Particle production and entanglement in a spherical-shell BEC

We study an interacting Bose gas confined to a spherical-shell potential, a geometry inspired by NASA's Cold Atom Laboratory aboard the International Space Station. In a spherical-shell Bose–Einstein condensate, low-energy phonon excitations satisfy a relativistic Klein–Gordon equation, realizing a quantum field simulator in a two-dimensional positively curved spacetime. By introducing a time-dependent interaction strength via a Feshbach resonance, we simulate an expanding universe where the changing scale factor induces analog particle creation. We derive mode equations governing the non-equilibrium dynamics of density and phase fluctuations during expansion. The created quasiparticles are entangled, and we quantify this entanglement using the logarithmic negativity. Finally, we discuss how analog particle production and entanglement manifest in experimentally measurable correlation functions.