arXiv subjects

C. A. Downing

Publications and source records attributed to C. A. Downing.

At least 19 recordsLinked to original sources

arXiv2026

Charging a quantum battery from the Bloch sphere

We reconsider the quantum energetics and quantum thermodynamics of the charging process of a simple, two-component quantum battery model made up of a charger qubit and a single--cell battery qubit. We allow for the initial quantum state of the charger to lie anywhere on the surface of the Bloch sphere, and find the generalized analytical expressions describing the stored energy, ergotropy and capacity of the battery, all of which depend upon the initial Bloch sphere polar angle in a manner evocative of the quantum area theorem. The origin of the ergotropy produced, as well as the genesis of the battery capacity, can be readily traced back to the quantum coherences and population inversions generated (and the balance between these two mechanisms is contingent upon the starting Bloch polar angle). Importantly, the ergotropic charging power and its associated optimal charging time display notable deviations from standard results which disregard thermodynamic considerations. Our theoretical groundwork may be useful for guiding forthcoming experiments in quantum energy science based upon coupled two-level systems.

quant-ph↗

arXiv2025

Energy storage in a continuous-variable quantum battery with nonlinear coupling

In the quantum world, the process of energy storage can be enhanced thanks to various nonclassical phenomena. This inspiring fact suggests quantum batteries as plausible sources of power for future quantum devices, at least in principle. However, thermodynamically not all of the energy stored in a quantum battery is useful for doing work. By considering a class of models based upon quantum continuous variables, here we show how the maximum extractable energy from a bosonic quantum battery can be intimately related to Heisenberg's uncertainty principle. We found that realizing minimum uncertainty essentially guarantees that all of the energy stored in a Gaussian quantum battery can be withdrawn and used to do work. For a standard system where the charger and battery are coupled linearly, this criterion is satisfied rather trivially. However, our theoretical results demonstrate that - for a quantum battery with nonlinear coupling - a state of minimum uncertainty can also be achieved nontrivially via the generation of quantum squeezing. We characterize the charging performance of our proposed continuous variable quantum batteries in detail, and we hope that our theory may be useful in the design of a new generation of efficient quantum batteries harnessing bosonic excitations, such as those built with photonic architectures.

quant-ph↗

arXiv2025

A first encounter with exceptional points in a quantum model

An exceptional point is a special point in parameter space at which two (or more) eigenvalues and eigenvectors coincide. The discovery of exceptional points within mechanical and optical systems has uncovered peculiar effects in their vicinity. Here we consider perhaps the simplest quantum model which exhibits an exceptional point and which allows for an analytical treatment. In particular, we re-examine a two-level atom driven by a laser and suffering from losses. The same exceptional point arises in several non-Hermitian matrices which determine various aspects of the dynamics of the system. There are consequences for some important observables, for example the spectrum evolves from being a Lorentzian-like singlet to a Mollow triplet upon passing through the exceptional point. Our analysis supports the perspective that viewing certain quantum systems through the lens of exceptional points offers some desirable explanatory advantages.

quant-ph↗

arXiv2024

Two-photon charging of a quantum battery with a Gaussian pulse envelope

Quantum energy science is rapidly emerging as a domain interested in the generation, transfer and storage of energy at the quantum level. In particular, quantum batteries have the scope to exploit the wonders of quantum mechanics in order to boost their performance as compared to their electrochemical equivalents. Here we show how an exponential enhancement in stored energy can be achieved with a quantum battery thanks to a two-photon charging protocol. We consider theoretically a quantum battery modelled as a quantum harmonic oscillator, which when driven by a quadratic field (manifested by a Gaussian pulse envelope) gives rise to squeezing of the battery. This quantum squeezing ensures that the population of the battery is driven exponentially up its bosonic energy ladder. Our results demonstrate a plausible mechanism for quickly storing a vast amount of energy in a quantum object defined by continuous variables, which may be explored experimentally in a variety of quantum optical platforms.

quant-ph↗

arXiv2024

Unconventional edge states in a two-leg ladder

Some popular mechanisms for restricting the diffusion of waves include introducing disorder (to provoke Anderson localization) and engineering topologically non-trivial phases (to allow for topological edge states to form). However, other methods for inducing somewhat localized states in elementary lattice models have been historically much less studied. Here we show how edge states can emerge within a simple two-leg ladder of coupled harmonic oscillators, where it is important to include interactions beyond those at the nearest neighbour range. Remarkably, depending upon the interplay between the coupling strength along the rungs of the ladder and the next-nearest neighbour coupling strength along one side of the ladder, edge states can indeed appear at particular energies. In a wonderful manifestation of a type of bulk-edge correspondence, these edge state energies correspond to the quantum number for which additional stationary points appear in the continuum bandstructure of the equivalent problem studied with periodic boundary conditions. Our theoretical results are relevant to a swathe of classical or quantum lattice model simulators, such that the proposed edge states may be useful for applications including waveguiding in metamaterials and quantum transport.

