Parametrically driving a quantum oscillator into exceptionality.

The mathematical objects employed in physical theories do not always behave well. Einstein's theory of space and time allows for spacetime singularities and Van Hove singularities arise in condensed matter physics, while intensity, phase and polarization singularities pervade wave physics. Within dissipative systems governed by matrices, singularities occur at the exceptional points in parameter space whereby some eigenvalues and eigenvectors coalesce simultaneously. However, the nature of exceptional points arising in quantum systems described within an open quantum systems approach has been much less studied. Here we consider a quantum oscillator driven parametrically and subject to loss. This squeezed system exhibits an exceptional point in the dynamical equations describing its first and second moments, which acts as a borderland between two phases with distinctive physical consequences. In particular, we discuss how the populations, correlations, squeezed quadratures and optical spectra crucially depend on being above or below the exceptional point. We also remark upon the presence of a dissipative phase transition at a critical point, which is associated with the closing of the Liouvillian gap. Our results invite the experimental probing of quantum resonators under two-photon driving, and perhaps a reappraisal of exceptional and critical points within dissipative quantum systems more generally.

Quantum topology in the ultrastrong coupling regime.

The coupling between two or more objects can generally be categorized as strong or weak. In cavity quantum electrodynamics for example, when the coupling strength is larger than the loss rate the coupling is termed strong, and otherwise it is dubbed weak. Ultrastrong coupling, where the interaction energy is of the same order of magnitude as the bare energies of the uncoupled objects, presents a new paradigm for quantum physics and beyond. As a consequence profound changes to well established phenomena occur, for instance the ground state in an ultrastrongly coupled system is not empty but hosts virtual excitations due to the existence of processes which do not conserve the total number of excitations. The implications of ultrastrong coupling for quantum topological systems, where the number of excitations are typically conserved, remain largely unknown despite the great utility of topological matter. Here we reveal how the delicate interplay between ultrastrong coupling and topological states manifests in a one-dimensional array. We study theoretically a dimerized chain of two-level systems within the ultrastrong coupling regime, where the combined saturation and counter-rotating terms in the Hamiltonian are shown to play pivotal roles in the rich, multi-excitation effective bandstructure. In particular, we uncover unusual topological edge states, we introduce a flavour of topological state which we call an anti-edge state, and we reveal the remarkable geometric-dependent renormalizations of the quantum vaccum. Taken together, our results provide a route map for experimentalists to characterize and explore a prototypical system in the emerging field of ultrastrong quantum topology.

Doublons, topology and interactions in a one-dimensional lattice.

We investigate theoretically the Bose-Hubbard version of the celebrated Su-Schrieffer-Heeger topological model, which essentially describes a one-dimensional dimerized array of coupled oscillators with on-site interactions. We study the physics arising from the whole gamut of possible dimerizations of the chain, including both the weakly and the strongly dimerized limiting cases. Focusing on two-excitation subspace, we systematically uncover and characterize the different types of states which may emerge due to the competition between the inter-oscillator couplings, the intrinsic topology of the lattice, and the strength of the on-site interactions. In particular, we discuss the formation of scattering bands full of extended states, bound bands full of two-particle pairs (including so-called 'doublons', when the pair occupies the same lattice site), and different flavors of topological edge states. The features we describe may be realized in a plethora of systems, including nanoscale architectures such as photonic cavities, optical lattices and qubits, and provide perspectives for topological two-particle and many-body physics.

Non-reciprocal population dynamics in a quantum trimer.

We study a quantum trimer of coupled two-level systems beyond the single-excitation sector, where the coherent coupling constants are ornamented by a complex phase. Accounting for losses and gain in an open quantum systems approach, we show how the mean populations of the states in the system crucially depend on the accumulated phase in the trimer. Namely, for non-trivial accumulated phases, the population dynamics and the steady states display remarkable non-reciprocal behaviour in both the singly and doubly excited manifolds. Furthermore, while the directionality of the resultant chiral current is primarily determined by the accumulated phase in the loop, the sign of the flow may also change depending on the coupling strength and the amount of gain in the system. This directionality paves the way for experimental studies of chiral currents at the nanoscale, where the phases of the complex hopping parameters are modulated by magnetic or synthetic magnetic fields.

Topological Phases of Polaritons in a Cavity Waveguide.

We study the unconventional topological phases of polaritons inside a cavity waveguide, demonstrating how strong light-matter coupling leads to a breakdown of the bulk-edge correspondence. We observe an ostensibly topologically nontrivial phase, which unexpectedly does not exhibit edge states. Our findings are in direct contrast to topological tight-binding models with electrons, such as the celebrated Su-Schrieffer-Heeger (SSH) model. We present a theory of collective polaritonic excitations in a dimerized chain of oscillating dipoles embedded inside a photonic cavity. The added degree of freedom from the cavity photons upgrades the system from a typical SSH SU(2) model into a largely unexplored SU(3) model. Tuning the light-matter coupling strength by changing the cavity size reveals three critical points in parameter space: when the polariton band gap closes, when the Zak phase changes from being trivial to nontrivial, and when the edge state is lost. These three critical points do not coincide, and thus the Zak phase is no longer an indicator of the presence of edge states. Our discoveries demonstrate some remarkable properties of topological matter when strongly coupled to light, and could be important for the growing field of topological nanophotonics.

