Light-matter interacting systems involving multilevel atoms are appealing platforms for testing equilibrium and dynamical phenomena. Here we explore a tricritical Dicke model, where an ensemble of three-level systems interacts with a single light mode, through two different approaches: a generalized Holstein-Primakoff mapping and a treatment using the Gell-Mann matrices. Both methods are found to be equivalent in the thermodynamic limit. In equilibrium, the system exhibits a rich phase diagram where both continuous and discrete symmetries can be spontaneously broken. We characterize all the different types of symmetries according to their scaling behaviors. Far from the thermodynamic limit, considering just a few tens of atoms, the system already exhibits features that could help characterize both second- and first-order transitions in a potential experiment. Importantly, we show that the tricritical behavior is preserved when dissipation is taken into account. Moreover, the system develops a rich steady-state phase diagram with various regions of bistability, all of them converging at the tricritical point. Having multiple stable normal and superradiant phases opens prospective avenues for engineering interesting steady states by a proper choice of initial states and/or parameter quenching.
Light-matter interacting systems involving multilevel atoms are appealing platforms for testing equilibrium and dynamical phenomena. Here we explore a tricritical Dicke model, where an ensemble of three-level systems interacts with a single light mode, through two different approaches: a generalized Holstein-Primakoff mapping and a treatment using the Gell-Mann matrices. Both methods are found to be equivalent in the thermodynamic limit. In equilibrium, the system exhibits a rich phase diagram where both continuous and discrete symmetries can be spontaneously broken. We characterize all the different types of symmetries according to their scaling behaviors. Far from the thermodynamic limit, considering just a few tens of atoms, the system already exhibits features that could help characterize both second- and first-order transitions in a potential experiment. Importantly, we show that the tricritical behavior is preserved when dissipation is taken into account. Moreover, the system develops a rich steady-state phase diagram with various regions of bistability, all of them converging at the tricritical point. Having multiple stable normal and superradiant phases opens prospective avenues for engineering interesting steady states by a proper choice of initial states and/or parameter quenching.
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.
Quantum optics is the field of physics that studies the interaction between light and matter under a fully quantum mechanical treatment. In recent decades, relentless advances in the technologies used for trapping, cooling, and controlling atoms and molecules have allowed us to finally start exploring experimentally the physics displayed by different cornerstone models of quantum optics originally proposed in the second half of the 20th century. In this thesis, we propose multiple extensions to those fundamental models, expanding the already interesting physics displayed by them into new and exciting directions. More specficially, we study these generalized models in the context of quantum phase transitions both in and out of equilibrium and show how new phases of matter can be unlocked in these extended models. In Chapters 1 and 2 we briefly introduce the reader to the realms of quantum phase transitions and quantum optics. Once the fundamental aspects of both of these fields are covered, we present the superradiant phase transition displayed in the Dicke and Rabi models in Chapter 3. This phase transition will be the central topic we will be orbiting around in the subsequent chapters. In Chapter 4 we propose a generalization of the quantum Rabi model, where N cavities, instead of one, are connected to each other through photon hopping. In this system, named the quantum Rabi ring, interesting chiral superradiant phases can develop as a function of the hopping phase and the geometry of the ring. In particular, we find that geometrical frustration plays a key role in determining the stable phases in equilibrium. Moreover, frustration manifests itself in the quantum Rabi ring through unconventional non-symmetric critical exponents, a phenomenon reported before, but hardly observed in condensed matter materials. Finally, in Chapter 5, we introduce a different extension to the Dicke model where instead of two-level atoms, three-level atoms are considered. In this system, which we have named the tricritical Dicke model, the superradiant phase transition can occur through first-order, second-order, and third-order critical points. We study the critical properties of the system in and out of equilibrium and find that in the open-system description, the tricritical points are still present but are now accompanied by regions of bistability where the final fate depends highly on the initial conditions. These regions of bistability represent potentially interesting environments to investigate dynamical features and steady-state preparation schemes. The critical phenomena displayed by the extended models proposed here, such as multicriticality, geometrically frustrated quantum phases, and chiral phases breaking time-reversal symmetry, are all features that have been observed, although not abundantly, or proposed in condensed matter physics. However, the unmatched tunability and control of atomic and molecular experimental platforms, where the models presented in this thesis are proposed to be realized, causes these extended models to become promising candidates for investigating these features in parameter regimes and conditions never explored before.
