Particle Pair Production in Analog Spacetime Realized in a Bose-Einstein Condensate

Cosmological particle production is one of the key findings of quantum field theory (QFT) in curved spacetimes. In this process, the expansion of space produces pairs of particles, even from an initial vacuum. This is equivalent to a one-dimensional quantum mechanical scattering problem, in which the time-dependence of the scale factor is incorporated in a scattering potential. Reflection on the potential gives rise to particle production. Here, this process is investigated in the analog system of a two-dimensional Bose-Einstein condensate of potassium-39. Its fundamental excitations are treated as a scalar field and the speed of sound sets the relevant scale. Expansion is simulated with a dynamical decrease of the speed of sound via a magnetic Feshbach resonance. We observe coherent oscillations of the density fluctuation power spectra which are a result of interference of the produced particle pairs. To probe the scattering analogy, we implement linear expansion of space, which is equivalent to a box potential, and find no particle production for modes that can be associated with resonances of the box. For periodic spacetimes, we find large particle production for momenta that correspond to the band gaps of the infinitely extended periodic potential. In one case, we find squeezing below the level of vacuum fluctuations, which is a witness for entanglement between the populated momentum modes.