Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Experimental Realization of The Dicke Quantum Phase Transition

Kristian Baumann

Published Jan 1, 2011• 2 citations
Publisher

Abstract

We report on the first experimental realization of the Dicke quantum phase transition realized in the quantum motion of a Bose–Einstein condensate coupled to an optical cavity. Conceptually, the transition is driven by cavity-mediated long-range interactions, giving rise to the emergence of a self-organized supersolid phase. The Dicke phase transition, predicted in 1973, has not been demonstrated experimentally before this work, both due to fundamental and technological reasons. These challenges have been overcome in the present thesis by employing atomic momentum states of a Bose-Einstein condensate, which are coupled via two-photon Raman transitions involving a cavity photon and a free-space pump photon. This open-system implementation of the Dicke model allows to tune all relevant parameters and offers a unique detection scheme to monitor the manybody system in real time. We demonstrate that the phase transition is accompanied by a macroscopically occupied cavity field and a striking change in the atomic momentum distribution, due to spontaneous self-organization of the atomic density on a checkerboard lattice. The boundary of the transition is mapped out by scanning two parameters of the Dicke model, to reveal a phase diagram in close agreement with the model description. Two different ordered configurations are allowed in the superradiant phase, giving rise to the concept of spontaneous symmetry breaking at the phase transition. We experimentally distinguish the symmetry-broken states and study the origin of the symmetry-breaking process. The finite spatial extension of our system induces a small symmetry-breaking field which changes randomly on each experimental realization. The influence of this field is studied and shown to diminish upon dynamically crossing the transition point with increasing transition rates.

DOI
10.3929/ethz-a-006961248

Related papers

The Dicke Quantum Phase Transition in a Superfluid Gas Coupled to an Optical Cavity

Kristian Baumann, Christine Guerlin, Ferdinand Brennecke +1 more

A phase transition describes the sudden change of state in a physical system, such as the transition between a fluid and a solid. Quantum gases provide the opportunity to establish a direct link between experiment and generic models which capture the underlying physics. A fundamental concept to describe the collective matter-light interaction is the Dicke model which 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-ranged interactions between the condensed atoms. These are 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. The work opens the field of quantum gases with long-ranged interactions, and provides access to novel quantum phases.

•Dec 16, 2009•2 citations

Observation of Spontaneous Symmetry Breaking at the Dicke Quantum Phase Transition

Kristian Baumann, Rafael Mottl, Ferdinand Brennecke +1 more

We study symmetry breaking at the Dicke quantum phase transition by coupling a motional degree of freedom of a Bose-Einstein condensate to the field of an optical cavity. Using an optical heterodyne detection scheme we observe symmetry breaking in real-time and distinguish the two superradiant phases. We explore the process of symmetry breaking in the presence of a small symmetry-breaking field, and study its dependence on the rate at which the critical point is crossed. Coherent switching between the two ordered phases is demonstrated.

•May 2, 2011•0 citations

Exploring Symmetry Breaking at the Dicke Quantum Phase Transition

Kristian Baumann, Rafael Mottl, Ferdinand Brennecke +1 more

We study symmetry breaking at the Dicke quantum phase transition by coupling a motional degree of freedom of a Bose-Einstein condensate to the field of an optical cavity. Using an optical heterodyne detection scheme, we observe symmetry breaking in real time and distinguish the two superradiant phases. We explore the process of symmetry breaking in the presence of a small symmetry-breaking field and study its dependence on the rate at which the critical point is crossed. Coherent switching between the two ordered phases is demonstrated.

arXiv:1105.0426•Physical Review Letters•Sep 30, 2011•426 citations

Self-ordered supersolid phase beyond Dicke superradiance in a ring cavity

Yuangang Deng, Su Yi

The supersolid phase characterized by the superfluid and long-range spatial periodicity of crystalline order is central to many branches of science ranging from condensed matter physics to ultracold atomic physics. Here we study a self-ordered checkerboard supersolid phase originating from dynamical spin-orbit coupling for a transversely pumped atomic Bose-Einstein condensate trapped in a ring cavity, corresponding to a superradiant anti-Tavis-Cummings phase transition. In particular, an undamped gapless Goldstone mode is observed in contrast to the experimentally realized lattice supersolid with a gapped roton mode for Dicke superradiance. This zero-energy mode reveals the rigidity of the self-ordered superradiant phase, which spontaneously breaks a continuous translational symmetry. Our work will highlight the significant opportunities for exploring long-lived supersolid matter by utilizing dynamical spin-orbit coupling in controllable optical cavities.

