When light and matter are weakly coupled, they can be described as two distinctive systems exchanging quanta of energy. By contrast, for very large coupling strength, the systems hybridize and form compounds that cannot be described in terms of light or matter only. In this Thesis, we study some exotic properties which arise in this regime. In particular, we are interested in the possibility to engineer quantum phase transitions in these systems. One direction we explore is the study of two-photon coupling, a mechanism in which matter creates or absorb photons by pairs. This mechanism creates a rich phase diagram containing both phase transitions and instabilities. A second topic is the use of these transitions for sensing applications. Indeed, near the critical point, the system becomes extremely sensitive to external perturbations. We study a setup in which a single qubit is coupled to a bosonic field. We show that even this finite-size system displays a phase transition, which can be used to measure the frequency of the qubit and the field with improved accuracy. This protocol could be used to develop small-scale sensors. Finally, we study how the ability of a system to perform certain metrological tasks could be used to characterize and quantify nonclassicality, by using the formalism of resource theories. The first three chapters present the main concepts and key results in the fields of ultrastrong light-matter coupling, superradiant phase transitions, and quantum metrology. I have strived to write these chapters pedagogically; they can be used by non-specialists or students as an introduction to these domains. The three other chapters present my own research contributions. Although most of those have already been published elsewhere, this manuscript contains additional results, remarks, and perspectives, and should be considered as an improved version of the original papers.
When light and matter are weakly coupled, they can be described as two distinctive systems exchanging quanta of energy. By contrast, for very large coupling strength, the systems hybridize and form compounds that cannot be described in terms of light or matter only. In this Thesis, we study some exotic properties which arise in this regime. In particular, we are interested in the possibility to engineer quantum phase transitions in these systems. One direction we explore is the study of two-photon coupling, a mechanism in which matter creates or absorb photons by pairs. This mechanism creates a rich phase diagram containing both phase transitions and instabilities. A second topic is the use of these transitions for sensing applications. Indeed, near the critical point, the system becomes extremely sensitive to external perturbations. We study a setup in which a single qubit is coupled to a bosonic field. We show that even this finite-size system displays a phase transition, which can be used to measure the frequency of the qubit and the field with improved accuracy. This protocol could be used to develop small-scale sensors. Finally, we study how the ability of a system to perform certain metrological tasks could be used to characterize and quantify nonclassicality, by using the formalism of resource theories. The first three chapters present the main concepts and key results in the fields of ultrastrong light-matter coupling, superradiant phase transitions, and quantum metrology. I have strived to write these chapters pedagogically; they can be used by non-specialists or students as an introduction to these domains. The three other chapters present my own research contributions. Although most of those have already been published elsewhere, this manuscript contains additional results, remarks, and perspectives, and should be considered as an improved version of the original papers.
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 In this paper we analyze properties of the phase transition that appears in a set of quantum optical models; Dicke, Tavis–Cummings, quantum Rabi, and finally the Jaynes–Cummings model. As the light-matter coupling is increased into the deep strong coupling regime, the ground state turns from vacuum to become a superradiant state characterized by both atomic and photonic excitations. It is pointed out that all four transitions are of the mean-field type, that quantum fluctuations are negligible, and hence these fluctuations cannot be responsible for the corresponding vacuum instability. In this respect, these are not quantum phase transitions. In the case of the Tavis–Cummings and Jaynes–Cummings models, the continuous symmetry of these models implies that quantum fluctuations are not only negligible, but strictly zero. However, all models possess a non-analyticity in the ground state in agreement with a continuous quantum phase transition. As such, it is a matter of taste whether the transitions should be termed quantum or not. In addition, we also consider the modifications of the transitions when photon losses are present. For the Dicke and Rabi models these non-equilibrium steady states remain critical, while the criticality for the open Tavis–Cummings and Jaynes–Cummings models is completely lost, i.e. in realistic settings one cannot expect a true critical behaviour for the two last models.