cond-mat.mes-hall↗

arXiv2024

Hyperbolic enhancement of a quantum battery

A quantum system which can store energy, and from which one can extract useful work, is known as a quantum battery. Such a device raises interesting issues surrounding how quantum physics can provide certain advantages in the charging, energy storage or discharging of the quantum battery as compared to their classical equivalents. However, the pernicious effect of dissipation degrades the performance of any realistic battery. Here we show how one can circumvent this problem of energy loss by proposing a quantum battery model which benefits from quantum squeezing. Namely, charging the battery quadratically with a short temporal pulse induces a hyperbolic enhancement in the stored energy, such that the dissipation present becomes essentially negligible in comparison. Furthermore, we show that when the driving is strong enough the useful work which can be extracted from the quantum battery, that is the ergotropy, is exactly equal to the stored energy. These impressive properties imply a highly efficient quantum energetic device with abundant amounts of ergotropy. Our theoretical results suggest a possible route to realizing high-performance quantum batteries, which could be realized in a variety of platforms exploiting quantum continuous variables.

quant-ph↗

arXiv2024

Energetics of a pulsed quantum battery

The challenge of storing energy efficiently and sustainably is highly prominent within modern scientific investigations. Due to the ongoing trend of miniaturization, the design of expressly quantum storage devices is itself a crucial task within current quantum technological research. Here we provide a transparent analytic model of a two-component quantum battery, composed of a charger and an energy holder, which is driven by a short laser pulse. We provide simple expressions for the energy stored in the battery, the maximum amount of work which can be extracted, both the instantaneous and the average powers, and the relevant charging times. This allows us to discuss explicitly the optimal design of the battery in terms of the driving strength of the pulse, the coupling between the charger and the holder, and the inevitable energy loss into the environment. We anticipate that our theory can act as a helpful guide for the nascent experimental work building and characterizing the first generation of truly quantum batteries.

quant-ph↗

arXiv2023

Quantum confinement in Dirac-like nanostructures

In Westminster Abbey, in a nave near to Newton's monument, lies a memorial stone to Paul Dirac. The inscription on the stone includes the relativistic wave equation for an electron: the Dirac equation. At the turn of the 21st century, it was discovered that this eponymous equation was not simply the preserve of particle physics. The isolation of graphene by Andre Geim and Konstantin Novoselov in Manchester led to the exploration of a novel class of materials - Dirac materials - whose electrons behave like Dirac particles. While the mobility of these quasi-relativistic electrons is attractive from the perspective of potential ultrafast devices, it also presents a distinct challenge: how to confine Dirac particles so as to avoid making inherently leaky devices? Here we discuss the unconventional quantum tunnelling of Dirac particles, we explain a strategy to create bound states electrostatically, and we briefly review some pioneering experiments seeking to trap Dirac electrons.

cond-mat.mes-hall↗

arXiv2023

A quantum battery with quadratic driving

Quantum batteries are energy storage devices built using quantum mechanical objects, which are developed with the aim of outperforming their classical counterparts. Proposing optimal designs of quantum batteries which are able to exploit quantum advantages requires balancing the competing demands for fast charging, durable storage and effective work extraction. Here we study theoretically a bipartite quantum battery model, composed of a driven charger connected to an energy holder, within two paradigmatic cases of a driven-dissipative open quantum system: linear driving and quadratic driving. The linear battery is governed by a single exceptional point which splits the response of the battery into two regimes, one of which induces a good amount of useful work. Quadratic driving leads to a squeezed quantum battery, which generates plentiful useful work near to critical points associated with dissipative phase transitions. Our theoretical results may be realized with parametric cavities or nonlinear circuits, potentially leading to the manifestation of a quantum battery exhibiting squeezing.

