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  • Letter
  • Open Access

Observation of a zero-energy excitation mode in the open Dicke model

Anton Bölian1,*, Phatthamon Kongkhambut1,2,3,*, Christoph Georges1, Roy D. Jara, Jr.4, José Vargas1, Jens Klinder1, Jayson G. Cosme4, Hans Keßler1,†, and Andreas Hemmerich1,‡

  • *These authors contributed equally to this work.
  • †Contact author: hkessler@physnet.uni-hamburg.de
  • ‡Contact author: andreas.hemmerich@uni-hamburg.de
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Phys. Rev. Research 7, L032056 – Published 10 September, 2025

DOI: https://doi.org/10.1103/4pzy-rchc

Abstract

Approaching phase boundaries in many-body systems can give rise to intriguing signatures in their excitation spectra. Here, we explore the excitation spectrum of a Bose-Einstein condensate strongly coupled to an optical cavity and pumped by an optical standing wave, which simulates the famous Dicke-Hepp-Lieb phase transition of the open Dicke model with dissipation arising due to photon leakage from the cavity. For weak dissipation, the excitation spectrum displays two strongly polaritonic modes. Close to the phase boundary, we observe an intriguing regime where the lower energetic of these modes, instead of showing the expected roton-type mode softening, is found to approach and persist at zero energy, well before the critical pump strength for the Dicke-Hepp-Lieb transition boundary is reached. Hence, a peculiar situation arises, where an excitation is possible at zero energy cost, but nevertheless no instability of the system is created.

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Phys. Rev. Research 7, L032056– Published 10 September, 2025
  • Received 10 February 2025
  • Accepted 14 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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