Curved and expanding spacetime geometries in Bose-Einstein condensates

Abstract

Phonons have the characteristic linear dispersion relation of massless relativistic particles. They arise as low energy excitations of Bose-Einstein condensates and, in nonhomogeneous situations, are governed by a space-and time-dependent acoustic metric. We discuss how this metric can be experimentally designed to realize curved spacetime geometries, in particular, expanding Friedmann-Lemaître-Robertson-Walker cosmologies, with negative, vanishing, or positive spatial curvature. A nonvanishing Hubble rate can be obtained through a time-dependent scattering length of the background condensate. For relativistic quantum fields this leads to the phenomenon of particle production, which we describe in detail. We explain how particle production and other interesting features of quantum field theory in curved spacetime can be tested in terms of experimentally accessible correlation functions.

Quantum field simulator for dynamics in curved spacetime

“…Theoretically we find Benchmarking of the quantum field simulator with time dependent correlations. Initial phase and amplitude of the heterodyne signal show quantitative agreement with analytical theory predictions [32] (solid lines). Of special interest is the dramatic signal of the initial phase for the 3 ms ramp.…”

“…The term 1/2 corresponds to vacuum fluctuations, the term |β k | 2 describes the populations of a mode k and the oscillating term contains the contributions from coherences. The Bogoliubov coefficients α k and β k , as well as the phase θ k = Arg(α k β k ), depend on the expansion history and are calculated by relating the quantum states before and after the expansion [32,48]. The initial distribution is taken to be of thermal form…”

“…with the metric g µν and √ g = −det(g µν ) (see details in [32]). For expanding spacetimes, this is the minimal model system for cosmological particle pair production.…”

“…errors from the fit. Here, the solid lines are theory predictions derived by analytically solving mode evolution equations for a free, massless, relativistic scalar field in a (2 + 1)-dimensional expanding spacetime [32].…”

Scalar quantum fields in cosmologies with 2+1 spacetime dimensions

“…In our companion paper [33] we have generalized the aforementioned mapping to spatially curved FLRW universes, which can be realized by enclosing the Bose-Einstein condensate with suitable trapping profiles and varying the scattering length over time to simulate expanding, as well as contracting, FLRW cosmologies. In this way, observing cosmological particle production becomes accessible in table-top experiments.…”