Ultra-cold atoms as quantum simulators for relativistic phenomena

The goal of this article is to review developments regarding the use of ultra-cold atoms as quantum simulators. Special emphasis is placed on relativistic quantum phenomena, which are presumably most interesting for the audience of this journal. After a brief introduction into the main idea of quantum simulators and the basic physics of ultra-cold atoms, relativistic quantum phenomena of linear fields are discussed, including Hawking radiation, the Unruh effect, cosmological particle creation, the Gibbons–Hawking and Ginzburg effects, super-radiance, Sauter–Schwinger and Breit–Wheeler pair creation, as well as the dynamical Casimir effect. After that, the focus is shifted to phenomena of non-linear fields, such as the sine–Gordon model, the Kibble–Zurek mechanism, false-vacuum decay, and quantum back-reaction. In order to place everything into proper context, the basic underlying mechanisms of these phenomena are briefly recapitulated before their simulators are discussed. Even though effort is made to provide a review as fair as possible, there can be no claim of completeness and the selection as well as the relative weights of the topics may well reflect the personal view and taste of the author.