Atomic, molecular, and optical (AMO) systems often feature great controllability. As such, they offer ideal platforms to explore various kinds of quantum phenomena. Designing artificial quantum systems that possess novel and exotic properties is one of the major tasks of theorists working in the AMO field. In this dissertation, we introduce our work on designing novel Hamiltonians which give rise to multicriticality or flat bands. In the first half of the dissertation, we study the multicriticality. Quantum many-body systems that support multicritical quantum phase transitions are quite rare. However, we find that, in an important generalization of the Dicke model, the superradiant quantum phase transitions 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. The phase transition happens both in the thermodynamic limit and the classical oscillator limit. We compare the quantum fluctuation in the two cases by calculating the atom-photon entanglement entropy. We find that the order of the criticality strongly affects the critical entanglement entropy. In the second half of the dissertation, we propose a powerful and convenient method to systematically design flat-band lattice models. Flat bands often lead to exotic strongly correlated emergent quantum phenomena. We use this method to generate several classes of lattice models, including models with both short- and long-range hoppings, both ordinary and magnetic translational symmetry, both topologically trivial and non-trivial flat bands.
Atomic, molecular, and optical (AMO) systems often feature great controllability. As such, they offer ideal platforms to explore various kinds of quantum phenomena. Designing artificial quantum systems that possess novel and exotic properties is one of the major tasks of theorists working in the AMO field. In this dissertation, we introduce our work on designing novel Hamiltonians which give rise to multicriticality or flat bands. In the first half of the dissertation, we study the multicriticality. Quantum many-body systems that support multicritical quantum phase transitions are quite rare. However, we find that, in an important generalization of the Dicke model, the superradiant quantum phase transitions 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. The phase transition happens both in the thermodynamic limit and the classical oscillator limit. We compare the quantum fluctuation in the two cases by calculating the atom-photon entanglement entropy. We find that the order of the criticality strongly affects the critical entanglement entropy. In the second half of the dissertation, we propose a powerful and convenient method to systematically design flat-band lattice models. Flat bands often lead to exotic strongly correlated emergent quantum phenomena. We use this method to generate several classes of lattice models, including models with both short- and long-range hoppings, both ordinary and magnetic translational symmetry, both topologically trivial and non-trivial flat bands.
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.
In this dissertation, I theoretically investigate the equilibrium properties of three strongly correlated multi-level quantum platforms -- synthetic dimension using ultracold Rydberg atoms, multi-flavor Fermi-Hubbard simulators with ultracold atoms, and magnon-spin coupled rare-earth orthoferrites -- using various numerical and analytical methods. After the broad research motivation in the first chapter, Chapter 2 introduces the general principles of quantum simulation using synthetic dimension platforms. Chapter 3 discusses the first realization with Rydberg atom platform to simulate the topological Su-Schrieffer-Heeger (SSH) model, and how environmental noise affects it. Chapter 4 shows the mean-field phase diagram of dipole-coupled ultracold Rydberg atom arrays exhibiting quantum strings and other ordered states. The connection of the thermal phase transition to that of a classical extended Potts model is also discussed from a renormalization (RG) and generalized duality perspective. These examples illustrate the versatility of synthetic dimension in simulating and engineering quantum phenomena. Chapters 5-6 explore the properties of multi-flavor Fermi-Hubbard models on square optical lattices using numerical linked-cluster expansions (NLCE). First, I show universal thermodynamics of SU(N) Fermi-Hubbard models above superexchange temperatures. Then, I discuss the agreement between numerical simulated equations of state and correlation functions to optical lattice experiments using 173Yb [SU(N)-symmetric interactions] and three spin-flavors of 6Li [spin-dependent interactions] at intermediate temperatures. Thermometry performed with this method agrees well with the model-independent thermometry. Lastly, I propose a method of computing observables at low temperatures in bipartite ordered states by adding a suitable boundary field to the NLCE. NLCE agreeing to quantum simulations at temperatures above the superexchange temperatures and a possibility to make accurate predictions at low temperatures for certain states make it a powerful algorithm to be used side-by-side with quantum simulations. Chapter 7 is based on the observation of magnonic superradiance in ErFeO3. The spin Hamiltonian reveals a simultaneous kink and mode-softening of two of the lower polaritons, strongly suggesting a superradiant phase transition. Its mapping to an extended Dicke model is also discussed. This is the first evidence towards a macroscopically squeezed spin state. Finally, I conclude with a broad discussion and an outlook in Chapter 8.
