A quantum critical point develops when matter undergoes a continuous transformation between distinct ground states at absolute zero. It hosts pronounced quantum fluctuations, which render the system highly susceptible to external perturbations. While light-matter coupling has rapidly moved forward as a means to probe and control quantum materials, the capacity of quantum critical fluctuations in the photon-mediated responses has been largely unexplored. Here we advance the notion that directly coupling a quantum critical mode to a quantized cavity field dramatically facilitates the realization of the elusive superradiant phase transition in equilibrium, circumventing at once the key obstacles that have prevented its attainment in spite of decades of pursuit. The superradiant phase transition develops far below the ultrastrong regime of light-matter couplings, and the transition is accompanied by the light-matter hybrid system showing strongly enhanced intrinsic squeezing and amplified quantum Fisher information. We also identify candidate cavity quantum materials platforms for validating the proposed effect. Our findings suggest a general principle by which quantum criticality amplifies the response to cavity photons. They also demonstrate that cavity coupling accesses the elevated quantum entanglement of the underlying matter at quantum criticality, thereby pointing to a pathway towards realizing the potential of highly collective quantum materials to expand the capacities of quantum information science. Quantum critical systems host strong fluctuations that can enhance their response to external fields. Here the authors show that directly coupling cavity-bound photons to a quantum critical material produces highly correlated light-matter states at modest light-matter couplings that access the matter’s enhanced quantum entanglement.
A quantum critical point develops when matter undergoes a continuous transformation between distinct ground states at absolute zero. It hosts pronounced quantum fluctuations, which render the system highly susceptible to external perturbations. While light-matter coupling has rapidly moved forward as a means to probe and control quantum materials, the capacity of quantum critical fluctuations in the photon-mediated responses has been largely unexplored. Here we advance the notion that directly coupling a quantum critical mode to a quantized cavity field dramatically facilitates the realization of the elusive superradiant phase transition in equilibrium, circumventing at once the key obstacles that have prevented its attainment in spite of decades of pursuit. The superradiant phase transition develops far below the ultrastrong regime of light-matter couplings, and the transition is accompanied by the light-matter hybrid system showing strongly enhanced intrinsic squeezing and amplified quantum Fisher information. We also identify candidate cavity quantum materials platforms for validating the proposed effect. Our findings suggest a general principle by which quantum criticality amplifies the response to cavity photons. They also demonstrate that cavity coupling accesses the elevated quantum entanglement of the underlying matter at quantum criticality, thereby pointing to a pathway towards realizing the potential of highly collective quantum materials to expand the capacities of quantum information science. Quantum critical systems host strong fluctuations that can enhance their response to external fields. Here the authors show that directly coupling cavity-bound photons to a quantum critical material produces highly correlated light-matter states at modest light-matter couplings that access the matter’s enhanced quantum entanglement.
We consider a model of a light-matter system, in which a system of fermions (or bosons) is coupled to a photonic mode that drives phase transitions in the matter degrees of freedom. Starting from a simplified analytical model, we show that the entanglement between light and matter vanishes at small and large coupling strength and shows a peak in the proximity of the transition. We perform numerical simulations for a specific model (relevant to both solid state and cold atom platforms) and show that the entanglement displays critical behavior at the transition and features maximum susceptibility, as demonstrated by a maximal entanglement capacity. Remarkably, light-matter entanglement provides direct access to critical exponents, suggesting another approach to measure universal properties without direct matter probes.
The hybridization between light and matter forms the basis to achieve cavity control over quantum materials. In this Letter we investigate a cavity coupled to a quantum chain of interacting spinless fermions by numerically exact solutions and perturbative analytical expansions. We draw two important conclusions about such systems: (i) Specific quantum fluctuations of the matter system play a pivotal role in achieving entanglement between light and matter; and (ii) in turn, light-matter entanglement is a key ingredient to modify electronic properties by the cavity. We hypothesize that quantum fluctuations of those matter operators to which the cavity modes couple are a general prerequisite for light-matter entanglement in the ground state. Implications of our findings for light-matter-entangled phases, cavity-modified phase transitions in correlated systems, and measurement of light-matter entanglement through Kubo response functions are discussed.
We present a quantum metrology protocol which relies on quenching a light-matter system exhibiting a superradiant quantum phase transition beyond its critical point. In the thermodynamic limit these systems can exhibit an exponential divergence of the quantum Fisher information in time, whose origin is the exponential growth of the number of correlated photons on an arbitrarily fast time scale determined by the coupling strength. This provides an exponential speed-up in the growth of the quantum Fisher information over existing critical quantum metrology protocols relying on quenching close to the critical point and observing power law behaviour. We demonstrate that the Cram\'er-Rao bound can be saturated in our protocol through the standard homodyne detection scheme. We explicitly show its advantage using the archetypal setting of the Dicke model and explore a quantum gas coupled to a single-mode cavity field as a potential platform. In this case an additional exponential enhancement of the quantum Fisher information can in practice be observed with the number of atoms N in the cavity, even in the absence of N-body coupling terms.
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.
We present a quantum metrology protocol which relies on quenching a light-matter system exhibiting a superradiant quantum phase transition beyond its critical point. In the thermodynamic limit these systems can exhibit an exponential divergence of the quantum Fisher information in time, whose origin is the exponential growth of the number of correlated photons on an arbitrarily fast time scale determined by the coupling strength. This provides an exponential speed-up in the growth of the quantum Fisher information over existing critical quantum metrology protocols observing power law behaviour. We demonstrate that the Cramer-Rao bound can be saturated in our protocol through the standard homodyne detection scheme. We explicitly show its advantage in the archetypal setting of the Dicke model and explore a quantum gas coupled to a single-mode cavity field as a potential platform. In this case an additional exponential enhancement of the quantum Fisher information can in practice be observed with the number of atoms N in the cavity, despite existing works suggesting a requirement of N-body coupling terms.
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.