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Phase diagram and dynamical phases of self-organization of a Bose-Einstein condensate in a transversely pumped red-detuned cavity

Julian Mayr1,2, Maria Laura Staffini1, Simon B. Jäger2, Corinna Kollath2, and Jonathan Keeling1

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Phys. Rev. A 113, 023312 – Published 12 February, 2026

DOI: https://doi.org/10.1103/1sj4-w9sd

Abstract

We study a transversely pumped atomic Bose-Einstein condensate coupled to a single-mode optical cavity, where effective atom-atom interactions are mediated by pump and cavity photons. A number of experiments and theoretical works have shown the formation of a superradiant state in this setup, where interference of pump and cavity light leads to an optical lattice in which atoms self-consistently organize. This self-organization has been extensively studied using the approximate Dicke model (truncating to two momentum states), as well as through numerical Gross-Pitaevskii simulations in one and two dimensions. Here, we perform a full mean-field analysis of the system, including all relevant atomic momentum states and the cavity field. We map out the steady-state phase diagram vs pump strength and cavity detuning, and provide an in-depth understanding of the instabilities that are linked to the emergence of spatiotemporal patterns. We find and describe parameter regimes where the mean field predicts bistability, regimes where the dynamics form chaotic trajectories, instabilities caused by resonances between normal mode excitations, and states with atomic dynamics but vanishing cavity field.

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Phys. Rev. A 113, 023312– Published 12 February, 2026
  • Received 5 September 2025
  • Revised 18 December 2025
  • Accepted 20 January 2026
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