Dirac equation for cold atoms in artificial curved spacetimes

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.

Towards quantum simulating QCD

“…Proposals for quantum simulator constructions already exist for some simple bosonic [26,27,28] and fermionic [29,30,31,32] field theories. Hence it is natural to ask whether our understanding of strongly coupled systems in nuclear and particle physics may benefit from quantum simulation.…”

An optical-lattice-based quantum simulator for relativistic field theories and topological insulators

“…Possible applications of such optical-lattice-based quantum simulations are numerous and diverse, ranging from the realization of Abelian and non-Abelian static gauge fields [11,[15][16][17][18] to that of quantum Hall states [19][20][21][22][23]; from the study of the anomalous quantum Hall effect [24,25] to the quantum spin Hall effect [26][27][28]; from 3D topological insulators [28,29], to flat-band physics with a non-trivial topological order [30,31], or non-Abelian anyons [32]. Recently, a great deal of effort has also been put in designing schemes where the exotic effects associated with relativistic quasiparticles, such as Klein tunneling and Zitterbewegung, arise in a controlled table-top experiment [33][34][35][36][37][38][39][40].…”

Local quantum thermometry using Unruh–DeWitt detectors

“…If they are slowly varying, they can be understood as a local time-lapse function |g 00 (x)| 1/2 of a static metric [2]:…”

“…Recently, quantum simulators built upon ultracold atomic gases [1] have been designed in order to explore the very interesting interplay between quantum mechanics and curved space-time [2], including the effects of dimensionality [3] or unusual topology [4]. Moreover, a detailed proposal for a quantum simulator to explore Unruh physics in cold atoms has been put forward [5].…”