Simulating Dirac models with ultracold atoms in optical lattices

Abstract

We present a general model allowing "quantum simulation" of one-dimensional Dirac models with 2- and 4-component spinors using ultracold atoms in driven 1D tilted optical latices. The resulting Dirac physics is illustrated by one of its well-known manifestations, Zitterbewegung. This general model can be extended and applied with great flexibility to more complex situations.Comment: 12 pages, 6 figures, accepted for Physical Review

Generalized lattice Wilson–Dirac fermions in (1 + 1) dimensions for atomic quantum simulation and topological phases

“…We hope that the proposal in this work will be used for the realization of atomic quantum simulators of 1D Dirac fermion physics for observing, e.g. the Zitterbewegung phenomena in lattice systems [23,[49][50][51][52], and other related models [22,53].…”

Dirac Equation in ( 1+1 )-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model

“…A paradigmatic example is the connection between the quantum Rabi model (QRM), which describes light-matter interaction, and relativistic quantum physics. The simulation of a Dirac fermion in Minkowski spacetime has been proposed and implemented in several platforms [41][42][43][44][45]. However, the connection between quantum optics and quantum theory in curved spacetime remains unexplored.…”

Analog quantum simulation of the spinor-four Dirac equation with an artificial gauge field

“…The model builds on the general approach introduced for the 1D case in Ref. [2]. A 2D "tilted" (or Wannier-Stark) lattice in the x, z plane [24] is described by the 2D (dimensionless) Hamiltonian…”

“…Although the Dirac equation represents a paradigm for modern field theory, this physics remained relatively elusive, restricted to high-energy situations or to exotic materials. Recent developments both in condensed matter and ultracold-atom systems have generated a burst of interest, in particular, the concept of "quantum simulator" opened a new window in the study of Dirac physics [1][2][3][4][5][6][7][8][9][10][11][12][13]. Inspired by an original insight of Feynman [14], a quantum simulator is a "simple" and controllable system that can mimic (some aspects of) the behavior of a more complex or less accessible ones.…”

“…In a previous work [2] we introduced a general model allowing to quantum-simulate a spinor-4 Dirac Hamiltonian in 1D without magnetic field. In the present work we shall i) generalize this approach to the 2D case, ii) introduce an artificial gauge field, and iii) demonstrate its ability to simulate known behaviors of the Dirac equation.…”