Final Report Summary - QUAGATUA (Quantum Gauge Theories and Ultracold Atoms)
Quantum technologies are THE technologies of the future. Universal quantum computers are among the most important achievements that quantum technologies will offer. While the way toward this achievement remains long and difficult, quantum computers of special purpose, a.k.a. quantum simulators already exist and start to compete with classical computers in the laboratories and on the market (D-wave systems).
Quantum simulators are experimental systems that are well controlled and that can mimic interesting and useful models of condensed matter or high energy physics. Such models are notoriously difficult to simulate with classical computers. A paradigm example is the, so called, Fermi Hubbard model that describes interacting electrons, hopping in a lattice. Many physicist believe that this model captures the nature of high temperature superconductivity. Understanding it better might lead in the future to design of superconductors at even higher temperatures -- that is why understanding the underlying model is of great fundamental, practical and technological importance.
Among the phenomena that one would like to mimic are evidently those that occur in strong magnetic field, with integer and fractional Hall effects being the paradigm examples. In such phenomena quantum matter orders in a novel way and exhibits topological, non-local order, that is particularly robust with respect to perturbations. Because of this robustness, integer quantum Hall effect is used nowadays to define a standard of electric resistance. Recently, novel types of topological materials have been discovered, such as topological insulators and topological superconductors; all of them can be regarded to be the systems under the influence of strong non-Abelian magnetic field, i.e. magnetic field that acts on particles in such a way that it additionally affects particle's internal degrees of freedom. These materials and discoveries rise our hopes for fascinating applications in spintronics, and quantum technologies.
Both the standard magnetic field and the non-Abelian gauge fields belong to a class of fields called gauge fields. In addition to condensed matter physics, gauge field theories are fundamental theories of matter and elementary particles. The, so called, standard model of elementary particles that unifies electromagnetic, weak and strong interactions, is a paradigm example of quantum gauge field theory. While our understanding of the standard model grows constantly, there are phenomena that are still far from understanding; these concern phenomena where strong correlations occur: quark confinement, quark-gluon plasma at high densities and temperatures. One way to understand such non-perturbative aspects of gauge theories is offered by lattice gauge theories (LGTs) which can be simulated quite efficiently with classic computers. Still, there are many open fundamental questions in the field of LGTs and quantum simulators of LGTs might help to answer these questions.
The ERC project QUAGATUA (QUAntum GAuge Theories and Ultracold Atoms) was devoted to theoretical design and investigations of possible quantum simulators of
i) systems under influence of strong, external gauge fields,
ii) systems in which low energy excitation are described by emergent quantum gauge field theory,
iii) systems that mimic lattice gauge theory models
The results of the project have stimulated numerous experimental efforts toward experimental realization of quantum simulators of artificial gauge fields and, more recently, toward simulators of lattice gauge theories. After 5 years of QUAGATUA we are still in the beginning of the road toward quantum technological applications of quantum simulators of gauge fields, but we have passed the first miles and milestones.
Quantum simulators are experimental systems that are well controlled and that can mimic interesting and useful models of condensed matter or high energy physics. Such models are notoriously difficult to simulate with classical computers. A paradigm example is the, so called, Fermi Hubbard model that describes interacting electrons, hopping in a lattice. Many physicist believe that this model captures the nature of high temperature superconductivity. Understanding it better might lead in the future to design of superconductors at even higher temperatures -- that is why understanding the underlying model is of great fundamental, practical and technological importance.
Among the phenomena that one would like to mimic are evidently those that occur in strong magnetic field, with integer and fractional Hall effects being the paradigm examples. In such phenomena quantum matter orders in a novel way and exhibits topological, non-local order, that is particularly robust with respect to perturbations. Because of this robustness, integer quantum Hall effect is used nowadays to define a standard of electric resistance. Recently, novel types of topological materials have been discovered, such as topological insulators and topological superconductors; all of them can be regarded to be the systems under the influence of strong non-Abelian magnetic field, i.e. magnetic field that acts on particles in such a way that it additionally affects particle's internal degrees of freedom. These materials and discoveries rise our hopes for fascinating applications in spintronics, and quantum technologies.
Both the standard magnetic field and the non-Abelian gauge fields belong to a class of fields called gauge fields. In addition to condensed matter physics, gauge field theories are fundamental theories of matter and elementary particles. The, so called, standard model of elementary particles that unifies electromagnetic, weak and strong interactions, is a paradigm example of quantum gauge field theory. While our understanding of the standard model grows constantly, there are phenomena that are still far from understanding; these concern phenomena where strong correlations occur: quark confinement, quark-gluon plasma at high densities and temperatures. One way to understand such non-perturbative aspects of gauge theories is offered by lattice gauge theories (LGTs) which can be simulated quite efficiently with classic computers. Still, there are many open fundamental questions in the field of LGTs and quantum simulators of LGTs might help to answer these questions.
The ERC project QUAGATUA (QUAntum GAuge Theories and Ultracold Atoms) was devoted to theoretical design and investigations of possible quantum simulators of
i) systems under influence of strong, external gauge fields,
ii) systems in which low energy excitation are described by emergent quantum gauge field theory,
iii) systems that mimic lattice gauge theory models
The results of the project have stimulated numerous experimental efforts toward experimental realization of quantum simulators of artificial gauge fields and, more recently, toward simulators of lattice gauge theories. After 5 years of QUAGATUA we are still in the beginning of the road toward quantum technological applications of quantum simulators of gauge fields, but we have passed the first miles and milestones.