Dirac Equation For Cold Atoms In Artificial Curved Spacetimes

TL;DR

This paper demonstrates how ultracold atoms in optical lattices with artificial gauge fields can simulate Dirac fermions in curved spacetimes, enabling experimental exploration of quantum field theories in gravitational backgrounds.

Contribution

It establishes an exact mapping between the Fermi-Hubbard model with non-Abelian gauge fields and Dirac fermions in curved spacetime, proposing feasible experimental realizations.

Findings

Mapping of Fermi-Hubbard Hamiltonian to Dirac gauge theory

Identification of spacetime metrics realizable with optical lattices

Analysis of 2+1D Rindler metric in cold atom systems

Abstract

We argue that the Fermi-Hubbard Hamiltonian describing the physics of ultracold atoms on optical lattices in the presence of artificial non-Abelian gauge fields, is exactly equivalent to the gauge theory Hamiltonian describing Dirac fermions in the lattice. We show that it is possible to couple the Dirac fermions to an "artificial" gravitational field, i.e. to consider the Dirac physics in a curved spacetime. We identify the special class of spacetime metrics that admit a simple realization in terms of a Fermi-Hubbard model subjected to an artificial SU(2) field, corresponding to position dependent hopping matrices. As an example, we discuss in more detail the physics of the 2+1D Rindler metric, its possible experimental realization and detection.