As a novel platform for exploring exotic quantum phenomena, the moir\'e lattice has garnered significant interest in solid-state physics, photonics, and cold-atom physics. While moir\'e lattices in two- and three-dimensional systems have been proposed for neutral cold atoms, the simpler one-dimensional moir\'e effect remains largely unexplored. We present a scheme demonstrating moir\'e effects in a one-dimensional cold-atom--cavity coupling system, which resembles a generalized open Dicke model exhibiting superradiant phase transitions. We reveal a strong link between the phase transition critical point and the one-dimensional moir\'e parameter. Evidence of the one-dimensional moir\'e effect is explicitly explored, including the cavity field spectrum, phase transition dynamics, and anomalous atomic diffusion. This work provides a new route for testing one-dimensional moir\'e effects with cold atoms and opens new possibilities in moir\'e metrology.
As a novel platform for exploring exotic quantum phenomena, the moir'e lattice has garnered significant interest in solid-state physics, photonics, and cold-atom physics. While moir'e lattices in two- and three-dimensional systems have been proposed for neutral cold atoms, the simpler one-dimensional moir'e effect remains largely unexplored. We present a scheme demonstrating moir'e effects in a one-dimensional cold-atom--cavity coupling system, which resembles a generalized open Dicke model exhibiting superradiant phase transitions. We reveal a strong link between the phase transition critical point and the one-dimensional moir'e parameter. Evidence of the one-dimensional moir'e effect is explicitly explored, including the cavity field spectrum, phase transition dynamics, and anomalous atomic diffusion. This work provides a new route for testing one-dimensional moir'e effects with cold atoms and opens new possibilities in moir'e metrology.
Moiré related physics in twisted bilayer two-dimensional (2D) materials has attracted widespread interest in condensed matter physics. Simulation of moiré related physics in cold atom platform is expected to outperform the 2D materials thanks to its advantage of higher tunablility. Here, we demonstrate that, the cold atom platform enables a new mechanism of moiré lattice formation, induced by interlayer interaction with intrinsic "dynamical" character, in contrast to conventional moiré lattice induced by "static" ways such as single-particle interlayer tunneling. Specifically, we consider a twisted bilayer Bose-Hubbard model with vanishing interlayer tunneling, and the bilayer is solely coupled through interlayer interaction that originates from contact interaction of atoms. We find that this system hosts a plethora of novel phases unique to this dynamical lattice, including a variety of Mott insulator (MI) and superfluid (SF) phases either preserving or breaking moiré lattice symmetry, phases with one layer in SF and the other in MI, "interlocked" MI, and self-localized phases at commensurate twist angles, which exhibits the characteristics of Bose glass and quasi-many-body localization in the absence of (quasi)disorder or quasicrystalline lattices. Our prediction can be readily observed in current experimental setup of twisted bilayer optical lattices, opening up new avenues for exploring the rich physics of interaction induced moiré systems in cold atoms.
In modern physics, the investigation of the interaction between light and matter is important from both a fundamental and an applied point of view. Cavity quantum electrodynamics (cavity QED) is the study of the interaction between light confined in a reflective cavity and atoms or other particles where the quantum nature of light photons is significant. The strong interaction between an exciton and cavity photon in a high-finesse microcavity can induce a hybrid light-matter eigenstate which is usually named as polariton in solid-state systems. This strong light-matter interaction can be achieved when this interaction is larger than all broadenings caused by other various factors e.g. electron phonon scattering and cavity loss. The polariton is now stimulating tremendous research interests due to its high potential in cavity quantum electrodynamics (QED) and the achievement of polaritonic devices. Moreover, when the interaction strength between an excitation and the cavity photon, quantified by vacuum Rabi frequency, becomes comparable to or larger than the corresponding electronic transition frequency in a cavity, the system can enter an ultrastrong coupling regime, which has been experimentally observed. In this regime, the standard rotating-wave approximation is no longer valid and the antiresonant term of the interaction Hamiltonian starts to play an important role, giving rise to exciting effects in cavity QED. The Aharonov-Bohm (AB) effect is a fundamental quantum phenomenon that bears the significance of the nature of electromagnetic fields and potentials. Besides its fundamental significance in quantum theory, its importance for applications in interferometric devices is omnipresent. Recently, since the 2D materials have triggered immense interest, some work has been done to integrate the AB effect with the electronic and transport properties of 2D materials. This thesis consists of two parts. In the first part, the light-matter coupling between cyclotron transition and photon is theoretically investigated in some 2-D materials such as the monolayer MoS2, graphene and monolayer black phosphorene (BP) systems. The results show that, in these 2-D materials, the ultrastrong light-matter coupling can be achieved at a high filling factor of Landau levels. Furthermore, we show that, in contrast to the case for conventional semiconductor resonators, the MoS2 system shows a vacuum instability. In