Curved spacetime from interacting gauge theories

Phonons in a Bose-Einstein condensate can be made to behave as if they propagate in curved spacetime by controlling the condensate flow speed. Seemingly disconnected to this, artificial gauge potentials can be induced in charge neutral atomic condensates by for instance coupling two atomic levels to a laser field. In this work, we connect these two worlds and show that synthetic interacting gauge fields, i.e. density-dependent gauge potentials, induce a non-trivial spacetime structure for the phonons. Whilst the creation of effective horizons for phonons solely depends on the flow speed of the condensate, this allows for the creation of new spacetime geometries which can be easily designed by tuning the transverse laser phase. By exploiting this new degree of freedom we show that effectively charged phonons in 2+1 dimensions can be simulated, which behave as if they move under the influence of both a gravitational and an electromagnetic field.