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.

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.

Long-range interactions in quantum gases are predicted to give rise to an excitation spectrum of roton character, similar to that observed in superfluid helium. We investigated the excitation spectrum of a Bose-Einstein condensate with cavity-mediated long-range interactions, which couple all particles to each other. Increasing the strength of the interaction leads to a softening of an excitation mode at a finite momentum, preceding a superfluid-to-supersolid phase transition. We used a variant of Bragg spectroscopy to study the mode softening across the phase transition. The measured spectrum was in very good agreement with ab initio calculations and, at the phase transition, a diverging susceptibility was observed. The work paves the way toward quantum simulation of long-range interacting many-body systems.

We experimentally study the influence of dissipation on the driven Dicke quantum phase transition, realized by coupling external degrees of freedom of a Bose-Einstein condensate to the light field of a high-finesse optical cavity. The cavity provides a natural dissipation channel, which gives rise to vacuum-induced fluctuations and allows us to observe density fluctuations of the gas in real-time. We monitor the divergence of these fluctuations over two orders of magnitude while approaching the phase transition, and observe a behavior that deviates significantly from that expected for a closed system. A correlation analysis of the fluctuations reveals the diverging time scale of the atomic dynamics and allows us to extract a damping rate for the external degree of freedom of the atoms. We find good agreement with our theoretical model including dissipation via both the cavity field and the atomic field. Using a dissipation channel to nondestructively gain information about a quantum many-body system provides a unique path to study the physics of driven-dissipative systems.driven-dissipative phase transitions | critical behavior | Dicke model | quantum gas | cavity QED E xperimental progress in the creation, manipulation, and probing of atomic quantum gases has made it possible to study highly controlled many-body systems and to access their phase transitions. This unique approach to quantum many-body physics has substantiated the notion of quantum simulation for key models of condensed matter physics (1, 2). There has been increasing interest in generalizing such an approach to nonequilibrium zero-temperature or quantum phase transitions in driven-dissipative systems (3), as occurring in condensed matter systems coupled to light (4,5) or in open electronic systems (6, 7). Among the most tantalizing questions is how vacuum fluctuations from the environment influence the critical behavior at a phase transition via quantum backaction. Related to this question is whether driven-dissipative phase transitions give rise to new universal behavior, and under which conditions they exhibit classical critical behavior with an effective temperature (8-12).Coupling quantum gases to the field of an optical cavity is a particularly promising approach to realize a driven-dissipative quantum many-body system with a well-understood and controlled dissipation channel. A further advantage of this scheme is that the dissipation channel of the cavity mode can be directly used to investigate the system in a nondestructive way via the leaking cavity field (13). Combining the experimental setting of cavity quantum electrodynamics with that of quantum gases (14-18) led to the observation of quantum backaction heating caused by cavity dissipation (19,20), as well as to the realization of the nonequilibrium Dicke quantum phase transition (21). Here, we study the influence of cavity dissipation on the fluctuation spectrum at the Dicke phase transition by connecting these approaches. We nondestructively observe diverging fluctuations of the o...

A Bose-Einstein condensate is dispersively coupled to a single mode of an ultra-high finesse optical cavity. The system is governed by strong interactions between the atomic motion and the light field even at the level of single quanta. While coherently pumping the cavity mode the condensate is subject to the cavity optical lattice potential whose depth depends nonlinearly on the atomic density distribution. We observe optical bistability already below the single photon level and strong back-action dynamics which tunes the coupled system periodically out of resonance.PACS 42.50.Wk · 42.65.Pc · 42.50.Pq · 67.85.Hj