monolayer MoS2 resonator, the diamagnetic term can still play an important role in determining magnetopolariton dispersion which is different from monolayer graphene system. The diamagnetic term arises from electron-hole asymmetry which indicates that electron-hole asymmetry can influence the quantum phase transition. Meanwhile, we show that, similar with some other 2D materials such as graphene and MoS2, the monolayer BP system shows a vacuum instability. However, in contrast with other 2D materials, the BP system displays a large energy gap between three branches of polaritons because of its strong anisotropic behavior in the eigenstates of the band structures. For the graphene system, we investigate the coupling of cyclotron transition and a multimode cavity described by a multimode Dicke model. This model exhibits a superradiant quantum phase transition, which we describe exactly in an effective Hamiltonian approach. The complete excitation spectrum in both the normal phase and superradiant phase regimes is given. At last, in contrast to the single mode case, multimode coupling of cavity photon and cyclotron transition can greatly reduce the critical vacuum Rabi frequency required for quantum phase transition, and dramatically enhance the superradiant emission by fast modulating the Hamiltonian. Our study provides new insights in cavity-controlled magneto-transport in these 2-D systems, which could lead to the development of polariton-based devices. The second part is a diversion from the main content of this thesis; readers who are not interested in foundational issues of physics can skip this part. For one charged quantum particle P moving in an electromagnetic vector potential Aˆµ = ( φˆ, - Aˆ ) created by some other charged particles, we can either use the framework of one particle quantum mechanics (OPQM) to calculate the evolutions of P, or we can treat this as an multi-particles problem in the framework of quantum field theory and calculate the evolution of P. These two methods need to be equivalent, i.e., they produce the same result for the evolution of P. One open question is how to describe the evolution of P within the framework of quantum field theory and show that these two methods yield the same result? In chapter 5, we are going to derive the OPQM from the quantum field theory, i.e., the quantum electrodynamics (QED) to be specific. We start with the discussions on the AB effect then raise a plausible interpretation within the QED framework. We provide a quantum treatment of the source of the electromagnetic potential and argue that the underlying mechanism in AB effect can be viewed as interactions between electrons described by QED theory where the interactions are mediated by virtual photons. On further analysis, we show that the framework of one particle quantum mechanics (OPQM) can be given, in general, as a mathematically approximated model which is reformulated from QED theory while the AB effect scheme provides a platform for our derivations. In addition, the classical Maxwell equations are derived from QED scattering process while both classical electromagnetic fields and potentials serve as mathematical tools that are constructed to approximate the interactions among elementary particles described by QED physics. This work opens up a new perspective on the nature of electromagnetic fields and potentials.
The Dicke model is a staple of theoretical cavity quantum electrodynamics (cavity QED), describing the interaction between an ensemble of atoms and a single radiation mode of an optical cavity. It is studied both quantum mechanically and semiclassically for two-level atoms, and demonstrates a rich variety of dynamics such as phase transitions, phase multistability, and chaos. In this work we explore an open, spin-1 Dicke model with independent co and counterrotating coupling terms as well as a quadratic Zeeman shift enabling control over the atomic energy-level structure. We investigate the stability of operator and moment equations under two approximations and show the system undergoes phase transitions. To compliment these results, we relax the aforementioned approximations and investigate the system semiclassically. We show evidence of phase transitions to steady-state and oscillatory superradiance in this semiclassical model, as well as the emergence of chaotic dynamics. The varied and complex behaviors admitted by the model highlights the need to more rigorously map its dynamics.
We present a comprehensive analysis of the dynamic diversity associated with superradiant phase transitions within a one-dimensional tight-binding electronic chain that is intrinsically coupled to a single-mode optical cavity. By employing the quantized electromagnetic vector potential through the Peierls substitution, the gauge-invariant coupled Bose-Fermi system facilitates momentum-dependent superradiant transitions and effectively avoids the second-order spurious phase transitions typically observed in Dicke-like models. The quantum phase transitions in this system are characterized by stable dynamics, including the displacement and squeezing of the cavity mode and the redistribution of electronic momentum in the solid chain. Distinct from multimode cavity QED systems with atomic gases, this single-mode optical configuration unveils a range of nonlinear phenomena, including multistability and diversity of spontaneous symmetry breaking. The setup allows for precise manipulation of superradiant phases in the weak coupling regime, effectively mitigating the adverse effects of quantum fluctuation divergences. The diverse attributes of these quantum phase transitions enhance our understanding of tunable quantum solid devices and underscore their potential applications in quantum information processing and metrology.
