arXiv subjects

Adam Stokes

Publications and source records attributed to Adam Stokes.

At least 19 recordsLinked to original sources

arXiv2026

Regularised Arbitrary Gauge non-Relativistic QED

We develop a regularised arbitrary-gauge formulation of nonrelativistic quantum electrodynamics and use it to compare Coulomb and multipolar descriptions with a Lorentzian form factor. We analyse the effect of regularisation in perturbation theory, including alternative partitions of the Hamiltonian into free and interaction parts, and the limits of the electric dipole approximation. The regularised multipolar gauge exhibits a cut-off-dependent trade-off between the strength of individual interaction terms and the localisation of material subsystems that suppresses direct inter-atomic interactions. We discuss the implications of the framework for short-range phenomena, including Dicke criticality.

quant-ph↗

arXiv2026

The role of polarization field terms in a model for a cavity quantum material

Constructing models for cavity quantum materials requires a careful treatment of the light-matter coupling. In general, one must specify matrix elements constructed from the material wavefunctions, which are often unknown in a tight-binding framework. The Peierls substitution is frequently used to avoid introducing these additional parameters in the multi-center dipole (or Peierls) gauge, under the assumption that contributions from intraband and interband dipole moments can be neglected. We present the derivation of the Peierls gauge description, including these dipole moment terms, in the passive view of canonical transformations. We construct a toy model for a multi-band system with two sites, which we couple to a uniform field in the Coulomb, dipole, and Peierls gauges. We find that all polarization field terms are required to describe multi-band coupling in the Peierls gauge. The Peierls substitution can only be justified under restriction to a single band in one dimension, provided one also ignores self-polarization corrections arising from bands outside the retained subspace. However, these corrections are frequently non-negligible. More generally, the Coulomb, dipole, and Peierls gauges define distinct partitions of the composite system into the light and matter subsystems. We illustrate the implications of this subsystem relativity for observables such as the photon number and on the performance of orbital truncations in each gauge.

cond-mat.mes-hall↗

arXiv2026

Dicke Superradiance in Extended 2D Quantum Arrays Coupled to Metasurface Bound States in the Continuum

Dicke superradiance is a collective phenomenon where the emission from ensembles of quantum emitters is coherently enhanced beyond the sum of each emitter's independent emission. Here, we propose a platform that exploits the delocalised nature of a high-Q, non-local mode supported by a dielectric metasurface (a so-called bound-state-in-the-continuum or BIC) to induce superradiant behaviour within an extended two-dimensional array of distant quantum emitters. We show that these BIC-mediated emitter interactions can span several wavelengths, thus overcoming the traditional subwavelength separation between emitters required in free space. We further show that reaching the idealised Dicke limit is possible in this system, provided that the emitters are coupled to the BIC mode efficiently enough, as quantified through the $\beta$-factor. Moreover, we demonstrate its experimental viability by analysing its robustness to realistic experimental imperfections. This work puts forward optical metasurfaces supporting BICs as a physically viable platform for realising the upper limits of cooperative emission in physically extended quantum emitter arrays.

quant-ph↗

arXiv2026

Sampling methods to describe superradiance in large ensembles of quantum emitters

Superradiance is a quantum phenomenon in which coherence between emitters results in enhanced and directional radiative emission. Many quantum optical phenomena can be characterized by the two-time quantum correlation function $g^{(2)}(t,\tau)$, which describes the photon statistics of emitted radiation. However, the critical task of determining $g^{(2)}(t,\tau)$ becomes intractable for large emitter ensembles due to the exponential scaling of the Hilbert space dimension with the number of emitters. Here, we analyse and benchmark two approximate numerical sampling methods applicable to emitter arrays embedded within electromagnetic environments, which generally provide upper and lower bounds for $g^{(2)}(t,0)$. We also introduce corrections to these methods (termed offset corrections) that significantly improve the quality of the predictions. The optimal choice of method depends on the total number of emitters, such that taken together, the two approaches provide accurate descriptions across a broad range of important regimes. This work therefore provides new theoretical tools for studying the well-known yet complex phenomenon of superradiance in large ensembles of quantum emitters.

quant-ph↗

arXiv2025

Long-range quantum emitter interactions mediated by a non-local metasurface: Application to qubit-qubit entanglement

