Quantum simulation of high-energy physics with ultracold atoms

Predicting the quantum dynamics of charged matter interacting with dynamical gauge fields poses an outstanding challenge in theoretical physics. Lacking a generally applicable computational method, quantum simulators offer a promising alternative. In this thesis, we contribute to the quantum simulation of high-energy physics, focusing on the platform of ultracold atoms. Using Wilson fermions, we propose to improve implementations of lattice gauge theories based on mixtures of cold atoms in optical lattices. Numerical benchmarks indicate that this makes the realization of Schwinger pair production feasible with current technology. Our proposal is modular and an elementary building is demonstrated experimentally. We further identify dynamical topological transitions, which we discovered in the massive Schwinger model, as a suitable target for quantum simulators. Defining a gauge-invariant order parameter, these transitions are shown to persist beyond weak coupling. In the second part of this thesis, we develop a framework for analyzing quantum simulators in terms of experimentally accessible irreducible correlation functions at equal times. We verify this approach numerically for the sine-Gordon model in thermal equilibrium, quantum simulated by two tunnel-coupled superfluids. Finally, we apply our analysis to the non-equilibrium dynamics of a spinor Bose gas, revealing suppressed effective interactions in a strongly-correlated infrared regime

Quantum simulation of lattice gauge theories using Wilson fermions

Quantum simulators have the exciting prospect of giving access to real-time dynamics of lattice gauge theories, in particular in regimes that are difficult to compute on classical computers. Future progress towards scalable quantum simulation of lattice gauge theories, however, hinges crucially on the efficient use of experimental resources. As we argue in this work, due to the fundamental non-uniqueness of discretizing the relativistic Dirac Hamiltonian, the lattice representation of gauge theories allows for an optimization that up to now has been left unexplored. We exemplify our discussion with lattice quantum electrodynamics in two-dimensional space-time, where we show that the formulation through Wilson fermions provides several advantages over the previously considered staggered fermions. Notably, it enables a strongly simplified optical lattice setup and it reduces the number of degrees of freedom required to simulate dynamical gauge fields. Exploiting the optimal representation, we propose an experiment based on a mixture of ultracold atoms trapped in a tilted optical lattice. Using numerical benchmark simulations, we demonstrate that a state-of-the-art quantum simulator may access the Schwinger mechanism and map out its non-perturbative onset.Comment: 19 pages, 11 figure

Quantum and classical spin network algorithms for qq-deformed Kogut-Susskind gauge theories

Treating the infinite-dimensional Hilbert space of non-abelian gauge theories is an outstanding challenge for classical and quantum simulations. Here, we introduce $q$-deformed Kogut-Susskind lattice gauge theories, obtained by deforming the defining symmetry algebra to a quantum group. In contrast to other formulations, our proposal simultaneously provides a controlled regularization of the infinite-dimensional local Hilbert space while preserving essential symmetry-related properties. This enables the development of both quantum as well as quantum-inspired classical Spin Network Algorithms for $q$-deformed gauge theories (SNAQs). To be explicit, we focus on SU(2)$_k$ gauge theories, that are controlled by the deformation parameter $k$ and converge to the standard SU(2) Kogut-Susskind model as $k \rightarrow \infty$. In particular, we demonstrate that this formulation is well suited for efficient tensor network representations by variational ground-state simulations in 2D, providing first evidence that the continuum limit can be reached with $k = \mathcal{O}(10)$. Finally, we develop a scalable quantum algorithm for Trotterized real-time evolution by analytically diagonalizing the SU(2)$_k$ plaquette interactions. Our work gives a new perspective for the application of tensor network methods to high-energy physics and paves the way for quantum simulations of non-abelian gauge theories far from equilibrium where no other methods are currently available.Comment: 5+4 pages, 4+1 figure

El Cash Pooling: gestión centralizada de la tesorería

Cash pooling consist of a method or management tool that more and more companies use to maintain balanced accounts between the different subsidiaries that are part of a business group. This paper is intended to mean an approach to a practice that is becoming more common in business groups looking to improve and be more efficient in managing its Treasury. So, in order to provide a better overview for this topic, in the next lines will be appreciated a theoretical research focused on the two main types of cash pooling practiced (notional and physical pooling), a brief mention of the differences of this practice in various parts of the world and also, a study of how to carry out a practical case in a multinational firm.El cash pooling es un método o herramienta de gestión por la que cada vez más empresas apuestan para mantener equilibradas las cuentas entre las diferentes filiales que forman parte de un grupo empresarial. El presente trabajo pretende significar una aproximación a una práctica que cada vez es más corriente en los grupos empresariales que buscan mejorar y ser más eficientes en la gestión de sus tesorerías. Así pues, para ofrecer la mejor visión de conjunto para este tema, en las líneas sucesivas se hace un recorrido en el que se apreciará un estudio teórico centrado en los dos tipos principales de cash pooling que se emplean (notional y physical pooling), así como una breve mención a las diferencias de esta práctica en varios lugares del mundo, y el estudio de cómo se llevaría a cabo un caso práctico en una conocida multinacionaUniversidad de Sevilla. Doble Grado en Derecho y en Finanzas y Contabilida