Cavity quantum electrodynamics (QED) studies the interaction between atoms and a single electromagnetic mode. When the atoms form a degenerate quantum gas, the resulting lightâ matter interaction reflects the underlying quantum statistics of the particles. Recently, degenerate Fermi gases have been coupled to optical cavities, enabling the exploration of strongly correlated fermionic systems with interactions mediated by cavity photons. Remarkably, when disorder is introduced into such systems, the resulting model realizes fermions with random, long-range interactions characteristic of the Sachdevâ Yeâ Kitaev Hamiltonian. This platform therefore offers a possible route toward the experimental investigation of holographic duality, linking strongly interacting quantum matter to black hole physics through the AdS/CFT correspondence. As a step toward realizing this model, we developed a new technology: the cavity microscope. This device combines the strong light-matter coupling of cavity QED with the micrometer-scale spatial resolution provided by high-numerical-aperture optics. This thesis presents the operation and the first experimental results obtained with this new platform. First, the high-resolution addressing capability of the cavity microscope was used to locally modify the level structure of thermal atoms within the cavity mode. This allowed us to extract spatially resolved information about the atomic density from a global cavity measurement. In doing so, we overcome a longstanding limitation of cavity QED experiments, where the spatial structure of the light-matter interaction is typically fixed by the cavity mode and cannot be freely tuned. Second, we implemented a tightly focused optical trap that enabled the extraction of a small degenerate Fermi gas from a larger atomic cloud, coupled to the cavity mode. We then systematically investigated the light-matter interaction between this tweezer-trapped Fermi gas and the cavity mode by studying the superradiant phase transition of atoms in the cavity. We find that the transition can be either facilitated or suppressed by the fermionic occupation of phase space. The crossover between these two regimes occurs when the scattering wavevector becomes approximately twice the Fermi wavevector, revealing the crucial role of Fermi statistics in cavity-mediated interactions. These results pave the way toward the deterministic preparation of few-fermion systems inside an optical cavity, enabling the study of finite-size and trap-filling effects in cavity QED. In an upgraded version of the cavity microscope, the number of atoms can approach the cavity cooperativity, bringing the system into a new regime where entanglement can extend across the entire ensemble. Finally, by introducing time-dependent randomization of cavity-mediated interactions, this platform could realize low-rank SYK models, opening the door to experimental investigations of fast scrambling, thermalization, and quantum chaos in strongly interacting quantum matter.
In this dissertation we focused on two topics: 1. atomic cooperative effect, including superradiance, subradiance and collective Lamb shift in an atomic ensemble; 2. novel topological effect in quantum optics system, such as Haldane model, synthetic magnetic field in superradiance lattice and synthetic spin-orbit interaction in Fock-state lattices. \n\nIn the first part, we start from the Dicke state, an N-particle atomic ensemble excited by a single photon. Due to the interaction of the atoms with a continuum of vacuum modes, the Dicke state has a larger decay rate compared with an isolated atom, termed the single photon superradiance. In the “opposite” case, the single-photon subradiance state does not decay because of the destructive interference of the atomic transitions. We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shifts cannot be neglected. We find that antisymmetric states are subradiant states for distributions with reflection symmetry. Continuous symmetry can also be used to achieve subradiance in an extended ensemble. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.\n\nIn the second part, we start from introducing the concepts, methods, and models from quantum optics or condensed matter physics. They include the timed-Dicke states, electromagnetically induced transparency, coupled wave equations, tight-binding model, band theory, Floquet theory, superradiance lattice, integer quantum Hall effect, Haldane model, etc.. Based upon these tools, we study three topological quantum optics systems: (i) a Haldane model with in situ tunable topological properties in a two-dimensional momentumspace superradiance lattice composed of timed Dicke states in electromagnetically induced transparency; (ii) a spin-orbit coupled Fock-state lattice, which introduce a novel quantum operation to generate mesoscopic superposition states, e.g., the NOON states and cat states; (iii) a synthetic magnetic field created in a quasi one dimensional superradiance lattice, which is predicted to be observed in thermal vapours of alkali atoms instead of only in cold atoms (as in previous experiments). This study aims to provide a novel, highly tunable platform simulating exotic phenomena in condensed matter physics and offers a basis of topological quantum optics and novel photonic devices.