Symmetries play a central role in organizing many-body quantum phases of matter and in revealing universal low-energy behavior. Systems with gapless excitations are especially rich, as symmetries can act in intricate ways on low-energy degrees of freedom, while enhanced correlations and entanglement open possibilities not available in gapped settings. This thesis studies two settings in which symmetry considerations give rise to qualitatively new phenomena in gapless quantum matter and correlated electronic systems. In the first part of the thesis, I study how the framework developed for gapped topological phases can be generalized to gapless systems, especially those arising at topological phase transitions. I show that symmetry can refine a fixed conformal field theory universality class into distinct symmetry-enriched critical phases that cannot be smoothly connected without breaking symmetry or leaving the critical theory. In Chapter 1, I show that transitions between distinct symmetry-protected topological phases can exhibit exotic boundary critical behavior not seen in gapped systems. In Chapter 2, I show that distinct gapless symmetry-enriched phases can meet at an anomalous multicritical point. In Chapter 3, I show that spatial interfaces provide an operational indicator of these phases, and that distinct symmetry-enriched criticalities are separated by non-invertible conformal defects. Together, these results show that subtle distinctions in symmetry-enriched criticality have robust and physically detectable consequences. In the second part of the thesis, I study how symmetry and strong interactions govern charge carriers in correlated electron systems. In Chapter 4, I develop a microscopic theory of the Josephson diode effect in Josephson junctions, showing that nonreciprocal supercurrents arise universally from finite Cooper-pair momentum when time-reversal and inversion symmetry are simultaneously broken. In Chapter 5, I study spin-polaron formation in a flat-band ferromagnetic Hubbard model and show that binding occurs in a regime where the conventional mechanisms based on kinetic frustration or nontrivial band topology do not apply, but instead exotic composite charge carriers arise from quantum geometry.
Emergence in systems of many electrons can lead to macroscopic demonstrations of quantum mechanics which are intrinsically many-body. A primary focus of this dissertation is the phenomena of fractionalization, where the effective quasiparticles which emerge at long distances exhibit fractional quantum numbers of the microscopic degrees of freedom. The interplay between these emergent degrees of freedom and the microscopic symmetries can lead to a number of exotic properties including competing orders and unconventional phase transitions. I explore this phenomena in a number of platforms. This includes quantum antiferromagnets which can give rise to \textit{quantum spin liquids}, where we predict critical properties of phase transitions between spin liquids and conventionally-ordered phases - due to the fractionalized excitations, such critical theories deviate from traditional Landau-Ginzburg predictions. I also study the interplay between fractionalized spin and charge excitations, as well as fractionalization in non-equilibrium contexts. The second goal of this dissertation is to investigate the properties of disordered, strongly interacting, zero dimensional systems which exemplify many notable properties of higher-dimensional systems, such as doping-induced quantum criticality and non-Fermi liquid transport. The effects of disorder play an essential role in these models, leading to phenomena such as spin glass phases and conductance fluctuations which we investigate through both numerical and analytical methods.
A system of ultracold atoms in an optical lattice provides a powerful platform for quantum simulation. In our laboratory, we use a quantum gas microscope to tune lattice parameters not only in a global scale but also at the level of individual sites. This allows us to control and detect the quantum state of interacting many-body systems as well as to engineer a broad class of Hamiltonians with high fidelity. Leveraging this versatility, we can realize several types of strongly correlated bosonic systems, which present intriguing behaviors and implement novel phases of matter. Analyzing snapshots of the atomic distribution with single-site resolution, we measure correlations and entanglement within these systems to reveal their main features, including non-equilibrium dynamics and quantum phase transitions. In this thesis, I present the works performed by our team for four different types of systems. First of all, I briefly introduce the behavior of a 1D disordered system in the critical regime between the thermal and the many-body-localized phases. In particular, we discuss what happens when a disordered and a non-disordered region are coupled via a single site. We find evidence for accelerated transport of thermal inclusion into the localized region, which shows the existence of a quantum avalanche, i.e. thermalization via accelerated transport throughout the localized system. In the second part, we realize a fractional quantum Hall state using an artificial gauge field, by implementing an adiabatic preparation protocol. We identify a topological phase transition in our system and characterize several key physical features expected for a Laughlin state by measuring density correlations and Hall conductivity. The next topic of this thesis relates to quantum magnetism. Mapping nearest hopping in a tilted optical lattice to spin flips, we realize a finite one-dimensional chain of 1/2-spins with closed boundary conditions. We perform an in-depth investigation on behaviors shown across the quantum phase transition between paramagnetic and antiferromagnetic ground states, including the evolution of the magnetization and Néel order parameter. Also, we find evidence for quantum superposition at the many-body level as a result of geometric frustration. In the last chapter, I report the experimental realization of a novel dipolar Bose-Hubbard Hamiltonian, based on a strongly tilted lattice system. When the tilt becomes the dominant energy scale, the Hamiltonian is fragmented, and the system behaves in a way that conserves dipole moment. Starting from a 1D chain of unity filled sites, we generate individual dipolar and anti-dipolar excitations at desired pinpoints. We observe quantum walks of these dipolar quasi-particles as well as their scattering dynamics, which allows us to study this new type of Hamiltonian using a bottom-up approach.
Certain lattice wave systems in translationally invariant settings have one or more spectral bands that are strictly flat or independent of momentum in the tight binding approximation, arising from either internal symmetries or fine-tuned coupling. These flat bands display remarkable strongly interacting phases of matter. Originally considered as a theoretical convenience useful for obtaining exact analytical solutions of ferromagnetism, flat bands have now been observed in a variety of settings, ranging from electronic systems to ultracold atomic gases and photonic devices. Here we review the design and implementation of flat bands and chart future directions of this exciting field.