Lloyd C. L. Hollenberg Centre for Quantum Computer Technology, School of Physics, University of Melbourne, VIC 3010, Australia Condensed matter physics studies complex systems of interacting particles to understand macroscopic and emergent phenomena of those systems. In general, sample perfection and homogeneity are critical to the observation of most many-body effects. Conversely, quantum optics has conventionally looked at interactions between some of the most perfect and isolated systems available, for example monochromatic optical fields and single atoms. The perfection and control of large ensembles of strongly interacting particles is extending to levels of uniformity never before reached, although often with only global control and readout, while quantum optical techniques are now increasingly allowing the treatment of systems of increasing complexity, but with the added advantage of local control and readout. Coupled cavity systems are ideally placed to straddle this gap of scales, i.e., local control of small systems vs global control of large systems, to give insight into both fields. Systems of interacting photons in coupled cavities have been predicted to show quantum phase transitions (QPTs), and may be important as quantum simulators of complex dynamics. But the nature of the interactions is subtly different from more conventional condensed matter models. Here we describe the emergence of Hubbard-like dynamics in coupled cavity systems spanning finite to infinite structures, the nature of the excitations involved, how these coupled cavity systems can be understood as the optical analog of a solid-state system, and prospects for structures that can be fabricated to demonstrate the required interactions.
Lloyd C. L. Hollenberg Centre for Quantum Computer Technology, School of Physics, University of Melbourne, VIC 3010, Australia Condensed matter physics studies complex systems of interacting particles to understand macroscopic and emergent phenomena of those systems. In general, sample perfection and homogeneity are critical to the observation of most many-body effects. Conversely, quantum optics has conventionally looked at interactions between some of the most perfect and isolated systems available, for example monochromatic optical fields and single atoms. The perfection and control of large ensembles of strongly interacting particles is extending to levels of uniformity never before reached, although often with only global control and readout, while quantum optical techniques are now increasingly allowing the treatment of systems of increasing complexity, but with the added advantage of local control and readout. Coupled cavity systems are ideally placed to straddle this gap of scales, i.e., local control of small systems vs global control of large systems, to give insight into both fields. Systems of interacting photons in coupled cavities have been predicted to show quantum phase transitions (QPTs), and may be important as quantum simulators of complex dynamics. But the nature of the interactions is subtly different from more conventional condensed matter models. Here we describe the emergence of Hubbard-like dynamics in coupled cavity systems spanning finite to infinite structures, the nature of the excitations involved, how these coupled cavity systems can be understood as the optical analog of a solid-state system, and prospects for structures that can be fabricated to demonstrate the required interactions.
Systems of strongly interacting atoms and photons, which can be realized wiring up individual cavity QED systems into lattices, are perceived as a new platform for quantum simulation. While sharing important properties with other systems of interacting quantum particles, here we argue that the nature of light-matter interaction gives rise to unique features with no analogs in condensed matter or atomic physics setups. By discussing the physics of a lattice model of delocalized photons coupled locally with two-level systems through the elementary light-matter interaction described by the Rabi model, we argue that the inclusion of counterrotating terms, so far neglected, is crucial to stabilize finite-density quantum phases of correlated photons out of the vacuum, with no need for an artificially engineered chemical potential. We show that the competition between photon delocalization and Rabi nonlinearity drives the system across a novel Z(2) parity symmetry-breaking quantum criticality between two gapped phases that share similarities with the Dicke transition of quantum optics and the Ising critical point of quantum magnetism. We discuss the phase diagram as well as the low-energy excitation spectrum and present analytic estimates for critical quantities.