arXiv:2201.07664•Physical Review Research•Jan 3, 2023•9 citations

Dicke-Model Phase Transition in the Quantum Motion of a Bose-Einstein Condensate in an Optical Cavity

Dávid Nagy, Gábor Kónya, Gergely Szirmai +1 more

We show that the motion of a laser-driven Bose-Einstein condensate in a high-finesse optical cavity realizes the spin-boson Dicke model. The quantum phase transition of the Dicke model from the normal to the superradiant phase corresponds to the self-organization of atoms from the homogeneous into a periodically patterned distribution above a critical driving strength. The fragility of the ground state due to photon measurement induced backaction is calculated.

arXiv:0912.3260•Physical Review Letters•Apr 2, 2010•397 citations

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

Julian Mayr, Maria Laura Staffini, Simon B. Jäger +2 more

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.

arXiv:2509.03445•Physical Review A•Jan 20, 2026•0 citations
We report on the first experimental realization of the Dicke quantum phase transition realized in the quantum motion of a Bose–Einstein condensate coupled to an optical cavity. Conceptually, the transition is driven by cavity-mediated long-range interactions, giving rise to the emergence of a self-organized supersolid phase. The Dicke phase transition, predicted in 1973, has not been demonstrated experimentally before this work, both due to fundamental and technological reasons. These challenges have been overcome in the present thesis by employing atomic momentum states of a Bose-Einstein condensate, which are coupled via two-photon Raman transitions involving a cavity photon and a free-space pump photon. This open-system implementation of the Dicke model allows to tune all relevant parameters and offers a unique detection scheme to monitor the manybody system in real time. We demonstrate that the phase transition is accompanied by a macroscopically occupied cavity field and a striking change in the atomic momentum distribution, due to spontaneous self-organization of the atomic density on a checkerboard lattice. The boundary of the transition is mapped out by scanning two parameters of the Dicke model, to reveal a phase diagram in close agreement with the model description. Two different ordered configurations are allowed in the superradiant phase, giving rise to the concept of spontaneous symmetry breaking at the phase transition. We experimentally distinguish the symmetry-broken states and study the origin of the symmetry-breaking process. The finite spatial extension of our system induces a small symmetry-breaking field which changes randomly on each experimental realization. The influence of this field is studied and shown to diminish upon dynamically crossing the transition point with increasing transition rates.
A phase transition describes the sudden change of state in a physical system, such as the transition between a fluid and a solid. Quantum gases provide the opportunity to establish a direct link between experiment and generic models which capture the underlying physics. A fundamental concept to describe the collective matter-light interaction is the Dicke model which 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-ranged interactions between the condensed atoms. These are 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. The work opens the field of quantum gases with long-ranged interactions, and provides access to novel quantum phases.
We study symmetry breaking at the Dicke quantum phase transition by coupling a motional degree of freedom of a Bose-Einstein condensate to the field of an optical cavity. Using an optical heterodyne detection scheme we observe symmetry breaking in real-time and distinguish the two superradiant phases. We explore the process of symmetry breaking in the presence of a small symmetry-breaking field, and study its dependence on the rate at which the critical point is crossed. Coherent switching between the two ordered phases is demonstrated.
We study symmetry breaking at the Dicke quantum phase transition by coupling a motional degree of freedom of a Bose-Einstein condensate to the field of an optical cavity. Using an optical heterodyne detection scheme, we observe symmetry breaking in real time and distinguish the two superradiant phases. We explore the process of symmetry breaking in the presence of a small symmetry-breaking field and study its dependence on the rate at which the critical point is crossed. Coherent switching between the two ordered phases is demonstrated.
The supersolid phase characterized by the superfluid and long-range spatial periodicity of crystalline order is central to many branches of science ranging from condensed matter physics to ultracold atomic physics. Here we study a self-ordered checkerboard supersolid phase originating from dynamical spin-orbit coupling for a transversely pumped atomic Bose-Einstein condensate trapped in a ring cavity, corresponding to a superradiant anti-Tavis-Cummings phase transition. In particular, an undamped gapless Goldstone mode is observed in contrast to the experimentally realized lattice supersolid with a gapped roton mode for Dicke superradiance. This zero-energy mode reveals the rigidity of the self-ordered superradiant phase, which spontaneously breaks a continuous translational symmetry. Our work will highlight the significant opportunities for exploring long-lived supersolid matter by utilizing dynamical spin-orbit coupling in controllable optical cavities.
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.