Phase transition in a Dicke model with a two-photon interaction

A. A. Bakasov

G. Comer Duncan

The effect of the antiresonant atom-field interactions on the phase-transition property of the Dicke model is studied. A phase transition is shown to exist when the following inequality is satisfied between the coupling constant $\ensuremath{\lambda}$ and the ratio of the atomic transition frequency to the field frequency $\ensuremath{\epsilon}$: ${\ensuremath{\lambda}}^{2}>\frac{\ensuremath{\epsilon}}{4}$. Relative to the Dicke-model result the necessary value of ${\ensuremath{\lambda}}^{2}$ is thus smaller by a factor of \textonequarter{}. In addition it is established that the critical temperature is higher than in the Dicke model. A further significant difference between the two models is reflected in the properties of the "photon statistics." In the present model an additional polynomial temperature dependence in the powers of the average number of photons per atom is found. It is concluded that the effect of the antiresonant terms is not negligible concerning the thermodynamic properties of the system, in contrast to the evidence for many time-dependent properties studied previously.

Louis Garbe, Peregrine Wade, Fabrizio Minganti +3 more

The Dicke model is a paradigmatic quantum-optical model describing the interaction of a collection of two-level systems with a single bosonic mode. Effective implementations of this model made it possible to observe the emergence of superradiance, i.e., cooperative phenomena arising from the collective nature of light-matter interactions. Via reservoir engineering and analogue quantum simulation techniques, current experimental platforms allow us not only to implement the Dicke model but also to design more exotic interactions, such as the two-photon Dicke model. In the Hamiltonian case, this model presents an interesting phase diagram characterized by two quantum criticalities: a superradiant phase transition and a spectral collapse, that is, the coalescence of discrete energy levels into a continuous band. Here, we investigate the effects of both qubit and photon dissipation on the phase transition and on the instability induced by the spectral collapse. Using a mean-field decoupling approximation, we analytically obtain the steady-state expectation values of the observables signaling a symmetry breaking, identifying a first-order phase transition from the normal to the superradiant phase. Our stability analysis unveils a very rich phase diagram, which features stable, bistable, and unstable phases depending on the dissipation rate.

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.

Lin Jiao, Han Pu

Interactions among emitters provide a powerful means of controlling collective light--matter phenomena, yet their role in superradiant criticality has not been thoroughly investigated. Here we construct a minimal model that can yield analytical insights --- a Dicke model with two interacting atoms coupled to a single mode cavity --- to study such interaction effects. We show that interaction changes the phase boundary, and may even completely suppress the atom-photon coupling threshold for superradiance and change the universality class of the phase transition. We further study the dissipative phase transition and quantum dynamics in the presence of dissipation channels such as photon loss and spin relaxation. Our results demonstrate important roles played by the atom-atom interaction and how it can be engineered to control atom-photon coupling.