Scalable quantum technologies demand long-range interactions between many distant quantum emitters (QEs). We introduce non-local metasurfaces supporting bound-states-in-the-continuum (BICs) as a promising platform to achieve this goal. We show that efficient QE interactions depend almost entirely on emitter-BIC coupling efficiencies ($\beta$-factors), which in our system can exceed $80\%$ even without additional mode engineering. These values rival those of 1D waveguides but are achieved here in a geometry that naturally accommodates large 2D QE arrays. Using this platform, we explore entanglement generation between two remote QEs, finding that it develops faster than in free space, is significantly amplified, and persists over separations spanning several emission wavelengths. Optimal inter-QE interactions require large $\beta$-factors but only moderately small Purcell factors, both within experimentally achievable ranges. Our results establish non-local metasurfaces as a practical and scalable platform for leading-edge quantum nanophotonics.

quant-ph↗

arXiv2025

Arbitrary gauge quantisation of light-matter theories with time-dependent constraints

We provide a general framework for the quantisation of light-matter theories with time-dependent holonomic constraints. Unless time dependence is present from the outset at the Lagrangian level, different gauges generally produce non-equivalent canonical theories. The irrotational gauge is defined as that which also yields a correct theory when time dependence is introduced at the Hamiltonian level. Our framework unifies examples of such gauges found in existing literature. In particular, we show that for describing time-dependent light-matter interactions the Coulomb gauge is not generally irrotational, so it does not enjoy any special status.

quant-ph↗

arXiv2025

Cauchy-Schwarz bound on the accuracy of truncated models in non-relativistic quantum electrodynamics

We show that the Cauchy-Schwarz inequality provides a simple yet general bound that limits the accuracy of light-matter theories which retain only finite numbers of material energy levels. A corollary is that unitary rotations within a truncated space cannot transform between gauges, because the contrary assumption yields incorrect predictions. In particular, a widespread model obtained using such a rotation and treated as a Coulomb gauge model within a substantial body of literature, yields incorrect predictions under this assumption. The simplest system of a single dipole coupled to a single photonic mode in one spatial dimension is analysed in detail.

quant-ph↗

arXiv2024

Guidelines for Correlative Imaging and Analysis of Reactive Lithium Metal Battery Materials

To unlock the full potential of lithium metal batteries, a deep understanding of lithium metal reactivity and its solid electrolyte interphase is essential. Correlative imaging, combining focused ion beam and electron microscopy offers a powerful approach for multi-scale characterization. However, the extreme reactivity of lithium metal and its SEI presents challenges in investigating deposition and stripping mechanisms. In this work, we systematically evaluated the storage stability of lithium metal in glovebox before and after electrochemical deposition. We then assessed different FIB ion sources for their impact on lithium metal lamella preparation for transmission electron microscopy. Furthermore, we examined cryogenic-TEM transfer methods, optimizing for minimal contamination during sample handling. Contrary to prior assumptions, we demonstrate that high resolution imaging of pure lithium metal at room temperature is achievable using inert gas transfer with an electron dose rate exceeding 1000 e/A2/s, without significant detectable damage. In contrast, SEI components, such as Li2CO3 and LiF display much greater sensitivity to electron beams, requiring cryogenic conditions and precise dose control for nano/atomic scale imaging. We quantified electron dose limits for these SEI components to track their structural evolution under irradiation. Based on these findings, we propose a robust protocol for lithium metal sample handling - from storage to atomic-level characterization - minimizing damage and contamination. This work paves the way for more accurate and reproducible studies, accelerating the development of next-generation lithium metal batteries by ensuing the preservation of native material properties during analysis.

cond-mat.mtrl-sci↗

arXiv2023

The gauge-relativity of quantum light, matter, and information

We describe the physical relativity of light and matter quantum subsystems, their correlations, and energy exchanges. We examine the most commonly adopted definitions of atoms and photons, noting the significant difference in their localisation properties when expressed in terms of primitive manifestly gauge-invariant and local fields. As a result, different behaviours for entanglement generation and energy exchange occur for different definitions. We explore such differences in detail using toy models of a single photonic mode interacting with one and two dipoles.

quant-ph↗

arXiv2022

Theory of photon condensation in an arbitrary gauge condensed matter cavity model

We derive an arbitrary-gauge criterion under which condensed matter within an electromagnetic field may transition to a photon condensed phase. Previous results are recovered by selecting the Coulomb-gauge wherein photon condensation can only occur for a spatially-varying field and can be interpreted as a magnetic instability. We demonstrate the gauge-invariance of our description directly, but since matter and photons are gauge-relative concepts we find more generally that photon condensation can occur within a spatially uniform field, and that the relative extent to which the instability is both magnetic and electric versus purely magnetic depends on the gauge.

quant-ph↗

arXiv2021

Non-conjugate quantum subsystems

We introduce an alternative way to understand the decomposition of a quantum system into interacting parts and show that it is natural in several physical models. This enables us to define a reduced density operator for a working system interacting with a thermal bath that is consistent with the inclusion of the interaction Hamiltonian within the working system's energy. We subsequently provide a self-consistent formulation of quantum thermodynamics that incurs non-trivial physical corrections to thermodynamic relations and quantities previously defined within the literature.