Quasichiral Interactions between Quantum Emitters at the Nanoscale.

We present a combined classical and quantum electrodynamics description of the coupling between two circularly polarized quantum emitters held above a metal surface supporting surface plasmons. Depending on their position and their natural frequency, the emitter-emitter interactions evolve from being reciprocal to nonreciprocal, which makes the system a highly tunable platform for chiral coupling at the nanoscale. By relaxing the stringent material and geometrical constraints for chirality, we explore the interplay between coherent and dissipative coupling mechanisms in the system. Thus, we reveal a quasichiral regime in which its quantum optical properties are governed by its subradiant state, giving rise to extremely sharp spectral features and strong photon correlations.

Bielectron vortices in two-dimensional Dirac semimetals.

Searching for new states of matter and unusual quasi-particles in emerging materials and especially low-dimensional systems is one of the major trends in contemporary condensed matter physics. Dirac materials, which host quasi-particles which are described by ultrarelativistic Dirac-like equations, are of a significant current interest from both a fundamental and applied physics perspective. Here we show that a pair of two-dimensional massless Dirac-Weyl fermions can form a bound state independently of the sign of the inter-particle interaction potential, as long as this potential decays at large distances faster than Kepler's inverse distance law. This leads to the emergence of a new type of energetically favorable quasiparticle: bielectron vortices, which are double-charged and reside at zero-energy. Their bosonic nature allows for condensation and may give rise to Majorana physics without invoking a superconductor. These novel quasi-particles arguably explain a range of poorly understood experiments in gated graphene structures at low doping.Two-dimensional Dirac semimetals are known to host fermionic excitations which can mimic physics usually found in ultrarelativistic quantum mechanics. Here, the authors unveil the existence of another type of quasiparticle, bielectron vortices, which are bosonic and may give rise to new types of condensates.

Localization of massless Dirac particles via spatial modulations of the Fermi velocity.

The electrons found in Dirac materials are notorious for being difficult to manipulate due to the Klein phenomenon and absence of backscattering. Here we investigate how spatial modulations of the Fermi velocity in two-dimensional Dirac materials can give rise to localization effects, with either full (zero-dimensional) confinement or partial (one-dimensional) confinement possible depending on the geometry of the velocity modulation. We present several exactly solvable models illustrating the nature of the bound states which arise, revealing how the gradient of the Fermi velocity is crucial for determining fundamental properties of the bound states such as the zero-point energy. We discuss the implications for guiding electronic waves in few-mode waveguides formed by Fermi velocity modulation.

The reactivity of CO2 and H2 at trapped electron sites at an oxide surface.

We investigate the reactivity to H2 of a chemisorbed CO2 species at electron traps on oxide surfaces, taking the single electron F(+) oxygen vacancy of the MgO(100) terrace as a model system. We find that multiple hydrogen addition steps form three interacting catalytic cycles, leading to the evolution of formaldehyde, methanol or methane. Our results have general implications for the reactivity of CO2 on metal oxides.

The reactivity of CO2 on the MgO(100) surface.

We investigate the adsorption of CO2 over an MgO(001) terrace, as calculated using an embedded cluster method. We find adsorbed geometries for CO2 on the perfect surface with energies which differ appreciably from previous studies, and observe that it is polarization of the surface rather than the inclusion of electron correlation which leads to this discrepancy. Our results suggest that both monodentate and tridentate carbonate formation on the MgO(001) surface are favourable processes, with the monodentate structure being of lower energy. Adsorption of CO2 is found to be favourable at both F(0) and F(+) terrace sites, but not at F(2+). We also find that chemisorption at oxygen vacancy sites with a single localized electron (F(+)) could provide a route for the conversion of CO2 to other products, and that this system may be a useful model for other, more effective catalysts.

The interaction of hydrogen with the {010} surfaces of Mg and Fe olivine as models for interstellar dust grains: a density functional theory study.

There is no consensus as yet to account for the significant presence of water on the terrestrial planets, but suggested sources include direct hydrogen adsorption from the parent molecular cloud after the planets' formation, and delivery of hydrous material via comets or asteroids external to the zone of the terrestrial planets. Alternatively, a more recent idea is that water may have directly adsorbed onto the interstellar dust grains involved in planetary formation. In this work, we use electronic structure calculations based on the density functional theory to investigate and compare the bulk and {010} surface structures of the magnesium and iron end-members of the silicate mineral olivine, namely forsterite and fayalite, respectively. We also report our results on the adsorption of atomic hydrogen at the mineral surfaces, where our calculations show that there is no activation barrier to the adsorption of atomic hydrogen at these surfaces. Furthermore, different surface sites activate the atom to form either adsorbed hydride or proton species in the form of hydroxy groups on the same surface, which indicates that these mineral surfaces may have acted as catalytic sites in the immobilization and reaction of hydrogen atoms to form dihydrogen gas or water molecules.