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.
In this thesis we explore different phenomena occurring in open quantum many-body systems. This is a research field which is becoming increasingly more important due to the experimental progress towards realization of quantum-simulators and quantum computers using a variety of platforms, from ultracold atoms to superconducting qubit arrays. These systems are inherently driven and open, and it is an ongoing effort to develop theoretical tools and approaches to study their non-equilibrium physics. In the first part of this thesis we explore the different non-equilibrium condensate phases of resonantly interacting bosons in the presence of coherent pump and incoherent losses. This study might be of relevance to existing Rydberg-polariton setups. We derive an effective non-equilibrium field-theory of this model and study its resulting phase diagram. We find a rich phase diagram in- cluding a phase where particles form a condensate of tightly bound molecules. By changing the detuning from the scattering resonance it is possible to drive an Ising phase transition from the molecule condensate phase to a more standard atom condensate phase. In the second part of this thesis we explore the many-body localization (MBL) transition in an open-driven system. Typically, coupling to a bath is expected to destroy localization and transform the sharp MBL transition to a crossover. Here we show how one can use the couplings to non- equilibrium baths in order to detect sharp signatures of the transition, including the divergence of the dynamical exponent in the Griffith regime of the ergodic phase. This is done by solving for the steady-state of the Lindblad quantum-master equation using matrix-product operator tech- niques. Our work here suggests a new scalable numerical approach to study the MBL transition. In the third part of this thesis we study the entanglement properties of measurement trajectories in a free-fermion system subject to dephasing noise. These trajectories describe the evolution of an open system when photons exiting the system are continuously monitored. We are inspired by recent works which studied the entanglement dynamics in hybrid quantum circuits consisting of random-unitary gates and projective measurements. There it was found that a phase transition between a phase with volume-law scaling of entanglement and an area-law phase occurs at a critical value of the measurement rate. In our case we find a new regime, where at weak noise rate the system exhibits logarithmic entanglement scaling, similar to that of (1 + 1)d conformal field- theories. For some measurement protocols, we find a transition to an area-law phase at a critical noise strength.
The counterintuitive properties of quantum mechanics have the potential to produce revolutionary new technology. The applications of these devices are both vital and diverse: the efficient generation of energy from light, sensing and measuring with exquisite precision, and information processing with unparalleled speed. In this thesis, I use the theory of open quantum systems to investigate quantum technologies for enhanced sensing and light absorption. In the first research chapter, we develop a new method for describing qubit dynamics in the Rabi model. We obtain a new expression for the ac Stark shift, which enables practical and precise qubit thermometry of an oscillator. In the second research chapter, we demonstrate that it is possible to invert the phenomenon of Dicke Superradiance using nanostructures and quantum control. This creates the possibility of a new class of quantum light absorption technologies with a super-linear scaling in the absorption rate. In the final research chapter, we investigate another means of enhancing light absorption. We show that phonon assisted transitions to ratchet states in rings allow absorbed excitions to be protected from reemission.
Quantum phenomena offer the possibility of measuring physical quantities with precision beyond classical limits. However, current progress is constrained by scalability, environmental noise, and challenges in practical integration. This highlights the necessity for novel approaches. An emerging paradigm in this direction is , which harnesses the enhanced susceptibility and nonclassical correlations that naturally occur near quantum phase transitions as resources for quantum-enhanced precision. This tutorial provides a pedagogical introduction to key concepts and a detailed overview of prominent quantum sensing strategies that exploit critical phenomena in metrology. Through examples of increasing complexity, the reader is guided through various critical quantum sensing protocols applied to different critical systems. Special emphasis is placed on the optimal scaling of estimation precision with respect to fundamental resources. Finally, we discuss how critical quantum metrology extends from idealized models to realistic open-system, dissipative regimes, and strongly correlated fermionic systems, outlining both the challenges and opportunities for future quantum technologies.