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 nontrivial parameter for adjusting the coupling ratio between a cavity and a three-level atom. The QTCP emerges at the intersection of a first- and second-order superradiant phase transitions according to Landau theory. By using finite-frequency scaling analyses for quantum fluctuations and the mean photon number, universal critical exponents differentiate the QTCP from the second-order critical point. We find 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.
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 nontrivial parameter for adjusting the coupling ratio between a cavity and a three-level atom. The QTCP emerges at the intersection of a first- and second-order superradiant phase transitions according to Landau theory. By using finite-frequency scaling analyses for quantum fluctuations and the mean photon number, universal critical exponents differentiate the QTCP from the second-order critical point. We find 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.
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.
Abstract We investigate the quantum phase transitions (QPTs) of the two-qubit quantum Rabi model with staggered qubit biases. In the limit of an infinite qubit-to-cavity frequency ratio, we analytically derive the mean-field Hamiltonian and the order-parameter-dependent energy density functional, which yields the ground-state energy and order parameter. The rich superradiant phase transitions (SRPTs), including both second- and first-order QPTs and a tricritical point (TCP), are analytically derived. Specifically, we derive the analytical expressions for all phase transition points, including the nonperturbative point of the first-order SRPT. The analytical findings are further corroborated by numerical finite-size scaling analysis. It is found that both the critical correlation-length and order-parameter exponents at the TCP differ from those of the original second-order SRPTs, implying that the TCP belongs to a new universality class. This work provides a reliable theoretical framework for designing new, simple experimental platforms to explore the rich QPTs.
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.
Abstract The existence of quantum tricriticality and exotic phases are found in a tricritical Dicke triangle (TDT) where three cavities, each one containing an ensemble of three-level atoms, are connected to each other through the action of an artificial magnetic field. The conventional superradiant phase (SR) is connected to the normal phase through first- and second-order boundaries, with tricritical points located at the intersection of such boundaries. Apart from the SR phase, a chiral superradiant (CSR) phase is found by tuning the artificial magnetic field. This phase is characterized by a nonzero photon current and its boundary presents chiral tricritical points (CTCPs). Through the study of different critical exponents, we are able to differentiate the universality class of the CTCP and TCP from that of second-order critical points, as well as find distinctive critical behavior among the two different superradiant phases. The TDT can be implemented in various systems, including atoms in optical cavities as well as the circuit QED system, allowing the exploration of a great variety of critical manifolds.
Quantum criticality usually occurs in many-body systems. Recently it was shown that the quantum Rabi model, which describes a two-level atom coupled to a single model cavity field, presents quantum phase transitions from a normal phase to a superradiate phase when the ratio between the frequency of the two-level atom and the frequency of the cavity field extends to infinity. In this work, we study quantum phase transitions in the quantum Rabi model from the fidelity susceptibility perspective. We found that the fidelity susceptibility and the generalized adiabatic susceptibility present universal finite-size scaling behaviors near the quantum critical point of the Rabi model if the ratio between frequency of the two-level atom and frequency of the cavity field is finite. From the finite-size scaling analysis of the fidelity susceptibility, we found that the adiabatic dimension of the fidelity susceptibility and the generalized adiabatic susceptibility of fourth order in the Rabi model are 4/3 and 2, respectively. Meanwhile, the correlation length critical exponent and the dynamical critical exponent in the quantum critical point of the Rabi model are found to be 3/2 and 1/3, respectively. Since the fidelity susceptibility and the generalized adiabatic susceptibility are the moments of the quantum noise spectrum which are directly measurable by experiments in linear response regime, the scaling behavior of the fidelity susceptibility in the Rabi model could be tested experimentally. The simple structure of the quantum Rabi model paves the way for experimentally observing the universal scaling behavior of the fidelity susceptibility at a quantum phase transition.
The quantum fluctuations of a quantum Rabi triangle are investigated using an analytical method that goes beyond mean-field theory. An artificial magnetic field applied in three cavities leads to the breaking of time-reversal symmetry, which is evident in the directional transfer of photons. In contrast to previous studies, we focus on the scaling exponents of quantum fluctuations of the local photon number and the position variance near the critical point. Specifically, the fluctuations of photons do not diverge as the coupling strength approaches the critical value from below for the chiral superradiant phase transition. Attributing to geometric frustration, two distinct scaling laws arise for the frustrated cavity and the remaining cavities. Specifically, in the frustrated cavity, the scaling exponent in the chiral superradiant phase differs from that without an artificial magnetic field for the frustrated antiferromagnetic superradiant phase. The unusual scaling exponents indicate distinct universality classes in contrast to the single-cavity Rabi one. We suggest that accurate critical exponents in few-body systems are useful for identifying exotic quantum phase transitions in light-matter coupling systems.