Experimental progress in atomic, molecular and optical physics, at the quantum level, as well as in condensed matter physics, has over the last few decades allowed us to not only observe quantum phenomena in nature, but also control them. This has led to the idea of “engineering” quantum systems, where microscopic constituents, such as single atoms, are manipulated in a precise manner to achieve some desired behaviour. By now, this has become a central theme in contemporary low-energy quantum physics. The change in viewpoint, from “observing” to “controlling,” leads to very different goals and opportunities, for experimentalists and theorists alike. This thesis contains seven publications on the following two related topics: i) engineering interactions in quantum systems, allowing for a large degree of control of system parameters, and ii) quantifying and understanding quantum correlations in dynamical quantum systems. The latter is an important goal in quantum information science, necessary to take advantage of quantum systems for information processing tasks, and thus expected to be central for future quantum technologies
The interaction of light with matter is at the heart of quantum optics, which itself enables insight into the fundamental aspects of quantum mechanics. First experimental access to this research field has been realized by coupling atoms to light. Here, the transition between discrete energy states of the atom is associated with the absorption and emission of a photon, a single quantum of the electromagnetic field. As a central aspect of quantum optics, the light-emitter interaction can be significantly enhanced by placing the emitter in optical cavity that is on resonance with the emitter. In recent years, this has led to a rapidly evolving research field known as cavity quantum electrodynamics (CQED). In CQED two different regimes are distinguished: the strong and the weak coupling regimes. In the strong coupling regime, the emitted photon is reflected from the cavity mirrors and eventually reabsorbed by the emitter. In contrast, the weak coupling regime describes the irreversible emission, where the photon leaks out of the cavity before it can be reabsorbed. Both the weak and strong coupling regimes enabled fundamental experiments for a better understanding of quantum optical phenomena. \n \n \n \nCQED grants access to the quantum world and hence offers potentially revolutionizing applications, particularly in the field of quantum information processing. A central aspect for the successful implementation of quantum applications is the system's scalability. Unfortunately, placing atoms deterministically inside a cavity remains technologically elaborate and hence minimizes the prospect of scaling a atom-CQED system. \n \nA possibility to address this issue is to implement CQED in the solid state, where sophisticated fabrication strategies allow miniaturization and scalability of the system. Particularly the development of self-assembled quantum dots (QD) in semiconductors represent a promising route. QDs can be considered as artificial atoms that mimic the atomic two-level system. These structures interact strongly with light and therefore have the potential for replacing atoms in CQED. As a central advantage, QDs are naturally trapped, which greatly simplifies the deterministic incorporation into the cavity. \n \nIn recent years, many efforts have been made to couple self-assembled QDs to microcavities. Generally, the successful implementation of CQED requires a cavity with a high quality factor Q and a low mode volume. In a majority of the approaches, the high Q/small mode volume cavities were monolithically defined around the QD, embedding the QD at a fixed position inside the cavity. Both the weak and strong coupling regimes have been reached with these systems. However, for future applications they suffer from several disadvantages. The fixed position of the QD inside the cavity minimizes the prospects for spectral tunability and spatial positioning the QD inside the cavity. Furthermore, prospects for further increasing of the cavity Q-factor and minimization of the mode volume remain limited in these systems. \n \nIn this thesis the mentioned disadvantages are addressed by developing a fully tunable miniaturized Fabry-Pérot microcavity with low mode volume. The design enables both spatial positioning of the emitter inside the cavity and spectral tunability. Successful coupling of a single QD to the microcavity is demonstrated including the strong coupling regime. Further a new approach to decrease the cavity mode volume is presented, where we demonstrate weak coupling is achieved
Over the last decade, quantum simulation and computation has progressed from a purely scientific testbed of quantum mechanics to a mature field that is starting to offer new insights into materials, quantum effects, and algorithms that are intractable with even the most state-of-the-art classical computation. Simulating certain quantum Hamiltonians that are theorized to be at the heart of high-Tc superconductivity, topological quantum systems such as the fractional quantum Hall effect or fundamental questions of thermalization quickly exceed the available memory of even the most advanced supercomputers – and in fact all memory in the world – due to the exponential growth of the Hilbert space with system size. As postulated by Feynman himself, the computational system best suited for solving quantum problems is to use a quantum system itself, as it can intrinsically represent the entanglement that is the key resource making quantum computing challenging but also promising. Apart from simulating problems in physics and chemistry, there is also tremendous excitement for quantum computers to provide speedups for general algorithms in optimization at a rate that is exponentially faster than existing classical programming. So far only a small class of algorithms has been actually proven to provide such a speedup, most prominently Shor's algorithm which can factor large prime numbers, and several other search and oracle algorithms. In the last two decades, many experiments using ultracold atoms, ions, or superconducting circuits have focused on analog quantum simulation. Here, a model Hamiltonian that is believed to capture all the relevant physics of the system of study is experimentally realized using different building blocks and interactions but replicating condensed matter effects at an increased scale. This has led to a number of bespoke experiments such as BEC/Fermigass machines, quantum gas microscopes and more exotic setups that are purpose built to study a particular effect. More recently, there has been a shift to develop more universal simulation platforms and optical tweezer arrays have emerged as a leading solution due to their high degree of reconfigurability. Through tremendous improvements in the degree of control and measurement of single qubits, error correction has become a viable route to build a true universal digital quantum computer. Even as we transition into the digital age of quantum simulation, certain classes of problems with additional physics constraints such as Fermionic statistics, gauge fields and lattice gauge theories still incur too large of an overhead to be encoded on these digital simulators. In this thesis, we use a highly degenerate twisted cavity to simulate the effect of a magnetic field on a two-dimensional system of interacting photons to enable realization of states of the quantum Hall effect. We design, build, and commission a new lens based cavity apparatus realizing a lowest Landau level for a mesoscopic number of modes. We demonstrate the integration of highly excited Rydberg atoms to mediate strong interactions and demonstrate photon blockade as well as mean field interactions. As a second application of cavities to quantum information leveraging our newfound comfort with intra-cavity optics, and experience with aberration modeling in resonators, we demonstrate a new class of small waist optical resonators enabled by lens-based cavities and then apply our understanding of optical aberrations in cavities to the development of a new class of cavity array. This Cavity Array Microscope (CAM) realizes a large number of cavities (up to currently 600) using only a fixed number of free space optics and is both scalable with constant overhead as well as compatible with Rydberg atoms. This platform provides a route to highly parallel quantum repeater operation or entanglement generation between atom arrays in the future.
