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Dicke quantum phase transition with a superfluid gas in an optical cavity


A phase transition describes the sudden change of state of a physical system, such as melting or freezing. Quantum gases provide the opportunity to establish a direct link between experiments and generic models that capture the underlying physics. The Dicke model describes a collective matter–light interaction and has been predicted to show an intriguing quantum phase transition. Here we realize the Dicke quantum phase transition in an open system formed by a Bose–Einstein condensate coupled to an optical cavity, and observe the emergence of a self-organized supersolid phase. The phase transition is driven by infinitely long-range interactions between the condensed atoms, induced by two-photon processes involving the cavity mode and a pump field. We show that the phase transition is described by the Dicke Hamiltonian, including counter-rotating coupling terms, and that the supersolid phase is associated with a spontaneously broken spatial symmetry. The boundary of the phase transition is mapped out in quantitative agreement with the Dicke model. Our results should facilitate studies of quantum gases with long-range interactions and provide access to novel quantum phases.

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Figure 1: Concept of the experiment.
Figure 2: Analogy to the Dicke model.
Figure 3: Observation of the phase transition.
Figure 4: Steady state in the self-organized phase.
Figure 5: Phase diagram.


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We thank G. Blatter, I. Carusotto, P. Domokos, A. Imamoglu, S. Leinss, R. Mottl, L. Pollet, H. Ritsch and M. Troyer for discussions. Financial funding from NAME-QUAM (European Commission Seventh Framework Programme Future and Emerging Technologies Open Scheme, grant number 225187) and QSIT (ETH Zürich) is acknowledged. C.G. acknowledges support from an ETH Fellowship.

Author information




The data was taken and analysed by K.B. and C.G. The theoretical analysis was mainly performed by F.B. and T.E. The relation to the Dicke model was realized by F.B. The experimental concept was developed by T.E. All authors contributed extensively to the discussion of the results as well as to the preparation of the manuscript.

Corresponding author

Correspondence to Tilman Esslinger.

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The authors declare no competing financial interests.

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Baumann, K., Guerlin, C., Brennecke, F. et al. Dicke quantum phase transition with a superfluid gas in an optical cavity. Nature 464, 1301–1306 (2010).

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