Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks

Tensor network algorithms provide a suitable route for tackling real-time dependent problems in lattice gauge theories, enabling the investigation of out-of-equilibrium dynamics. We analyze a U(1) lattice gauge theory in (1+1) dimensions in the presence of dynamical matter for different mass and electric field couplings, a theory akin to quantum-electrodynamics in one-dimension, which displays string-breaking: the confining string between charges can spontaneously break during quench experiments, giving rise to charge-anticharge pairs according to the Schwinger mechanism. We study the real-time spreading of excitations in the system by means of electric field and particle fluctuations: we determine a dynamical state diagram for string breaking and quantitatively evaluate the time-scales for mass production. We also show that the time evolution of the quantum correlations can be detected via bipartite von Neumann entropies, thus demonstrating that the Schwinger mechanism is tightly linked to entanglement spreading. To present the variety of possible applications of this simulation platform, we show how one could follow the real-time scattering processes between mesons and the creation of entanglement during scattering processes. Finally, we test the quality of quantum simulations of these dynamics, quantifying the role of possible imperfections in cold atoms, trapped ions, and superconducting circuit systems. Our results demonstrate how entanglement properties can be used to deepen our understanding of basic phenomena in the real-time dynamics of gauge theories such as string breaking and collisions.Comment: 15 pages, 25 figures. Published versio

Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation

We show that gauge invariant quantum link models, Abelian and non-Abelian, can be exactly described in terms of tensor networks states. Quantum link models represent an ideal bridge between high-energy to cold atom physics, as they can be used in cold-atoms in optical lattices to study lattice gauge theories. In this framework, we characterize the phase diagram of a (1+1)-d quantum link version of the Schwinger model in an external classical background electric field: the quantum phase transition from a charge and parity ordered phase with non-zero electric flux to a disordered one with a net zero electric flux configuration is described by the Ising universality class.Comment: 9 pages, 9 figures. Published versio

Quantum-enhanced gyroscopy with rotating anisotropic Bose–Einstein condensates

High-precision gyroscopes are a key component of inertial navigation systems. By considering matter wave gyroscopes that make use of entanglement it should be possible to gain some advantages in terms of sensitivity, size, and resources used over unentangled optical systems. In this paper we consider the details of such a quantum-enhanced atom interferometry scheme based on atoms trapped in a carefully-chosen rotating trap. We consider all the steps: entanglement generation, phase imprinting, and read-out of the signal and show that quantum enhancement should be possible in principle. While the improvement in performance over equivalent unentangled schemes is small, our feasibility study opens the door to further developments and improvements

Loops and Strings in a Superconducting Lattice Gauge Simulator

We propose an architecture for an analog quantum simulator of electromagnetism in 2+1 dimensions, based on an array of superconducting fluxonium devices. The encoding is in the integer (spin-1 representation of the quantum link model formulation of compact U(1) lattice gauge theory. We show how to engineer Gauss' law via an ancilla mediated gadget construction, and how to tune between the strongly coupled and intermediately coupled regimes. The witnesses to the existence of the predicted confining phase of the model are provided by nonlocal order parameters from Wilson loops and disorder parameters from 't Hooft strings. We show how to construct such operators in this model and how to measure them nondestructively via dispersive coupling of the fluxonium islands to a microwave cavity mode. Numerical evidence is found for the existence of the confined phase in the ground state of the simulation Hamiltonian on a ladder geometry.Comment: 17 pages, 5 figures. Published versio

Engineering entanglement for metrology with rotating matter waves

Entangled states of rotating, trapped ultracold bosons form a very promising scenario for quantum metrology. In order to employ such states for metrology, it is vital to understand their detailed form and the enhanced accuracy with which they could measure phase, in this case generated through rotation. In this work, we study the rotation of ultracold bosons in an asymmetric trapping potential beyond the lowest Landau level (LLL) approximation. We demonstrate that while the LLL can identify reasonably the critical frequency for a quantum phase transition and entangled state generation, it is vital to go beyond the LLL to identify the details of the state and quantify the quantum Fisher information (which bounds the accuracy of the phase measurement). We thus identify a new parameter regime for useful entangled state generation, amenable to experimental investigation

Modeling Macro-Sized, High Aspect Ratio Through-Hole Filling by Multi-Component Additive-Assisted Copper Electrodeposition

A multi-element, time-dependent model is used to examine additive-assisted copper electroplating in macro-channels. This model is an adaptation of the work of Akolkar and Landau [J. Electrochem. Soc., 156, D351 (2009)], used to describe plating in micro-vias for integrated circuits. Using their method for describing species movement in the channel, the model has been expanded to include transport and adsorption limitations of the inhibitor and accelerator, as well as the copper ions in solution. The model is used to investigate copper plating as an infiltration method across many size scales and aspect ratios. Biomorphic graphite scaffolds produced from wood are used as a representative system and the results of a two-additive bath are used to characterize the behavior of the additives and determine the effectiveness of the plating. The results indicate that at macro-scales, channel dimensions play an increasingly important role in dictating the behavior of additive-assisted plating. Because additive systems are designed to establish differential surface coverage within the channel, the success of which is determined by the additive's rates of diffusion and adsorption, certain size scale/aspect ratio combinations preclude such coverage. A guide for sample geometries that may be successfully infiltrated with a two-additive bath is provided

Redox Chemistry and Molybdenum Burial in a Mesoproterozoic Lake

While marine sediments have been used to constrain a history of redox chemistry throughout the Precambrian, far fewer data have been generated from lakes. With major biological innovations thought to have occurred in Proterozoic lakes, understanding their chemistry is critical for understanding the evolution of eukaryotic life. We use sediment geochemistry to characterize the redox conditions of the Nonesuch Formation (~1.1 Ga) and a modern analogue for the Proterozoic: the Middle Island Sinkhole in Lake Huron (USA). Iron speciation, Mo contents, and Mo‐U covariation demonstrate oxic and anoxic—not euxinic—environments, with no clear indicators of enhanced biological productivity in the Nonesuch Formation. Moderate Mo enrichments observed in the Nonesuch Formation are not attributed to euxinia, but instead to an authigenic particulate shuttle. We suggest that the Fe and Mo sediment geochemistry of these lacustrine systems reflect only local water column and sediment burial conditions and not atmospheric oxygenation.Plain Language SummaryLakes are proposed to have been critical environments for the evolution of life during the Proterozoic (~2.5 to 0.5 billion years ago). However, relatively little is known about the chemistry of ancient lakes, including the availability of oxygen for biological productivity, and how local oxygen availability can be extrapolated to understand global oxygen availability. In addition, with no lakes remaining from the Proterozoic, the only way to study ancient lakes is to use the chemistry of the sediments left behind. This study uses the sediment chemistry of elements that are sensitive to oxygen to understand oxygen availability in a Proterozoic lake environment. These data were then compared to modern lake environments with known chemistry and oxygen levels in order to interpret the results better. We found that oxygen availability in the Proterozoic lake was variable, with no clear indicators of abundant biological productivity. We conclude that ancient lake sediments only constrain the chemistry of the local environment, with no major implications for global or even regional atmospheric oxygenation.Key PointsFe, Mo, and U sediment geochemistry of the Nonesuch Formation (~1.1 Ga; USA) indicate fluctuating oxic and anoxic redox chemistryMo and U covariation in the Nonesuch Formation and modern analogue sediments confirm euxinia is not necessary for moderate Mo burialComparison of Nonesuch Formation and modern analogue indicates that Proterozoic lakes are unlikely to constrain atmospheric oxygenPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/150528/1/grl59087_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/150528/2/grl59087.pd