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In this paper, we formulate quantum field theory on an analogue curved spacetime in a Bose-Einstein condensate where quantum particles on curved spacetime are equated with Bogoliubov quasi-particle excitations on the Bose-Einstein condensate. By using our formulation, we numerically investigate a particle creation in analogue expanding Universe which can be expressed as Bogoliubov quasiparticles in an expanding Bose-Einstein condensate and obtain its spectrum which shows the thermal Maxwell-Boltzmann distribution, the temperature of which can be experimentally accessible. This is the first direct numerical simulation for the particle creation and its spectrum on analogue curved spacetime by using the system of Bose-Einstein condensates.

Particle creation in bose-einstein condensates: Numerical analysis of the Bogoliubov–de Gennes equation for trapped ultracold atoms