filled band, domain walls have fractional quantum numbers. Our work establishes a new general approach for probing the topological structure of Bloch bands inoptical lattices. PUBLICATION ABSTRACT
We consider a spin-1/2 fermionic ladder with spin-orbit coupling and a perpendicular magnetic field, which shares important similarities with topological superconducting wires. We fully characterize ...the symmetry-protected topological phase of this ladder through the identification of fractionalized edge modes and non-trivial spin winding numbers. We propose an experimental scheme to engineer such a ladder system with cold atoms in optical lattices, and we present two protocols that can be used to extract the topological signatures from density and momentum-distribution measurements. We then consider the presence of interactions and discuss the effects of a contact on-site repulsion on the topological phase. We find that such interactions could enhance the extension of the topological phase in certain parameters regimes.
The postulate of gauge invariance in nature does not lend itself directly to implementations of lattice gauge theories in modern setups of quantum synthetic matter. Unavoidable gauge-breaking errors ...in such devices require gauge invariance to be enforced for faithful quantum simulation of gauge-theory physics. This poses major experimental challenges, in large part due to the complexity of the gauge-symmetry generators. Here, we show that gauge invariance can be reliably stabilized by employing simplified local pseudogenerators designed such that within the physical sector they act identically to the actual local generator. Dynamically, they give rise to emergent exact gauge theories up to time scales polynomial and even exponential in the protection strength. This obviates the need for implementing often complex multibody full gauge symmetries, thereby further reducing experimental overhead in physical realizations. We showcase our method in the Z_{2} lattice gauge theory, and discuss experimental considerations for its realization in modern ultracold-atom setups.
The sine-Gordon model emerges as a low-energy theory in a plethora of quantum many-body systems. Here, we theoretically investigate tunnel-coupled Bose-Hubbard chains with strong repulsive ...interactions as a realization of the sine-Gordon model deep in the quantum regime. We propose protocols for quantum gas microscopes of ultracold atoms to prepare and analyze solitons, which are the fundamental topological excitations of the emergent sine-Gordon theory. With numerical simulations based on matrix product states, we characterize the preparation and detection protocols and discuss the experimental requirements.
We propose a scheme to implement Kitaev’s honeycomb model with cold atoms, based on a periodic (Floquet) drive, in view of realizing and probing non-Abelian chiral spin liquids using quantum ...simulators. We derive the effective Hamiltonian to leading order in the inverse-frequency expansion, and show that the drive opens up a topological gap in the spectrum without mixing the effective Majorana and vortex degrees of freedom. We address the challenge of probing the physics of Majorana fermions, while having access only to the original composite spin degrees of freedom. Specifically, we propose to detect the properties of the chiral spin liquid phase using gap spectroscopy and edge quenches in the presence of the Floquet drive. The resulting chiral edge signal, which relates to the thermal Hall effect associated with neutral Majorana currents, is found to be robust for realistically prepared states. By combining strong interactions with Floquet engineering, our work paves the way for future studies of non-Abelian excitations and quantized thermal transport using quantum simulators.
We introduce a method for quantum simulation of U(1) lattice gauge theories coupled to matter, utilizing alkaline-earth(-like) atoms in state-dependent optical lattices. The proposal enables the ...study of both gauge and fermionic matter fields without integrating out one of them in one and two dimensions. We focus on a realistic and robust implementation that utilizes the long-lived metastable clock state available in alkaline-earth(-like) atomic species. Starting from an ab initio modeling of the experimental setting, we systematically carry out a derivation of the target U(1) gauge theory. This approach allows us to identify and address conceptual and practical challenges for the implementation of lattice gauge theories that—while pivotal for a successful implementation—have never been rigorously addressed in the literature: those include the specific engineering of lattice potentials to achieve the desired structure of Wannier functions and the subtleties involved in realizing the proper separation of energy scales to enable gauge-invariant dynamics. We discuss realistic experiments that can be carried out within such a platform using the fermionic isotope ^{173}Yb, addressing via simulations all key sources of imperfections, and provide concrete parameter estimates for relevant energy scales in both one- and two-dimensional settings.
Quantum simulators have made a remarkable progress towards exploring the dynamics of many-body systems, many of which offer a formidable challenge to both theoretical and numerical methods. While ...state-of-the-art quantum simulators are, in principle, able to simulate quantum dynamics well outside the domain of classical computers, they are noisy and limited in the variability of the initial state of the dynamics and the observables that can be measured. Despite these limitations, here we show that such a quantum simulator can be used to in effect solve for the dynamics of a many-body system. We develop an efficient numerical technique that facilitates classical simulations in regimes not accessible to exact calculations or other established numerical techniques. The method is based on approximations that are well suited to describe localized one-dimensional Fermi-Hubbard systems. Since this new method does not have an error estimate and the approximations do not hold in general, we use a neutral-atom Fermi-Hubbard quantum simulator with L_{exp}≃290 lattice sites to benchmark its performance in terms of accuracy and convergence for evolution times up to 700 tunneling times. We then use these approximations in order to derive a simple prediction of the behavior of interacting Bloch oscillations for spin-imbalanced Fermi-Hubbard systems, which we show to be in quantitative agreement with experimental results. Finally, we demonstrate that the convergence of our method is the slowest when the entanglement depth developed in the many-body system we consider is neither too small nor too large. This represents a promising regime for near-term applications of quantum simulators.
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