Simulation of non-Abelian lattice gauge fields with a single-component gas

Abstract

We show that non-Abelian lattice gauge fields can be simulated with a single component ultra-cold atomic gas in an optical lattice potential. An optical lattice can be viewed as a Bravais lattice with a N -point basis. An atom located at different points of the basis can be considered as a particle in different internal states. The appropriate engineering of tunneling amplitudes of atoms in an optical lattice allows one to realize U(N ) gauge potentials and control a mass of particles that experience such non-Abelian gauge fields. We provide and analyze a concrete example of an optical lattice configuration that allows for simulation of a static U(2) gauge model with a constant Wilson loop and an adjustable mass of particles. In particular, we observe that the non-zero mass creates large conductive gaps in the energy spectrum, which could be important in the experimental detection of the transverse Hall conductivity.

Loading ultracold gases in topological Floquet bands: the fate of current and center-of-mass responses

“…constitutes a more stable observable, as the time-integration in Eq. (20), when performed over reasonable observation times t 2π/∆ gap , annihilates the contribution from the oscillating inter-band velocity. Finally, we discuss the relevant case where the bands are filled in a uniform manner after the ramp, i.e.…”

“…when the coefficients α and β are constant numbers. In this case, the band-velocity contribution to the COM dynamics (20) vanishes. Furthermore, the contribution due to the anomalous velocity is then directly proportional to the Chern numbers of the individual (Floquet) bands, ν 1 and ν 2 .…”

“…Furthermore, the contribution due to the anomalous velocity is then directly proportional to the Chern numbers of the individual (Floquet) bands, ν 1 and ν 2 . In the long-time limit, where the inter-band velocity contribution vanishes, the COM displacement (20) then yields…”

Quantum simulation of the Abelian-Higgs lattice gauge theory with ultracold atoms

“…Other quantum systems that have been considered for quantum simulations of lattice gauge theories are superconducting circuits [84,85], trapped ions [86,87] and Rydberg atoms [16,88]. Discrete symmetry groups have been considered as well, both for analog [70,89,90] and digital simulations [91,92], as well as non-abelian theories [93][94][95][96][97][98][99][100]. A general formalism for digital simulations of lattice gauge theories with ultracold atoms can be found in [91].Recently, the first experimental realization of a quantum simulation of a lattice gauge theory was performed [101], where the real-time dynamics of the Schwinger model were simulated on a few-qubit trapped-ion quantum computer.…”

Digital quantum simulation of lattice gauge theories in three spatial dimensions

“…There are also differences in the proposed simulation scheme: the first one is the analogue approach, where not only the degrees of freedom of the simulated system are mapped to those of the simulating one: by appropriately tailoring the interactions of the simulator, its Hamiltonian is exactly or approximately mapped to the desired one (which can be adiabatically changed). Quantum simulations of this type have been proposed, mostly using ultracold atoms [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], as well as trapped ions [45,46] and superconducting qubits [47,48]. Another approach-the digital one-is based on an idea of Feynman [49], to use a quantum computer (i.e.…”