Non-Abelian gauge fields

Abstract

Building a universal quantum computer is a central goal of emerging quantum technologies, which has the potential to revolutionize science and technology. Unfortunately, this future does not seem to be very close at hand. However, quantum computers built for a special purpose, i.e. quantum simulators , are currently developed in many leading laboratories. Many schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots, photonic networks, or superconducting circuits. The progress in experimental implementations is more than spectacular.Particularly interesting are those systems that simulate quantum matter evolving in the presence of gauge fields.In the quantum simulation framework, the generated (synthetic) gauge fields may be Abelian, in which case they are the direct analogues of the vector potentials commonly associated with magnetic fields. In condensed matter physics, strong magnetic fields lead to a plethora of fascinating phenomena, among which the most paradigmatic is perhaps the quantum Hall effect. The standard Hall effect consists in the appearance of a transverse current, when a longitudinal voltage difference is applied to a conducting sample. For quasi-two-dimensional semiconductors at low temperatures placed in very strong magnetic fields, the transverse conductivity, the ratio between the transverse current and the applied voltage, exhibits perfect and robust quantization, independent for instance of the material or of its geometry. Such an integer quantum Hall effect, is now understood as a deep consequence of underlying topological order. Although such a system is an insulator in the bulk, it supports topologically robust edge excitations which carry the Hall current. The robustness of these chiral excitations against backscattering explains the universality of the quantum Hall effect. Another interesting and related effect, which arises from the interplay between strong magnetic field and lattice potentials, is the famous Hofstadter butterfly: the energy spectrum of a single particle moving on a lattice and subjected to a strong magnetic field displays a beautiful fractal structure as a function of the magnetic flux penetrating each elementary plaquette of the lattice.When the effects of interparticle interactions become dominant, two-dimensional gases of electrons exhibit even more exotic behaviour leading to the fractional quantum Hall effect. In certain conditions such a strongly interacting electron gas may form a highly correlated state of matter, the prototypical example being the celebrated Laughlin quantum liquid. Even more fascinating is the behaviour of bulk excitations (quasi-hole and quasi-particles): they are neither fermionic nor bosonic, but rather behave as anyons with fractional statistics intermediate between the two. Moreover, for some specific filling factors (ratio between the electronic density and the flux density), these an...

Unruh effect for interacting particles with ultracold atoms

“…The quantitative differences might be due to the different dispersion relations away from the Dirac points. At T = 0 we recover the critical value |U c | ≈ 3 as obtained for an attractive π-flux model [131]. For T > 0, the critical interaction increases.…”

“…At the half filling for the noninteracting system U = 0, we have ∆ = 0 and the ground state of the Minkowski Dirac Hamiltonian (23) is a Dirac semimetal with two valence and conduction bands touching at Dirac points [128][129][130][131][132]. Similarly to a standard BCS theory [120,121], in a half-filled attractive Fermi Hubbard model on a square lattice even arbitrarily small attractive interactions U < 0 give rise to a nonzero ∆ pairing [133][134][135].…”

Light-induced gauge fields for ultracold atoms

“…In this Section, we describe how interacting BECs and degenerate Fermi gases behave in the presence 51 of an external gauge potential, focusing on the case where atoms are subjected to a synthetic SOC. The interplay between interactions and synthetic magnetic fields induced by rotation were described in the review by Cooper [60]; for a more complete overview on interacting spin-orbit-coupled atomic gases, consider the reviews by H. Zhai [216,242] and X. Zhou et al [243], as well as other articles recently published in the special issue on non-Abelian gauge fields edited by Gerbier et al [244].…”

Topological Properties of Linear Circuit Lattices

“…This provides a platform to synthesize background gauge fields using linear circuits in parallel to studies with more complex elements [7,19] and to intense investigations using ultracold atoms (e.g. [20][21][22][23] and refs. therein).…”