Abstract Quantum phase transitions with multicritical points are fascinating phenomena occurring in interacting quantum many-body systems. However, multicritical points predicted by theory have been rarely verified experimentally; finding multicritical points with specific behaviors and realizing their control remains a challenging topic. Here, we propose a system that a quantized light field interacts with a two-level atomic ensemble coupled by microwave fields in optical cavities, which is described by a generalized Dicke model. Multicritical points for the superradiant quantum phase transition are shown to occur. We determine the number and position of these critical points and demonstrate that they can be effectively manipulated through the tuning of system parameters. Particularly, we find that the quantum critical points can evolve into a Lifshitz point (LP) if the Rabi frequency of the light field is modulated periodically in time. Remarkably, the texture of atomic pseudo-spins can be used to characterize the quantum critical behaviors of the system. The magnetic orders of the three phases around the LP, represented by the atomic pseudo-spins, are similar to those of an axial next-nearest-neighboring Ising model. The results reported here are beneficial for unveiling intriguing physics of quantum phase transitions and pave the way towards to find novel quantum multicritical phenomena based on the generalized Dicke model.
Abstract Quantum phase transitions with multicritical points are fascinating phenomena occurring in interacting quantum many-body systems. However, multicritical points predicted by theory have been rarely verified experimentally; finding multicritical points with specific behaviors and realizing their control remains a challenging topic. Here, we propose a system that a quantized light field interacts with a two-level atomic ensemble coupled by microwave fields in optical cavities, which is described by a generalized Dicke model. Multicritical points for the superradiant quantum phase transition are shown to occur. We determine the number and position of these critical points and demonstrate that they can be effectively manipulated through the tuning of system parameters. Particularly, we find that the quantum critical points can evolve into a Lifshitz point (LP) if the Rabi frequency of the light field is modulated periodically in time. Remarkably, the texture of atomic pseudo-spins can be used to characterize the quantum critical behaviors of the system. The magnetic orders of the three phases around the LP, represented by the atomic pseudo-spins, are similar to those of an axial next-nearest-neighboring Ising model. The results reported here are beneficial for unveiling intriguing physics of quantum phase transitions and pave the way towards to find novel quantum multicritical phenomena based on the generalized Dicke model.
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.
Quantum many-body systems that support high-order quantum phase transitions are quite rare. Here we consider an important generalization of the Dicke model in which an ensemble of multilevel atoms, instead of two-level atoms as in the conventional Dicke model, interact with a single photonic mode, and show that this generalized Dicke model can become multicritical. For a subclass of experimentally realizable schemes, multicritical conditions of arbitrary order can be expressed analytically in compact forms. As such, experiments can be readily designed to achieve quantum phase transition of desired order. We also calculate the atom-photon entanglement entropy for both critical and noncritical cases and find that the order of the criticality strongly affects the critical entanglement entropy: higher order yields stronger entanglement. Our work provides deep insight into quantum phase transitions and multicriticality.
We demonstrate the emergence of nonreciprocal superradiant phase transitions and novel multicriticality in a cavity quantum electrodynamics system, where a two-level atom interacts with two counterpropagating modes of a whispering-gallery-mode microcavity. The cavity rotates at a certain angular velocity and is directionally squeezed by a unidirectional parametric pumping χ^{(2)} nonlinearity. The combination of cavity rotation and directional squeezing leads to nonreciprocal first- and second-order superradiant phase transitions. These transitions do not require ultrastrong atom-field couplings and can be easily controlled by the external pump field. Through a full quantum description of the system Hamiltonian, we identify two types of multicritical points in the phase diagram, both of which exhibit controllable nonreciprocity. These results open a new door for all-optical manipulation of superradiant transitions and multicritical behaviors in light-matter systems, with potential applications in engineering various integrated nonreciprocal quantum devices.
Control and manipulation of quantum engineered systems allows for the utilization of time-dependent parametric modulations for accessing novel out-of-equilibrium phenomena. In the absence of such driving, the dissipative Dicke model exhibits a fascinating out-of-equilibrium many-body phase transition as a function of a coupling between a driven photonic cavity and numerous two-level atoms. We study the effect of a parametric modulation of this coupling and discover a rich phase diagram as a function of the modulation strength. We find that in addition to the established normal and super-radiant phases, a new phase with pulsed superradiance, which we term dynamical normal phase, appears when the system is parametrically driven. Employing different methods, we characterize the different phases and the transitions between them. Specific heed is paid to the role of dissipation in determining the phase boundaries. Our analysis paves the road for the experimental study of dynamically stabilized phases of interacting light and matter.
The Dicke model describing an ensemble of two-state atoms interacting with a single quantized mode of the electromagnetic field (with omission of the ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{A}}^{2}$ term) exhibits a zero-temperature phase transition at a critical value of the dipole coupling strength. We propose a scheme based on multilevel atoms and cavity-mediated Raman transitions to realize an effective Dicke model operating in the phase transition regime. Optical light from the cavity carries signatures of the critical behavior, which is analyzed for the thermodynamic limit where the number of atoms is very large.
Abstract Quantum tricriticality, a unique form of high-order criticality, is expected to exhibit fascinating features including unconventional critical exponents and universal scaling laws. However, a quantum tricritical point (QTCP) is much harder to access, and the corresponding phenomena at tricriticality have rarely been investigated. In this study, we explore a tricritical quantum Rabi model, which incorporates a non-trivial parameter to adjust the coupling ratio between a cavity and a three-level atom. The QTCP emerges at the intersection of first- and second-order superradiant phase transitions according to Landau theory. By using finite-frequency scaling analysis on quantum fluctuations and the average photon number, universal critical exponents differentiate the QTCP from the second-order critical point. Our results indicate that the phase transition at the tricritical point goes beyond the conventional second-order phase transition. Our work explores an interesting direction in the generalization of the well-known Rabi model for the study of higher-order critical points due to its high control and tunability.