The dissipative phase transitions in the open transverse and longitudinal Dicke-Ising model (DIM), which incorporates nearest-neighbor Ising-type spin interactions into the Dicke framework, are investigated within a mean-field approach and further validated by detailed stability analysis. While the dissipative phase diagram of the transverse DIM is only slightly shifted upward compared with its ground-state counterpart, dissipation in the longitudinal DIM stabilizes bistable nonequilibrium steady states and induces first-order phase transitions that are absent in the ground-state phase diagram. This bistable phase is characterized by the coexistence of superradiant and antiferromagnetic orders, and it converts a ground-state triple point into a tetracritical point, at which the boundaries of the first- and second-order transitions intersect. Our results reveal that the interplay among spin interactions, light-matter coupling, and dissipation supports a diverse set of nonequilibrium phase transitions and provides broad tunability of the phase diagram. These findings offer a theoretical foundation for exploring nonequilibrium physics in realistic open solid-state quantum systems.
In this doctoral thesis, the thermodynamic phases und phase transitions of a generalised Dicke model are studied and characterised. Both, finite and vanishing temperatures are considered. The Dicke model of quantum optics describes collective phenomena which occur when light interacts with a many-atom system. In the thermodynamic limit, a so-called Hepp–Lieb superradiant phase transition sets in. A superradiant phase develops for low temperatures or strong coupling between light and atoms, which is characterised by a macroscopic excitation of the light field and a spontaneous, collective polarisation of the atoms. This thesis discusses a generalised version of the Dicke model, which is described by a quantum mechanical system consisting of three-level atoms in Lambda-configuration and two modes of a resonator. By means of the Holstein–Primakoff transformation, the Hamiltonian of this system is written in terms of four interacting, non-linear oscillators, which can be linearised in the thermodynamic limit, yielding the ground-state energy as well as the low-energy excitations. The phase diagram consisting of two superradiant phases separated by continuous and first-order phase transitions is derived. In order to clarify the question whether or not the superradiant phase transition of this generalised Dicke model can be observed experimentally for real atoms, the significance of the diamagnetic term is discussed. In contrast to the original Dicke model, superradiant phase transitions are possible in principle. This is due to the first-order phase transitions. In addition, a no-go theorem for continuous superradiant phase transitions is presented. The argument is based on the Thomas–Reiche–Kuhn sum rule. Last, we study the superradiant phase transition of the generalised Dicke model at finite temperatures. Therefore, the partition sum is computed and analysed in the thermodynamic limit using Laplace’s method. At finite temperatures, the properties of the phase diagram and phases remain. However, here all phase transitions are of first order.
The Dicke model (DM) serves as a paradigm for understanding collective light-matter interactions. We introduce the chiral Dicke model, a generalization where an atomic ensemble couples to a two-mode cavity via chiral interactions. Unlike the standard DM, the chiral DM is endowed with an inherent continuous U(1) symmetry associated with angular momentum conservation. The ground-state phase diagram and the associated quantum phase transitions are charted out, revealing a U(1)-broken superradiant phase that spans a broad parameter space. We demonstrate that the spectrum of quantum fluctuations is highly tunable in both the symmetric and broken phases. Strikingly, our calculations reveal that the system exhibits `multiversality', where distinct universality classes govern the transition between the same two phases. In particular, along a special line in parameter space, the dynamical critical exponent for the normal-superradiant phase transition changes from zν=1 to zν=1/2. Our work establishes the chiral Dicke model as a powerful platform to realize novel quantum phases and multiversal critical phenomena in light-matter coupled systems.
We study a three-level Dicke model in V configuration under both closed and open conditions. With independently tunable corotating and counterrotating coupling strength of the interaction Hamiltonian, this model is a generalization of the standard Dicke model that features multiple distinct parameter regimes. Based on a mean-field approach and third quantization analysis, it is found that the system exhibits rich quantum phase behaviors, including distinct superradiant fixed points, multiphase coexistence, and limit-cycle oscillation. In particular, the cavity dissipation stabilizes a family of inverted spin-coherent steady states whose stability region can be enlarged or reduced by properly tuning the imbalance between the corotating and counterrotating interactions. This property provides a conceptually different scenario to prepare the coherent atomic state with high fidelity.