Present-day experiments have started to couple traditional simulations of ultracold atom experiments with quantum light-fields in cavities. This has provided a wealth of op- portunities to enlarge the number of interaction potentials: cavity mediated long-range interactions compete with kinetic energies, longitudinal fields, short-ranged collisional or magnetic spin-spin interactions. The intracavity many-body lattice models often have to be maintained far from equilibrium through the presence of external driving lasers that help to boost and engineer the various interaction potentials. The steady influx of energy is compensated by a steady stream of energy out of the atom-cavity system for example by photon losses or atomic spontaneous emission. Several experiments have demonstrated that such environments can give rise to new competing quantum phases. \nBut this long-standing ambition to push for models with tailorable interaction potentials can bring with it also considerable challenges in their theoretical description, since sponta- neous symmetry breaking transitions in many body lattice systems coupled to dynamical light-fields with single-photon character occur in the presence of drive and dissipation for the photonic force carriers. This clearly calls for model systems where the above men- tioned interplay of interactions, drive, dissipation and cooperative many-body behaviour can be theoretically studied to provide simple, experimentally verifiable predictions. \nThe Dicke model is, through its simplicity (an exactly solved ferromagnet with infinite range atom-atom interactions mediated by a single cavity mode), an exceptionally well- suited candidate. As the generic model for atom-light interactions, it has been experimen- tally realized in a variety of modern quantum optical systems, highlighting its relevance for present-day research. The Dicke model is also highly versatile itself. It has been extended into the dissipative realm, was promoted to account for multiple optical light modes and was used to describe multiple, coupled single-mode cavity structures. It was adapted to treat spin-selective coupling to a cavity to describe superradiance phase tran- sitions in multi-level atomic systems. Moreover, it was realised in electronic circuits where the dipole coupling of real atoms to single mode fields is replaced by a capacitive cou- pling of artificial atoms to a resonator mode. This illustrates that the Dicke model and its extended variants are ’future-proof’ and continue to be of relevance for fundamental light-matter interactions and for driven-dissipative phase transitions. \nIn this thesis, we investigate magnetic phase transitions in driven-dissipative atomic en- sembles interacting with quantum light. We present three research projects on variants of cooperative radiation of an ensemble of laser driven two-level atoms in a single mode optical cavity, as described by the Dicke model. \nThroughout the chapters 2,3 and 4 that contain the main body of research of this thesis, we investigate phase transitions between non-equilibrium stationary states in engineered quantum-optical systems each of which extends the conventional Dicke model physics. As a starting point, we map the quantum equations of motion onto a set of semiclassical nonlinear stochastic equations and analyse their stationary states and instabilities with master equations for atomic spin and photon mean-field amplitudes. These are used to obtain experimentally relevant parameters such as critical atom-light couplings for phase transitions, phase diagrams and properties of stationary non-equilibrium states in addition to cavity output spectra that identify the imprint of magnetic correlations in the light-field. \nIn chapter 2, we help resolve a discrepancy between earlier experimental investigations of the critical atom-light coupling strength for the superradiance transition in the Dicke model: higher external pumping strengths than theoretically predicted were needed to observe a coherent, superradiant state of the light field in an optical cavity. By including incoherent spontaneous emission of atomic excitations, we extend the dissipative Dicke model to a two loss channel variant containing both photon leakage and atomic decay that reproduces the experimentally observed critical atom-light coupling. \nRecent experiments have started to interface quantum many body lattice models with coherent cavity fields, thereby allowing to realize new quantum phases through competing atom-cavity and atom-atom interactions. In chapter 3, we consider a simplified model for such a set-up where a single quantized mode of the light-field interacts with an ensemble of Rydberg-dressed atoms inside a high finesse optical cavity. This model provides a base case for further studies of quantum magnets in optical cavities. At the heart of this model is a competition of short- (dipolar atom-atom) and long-range (atom-light) interactions at the Hamiltonian level in the presence of both spontaneous emission and photon leak- age through the cavity mirrors. We show that different magnetic phases can coexist with coherent atomic radiation and provide clear experimental signatures to identify the mag- netic structure and intra-cavity dynamics. We suggest an experimental level-scheme for a quantum optical implementation of our model. \nIn chapter 4 we consider a generic, collective decay for many-body excitations in the paradigmatic Dicke model. This extension drastically enriches the dynamics as it induces a bicritical point and a bistable regime dominated by true non-equilibrium fluctuations that induce a dissipative first-order phase transition that can only be resolved by including finite fluctuation corrections with the help of stochastic Langevin equations. We investigate the hysteretic response to time-dependent ramps of the atom-light coupling. Discontinuous first-order phase transitions where metastable states coexist in a hysteresis domain have been investigated in recent dissipative quantum-optical experiments. We review noise- activation far from thermal equilibrium in chapter 5.