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Emergent quantum field theories on curved spacetimes in spinor Bose-Einstein condensates: From scalar to Proca fields

Christian F. Schmidt1,*,†, Simon Brunner2,3,*,‡, and Stefan Floerchinger2,1,§

  • *These authors contributed equally to this work.
  • †Contact author: christian.schmidt@uni-jena.de
  • ‡Contact author: simon.brunner@uibk.ac.at
  • §Contact author: stefan.floerchinger@uni-jena.de
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Phys. Rev. A 112, 053321 – Published 18 November, 2025

DOI: https://doi.org/10.1103/fnbn-yp2m

Abstract

We consider excitations of a spin-1 Bose-Einstein-condensate in the vicinity of different mean-field configurations and derive mappings to emergent relativistic quantum field theories minimally coupled to curved acoustic spacetimes. The quantum fields are typically identified with Nambu-Goldstone bosons, such that the structure of the analog quantum field theories on curved spacetimes depends on the (spontaneous) symmetry breaking pattern of the respective ground state. The emergent spacetime geometries are independent of each other and exhibit bimetricity in the polar and antiferromagnetic phase, whereas one has trimetricity in the ferromagnetic phase. Compared to scalar BECs, the spinor degrees of freedom allow us to investigate massive vector and scalar fields where the former is a spin-nematic rotation mode in the polar phase, which can be cast into a Proca field that is minimally coupled to a curved spacetime that emerges on length scales larger than the spin-healing length. Finally, we specify the Zeeman couplings and the condensate trap to be spacetime-dependent such that a cosmological Friedmann-Lemaître-Robertson-Walker metric can be achieved. This work enables a pathway towards quantum-simulating cosmological particle production of Proca quanta via quenching the quadratic Zeeman coefficient or via magnetic field ramps, which both result in the creation of spin-nematic squeezed states.

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Phys. Rev. A 112, 053321– Published 18 November, 2025
  • Received 23 June 2025
  • Accepted 23 October 2025
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