quant-ph↗

arXiv2023

Unbalanced gain and loss in a quantum photonic system

Theories in physics can provide a kind of map of the physical system under investigation, showing all of the possible types of behavior which may occur. Certain points on the map are of greater significance than others, because they describe how the system responds in a useful or interesting manner. For example, the point of resonance is of particular importance when timing the pushes onto a person sat on a swing. More sophisticatedly, so-called exceptional points have been shown to be significant in optical systems harbouring both gain and loss, as typically described by non-Hermitian Hamiltonians. However, expressly quantum points of interest -- be they exceptional points or otherwise -- arising in quantum photonic systems have been far less studied. Here we consider a paradigmatic model: a pair of coupled qubits subjected to an unbalanced ratio of gain and loss. We mark on its map several flavours of both exceptional and critical points, each of which are associated with unconventional physical responses. In particular, we uncover the points responsible for characteristic spectral features and for the sudden loss of quantum entanglement in the steady state. Our results provide perspectives for characterizing quantum photonic systems beyond effective non-Hermitian Hamiltonians, and suggest a hierarchy of intrinsically quantum points of interest.

quant-ph↗

arXiv2023

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.

quant-ph↗

arXiv2023

Resonance fluorescence of two asymmetrically pumped and coupled two-level systems

We study a driven-dissipative duo of two-level systems in an open quantum systems approach, modelling a pair of atoms or (more generally) meta-atoms. Allowing for complex-valued couplings in the setup, which are of both a coherent and incoherent character, gives rise to a diverse coupling landscape. We consider several points on this landscape, for example where the coupling between the two coupled two-level systems is dominated by coherent, incoherent, unsymmetrical and even unidirectional interactions. Traversing the coupling terrain leads to remarkable features in the populations of the pair, correlations and optical spectra. Most notably, the famous Mollow triplet spectrum for a single atom may be superseded for a pair by a Mollow quintuplet (or even by a spectral singlet) and the setup allows for population trapping to arise, all depending upon the precise nature of the coupling between the two-level systems.

quant-ph↗

arXiv2022

Directionality between driven-dissipative resonators

The notion of nonreciprocity, in essence when going forwards is different from going backwards, emerges in all branches of physics from cosmology to electromagnetism. Intriguingly, the breakdown of reciprocity is typically associated with extraordinary phenomena, which may be readily capitalized on in the design of (for example) nontrivial electromagnetic devices when Lorentz reciprocity is broken. However, in order to enable the exploitation of nonreciprocal-like effects in the next generation of quantum technologies, basic quantum optical theories are required. Here we present a versatile model describing a pair of driven-dissipative quantum resonators, where the relative phase difference between the coherent and incoherent couplings induces an asymmetry. The interplay between the diverse dissipative landscape - which encompasses both intrinsic losses and dissipative couplings - and the coherent interactions leads to some remarkable consequences including highly directional (or even one-way) energy transport. Our work proffers the tantalizing prospect of observing dissipation-induced quantum directionality in areas like photonics or cavity magnonics (spin waves), which may aid the design of unconventional nanoscopic devices.

quant-ph↗

arXiv2022

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 twolevel 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.

quant-ph↗

arXiv2021

Exceptional points in oligomer chains

Symmetry underpins our understanding of physical law. Open systems, those in contact with their environment, can provide a platform to explore parity-time symmetry. While classical parity-time symmetric systems have received a lot of attention, especially because of the associated advances in the generation and control of light, there is much more to be discovered about their quantum counterparts. Here we provide a quantum theory which describes the non-Hermitian physics of chains of coupled modes, which has applications across optics and photonics. We elucidate the origin of the exceptional points which govern the parity-time symmetry, survey their signatures in quantum transport, study their influence for correlations, and account for long-range interactions. We also find how the locations of the exceptional points evolve as a function of the chain length and chain parity, capturing how an arbitrary oligomer chain transitions from its unbroken to broken symmetric phase. Our general results provide perspectives for the experimental detection of parity-time symmetric phases in one-dimensional arrays of quantum objects, with consequences for light transport and its degree of coherence.

cond-mat.mes-hall↗

arXiv2021

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 nontrivial accumulated phases, the population dynamics and the steady states display remarkable nonreciprocal behavior 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.14 pages

cond-mat.mes-hall↗

arXiv2021

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 and optical lattices, and provide perspectives for topological many-body physics.

cond-mat.mes-hall↗

arXiv2020

Polaritonic Tamm states induced by cavity photons

We consider a periodic chain of oscillating dipoles, interacting via long-range dipole-dipole interactions, embedded inside a cuboid cavity waveguide. We show that the mixing between the dipolar excitations and cavity photons into polaritons can lead to the appearance of new states localized at the ends of the dipolar chain, which are reminiscent of Tamm surface states found in electronic systems. A crucial requirement for the formation of polaritonic Tamm states is that the cavity cross-section is above a critical size. Above this threshold, the degree of localization of the Tamm states is highly dependent on the cavity size, since their participation ratio scales linearly with the cavity cross-sectional area. Our findings may be important for quantum confinement effects in one-dimensional systems with strong light-matter coupling.

physics.optics↗