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

📝 Abstract

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.

💡 Analysis

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.

📄 Content

The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity Kristian Baumann, Christine Guerlin,∗Ferdinand Brennecke, and Tilman Esslinger† Institute for Quantum Electronics, ETH Z¨urich, CH–8093 Z¨urich, Switzerland (Dated: May 28, 2018) 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-range 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-range interactions, and provides access to novel quantum phases. INTRODUCTION The realization of Bose-Einstein condensation (BEC) in a dilute atomic gas1,2 marked the beginning of a new approach to quantum many-body physics. Meanwhile, quantum degenerate atoms are regarded as an ideal tool to study many-body quantum systems in a very well controlled way. Excellent examples are the BEC-BCS crossover3–5 and the observation of the superfluid to Mott-insulator transition6. The high control available over these many-body systems has also stimulated the notion of quantum simulation7,8, one of the goals being to generate a phase diagram of an underlying Hamiltonian. However, the phase transitions and crossovers which have been experimentally investigated with quantum gases up to now are conceptually similar since their physics is gov- erned by short-range interactions. In order to create many-body phases dominated by long-range interactions different routes have been sug- gested, most of which exploit dipolar forces between atoms and molecules9. A rather unique approach con- siders atoms inside a high-finesse optical cavity, so that the cavity field mediates infinitely long-range forces be- tween all atoms10,11. In such a setting a phase transi- tion from a Bose-Einstein condensate to a self-organized phase has been predicted once the atoms induce a suf- ficiently strong coupling between a pump field and an empty cavity mode12,13. Indeed, self-organization of a classical, laser-cooled atomic gas in an optical cav- ity was observed experimentally14. Conceptually re- lated experiments studied the atom-induced coupling between a pump field and a vacuum mode using ul- tracold or condensed atoms. This led to the observa- tion of free-space15,16 and cavity-enhanced17 superradi- ant Rayleigh scattering, as well as to collective atomic re- coil lasing17,18. Both phenomena did not support steady- state quantum phases, and became visible in transient matter wave pulses. A rather general objective of many-body physics is to understand quantum phase transitions19 and to un- ravel their connection to entanglement20,21. An impor- tant concept within this effort is a system of interacting spins in which each element is coupled to all others with equal strength. The most famous example for such an in- finitely coordinated22 spin system is the Dicke model23, which has been predicted to exhibit a quantum phase transition more than thirty years ago24,25. The Dicke model considers an ensemble of two-level atoms, i.e. spin- 1/2 particles, coupled to a single electromagnetic field mode. For sufficient coupling this system enters a super- radiant phase with macroscopic occupation of the field mode. A promising route to realize this transition has been proposed recently in the setting of cavity quantum electrodynamics by Carmichael and coworkers26. In their scheme strong coupling between two ground states of an atomic ensemble is induced by balanced Raman transi- tions involving a cavity mode and a pump field. This idea circumvents the thought to be unattainable condition for the Dicke quantum phase transition which requires a cou- pling strength on the order of the energy separation be- tween the two involved atomic levels. In this work we realize the Dicke quantum phase transi- tion in an open system and observe self-organization of a Bose-Einstein condensate. In the experiment, a conden- sate is trapped inside an ultrahigh-finesse optical cavity, and pumped from a direction transverse to the cavity axis, as shown in figure 1. We will theoretically s

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