quant-ph↗

arXiv2021

Identification of Poincare-gauge and multipolar nonrelativistic theories of QED

For over six decades, quantum electrodynamics (QED) in multipolar form has been an invaluable tool for understanding quantum-scale atomic and molecular interactions. However, its relation to the Poincare-gauge has been a recent topic of controversy and debate. It was claimed by Rousseau and Felbacq in the article Scientific Reports 7, 11115 (2017) that Hamiltonian multipolar QED is not the same as Poincare-gauge QED and that it is not generally equivalent to Coulomb-gauge QED. This claim has subsequently been refuted, but since both sides of the debate appear technically sound, a clear reconciliation remains to be given. This task is of paramount importance due to the widespread use of multipolar QED in quantum optics and atomic physics. Here, unlike in other responses, we adopt the same method as Rousseau and Felbacq of using Dirac's constrained quantisation procedure. However, our treatment shows that Poincare-gauge and multipolar QED are identical. We identify the precise source of the apparent incompatibility of previous results as nothing more than a semantic mismatch. In fact there are no inconsistencies. Our results firmly and rigorously solidify the multipolar theory.

quant-ph↗

arXiv2020

Implications of gauge freedom for nonrelativistic quantum electrodynamics

Gauge freedom in quantum electrodynamics (QED) outside of textbook regimes is reviewed. It is emphasized that QED subsystems are defined relative to a choice of gauge. Each definition uses different gauge-invariant observables. This relativity is eliminated only if a sufficient number of Markovian and weak-coupling approximations are employed. All physical predictions are gauge invariant, including subsystem properties such as photon number and entanglement. However, subsystem properties naturally differ for different physical subsystems. Gauge ambiguities arise not because it is unclear how to obtain gauge-invariant predictions, but because it is not always clear which physical observables are the most operationally relevant. The gauge invariance of a prediction is necessary but not sufficient to ensure its operational relevance. It is shown that, in controlling which gauge invariant observables are used to define a material system, the choice of gauge affects the balance between the material system's localization and its electromagnetic dressing. Various implications of subsystem gauge relativity for deriving effective models, for describing time-dependent interactions, for photodetection theory, and for describing matter within a cavity are reviewed.

quant-ph↗

arXiv2020

Gauge non-invariance due to material truncation in ultrastrong-coupling QED

Gauge non-invariance due to material truncation has recently been explored in a number of contexts in strong-coupling QED. We show that the approach proposed recently in Nature Physics 15, 803 (2019) rests on an incorrect mathematical assertion and so does not resolve gauge non-invariance. It produces new two-level models that are not equivalent in different gauges. The new Coulomb-gauge model is inaccurate for the regimes considered in Nature Physics 15, 803 (2019), for which the multipolar-gauge quantum Rabi model is accurate. The models analysed in Nature Physics 15, 803 (2019) do not result from the argument provided in the main text, but instead from truncation within the multipolar-gauge followed by the application of a truncated phase-invariance principle. More generally, this principle can be applied following truncation in any gauge and it yields an equivalence class of truncated models within the gauge chosen. Equivalence classes belonging to different gauges are not equivalent and the truncated phase-invariance principle does not provide an argument to prefer a particular class. In general, the optimal class depends on the physical situation, including the observables, the parameter regime, and the number of field modes being considered. We also emphasise that gauge-ambiguities are not synonymous with gauge non-invariance due to approximations. Independent of material truncation subsystem predictions can be vastly different depending on the theoretical definitions of the subsystems, which are controlled by the gauge choice. This constitutes an example of vector-space relativity that in no way contradicts gauge-invariance. However, within ultrastrong-coupling regimes this relativity can no longer be ignored.

quant-ph↗

arXiv2019

Uniqueness of the Phase Transition in Many-Dipole Cavity Quantum Electrodynamical Systems

The possibility of a superradiant phase transition in light-matter systems is the subject of much debate, due to numerous apparently conflicting no-go and counter no-go theorems. Using an arbitrary gauge approach we show that a unique phase transition does occur in archetypal many-dipole cavity QED systems, and that it manifests unambiguously via a macroscopic gauge-invariant polarisation. We find that the gauge choice controls the extent to which this polarisation is included as part of the radiative quantum subsystem and thereby determines the degree to which the abnormal phase is classed as superradiant. This resolves the long-standing paradox of no-go and counter no-go theorems for superradiance, which are shown to refer to different definitions of radiation.

quant-ph↗

arXiv2019

Ultrastrong time-dependent light-matter interactions are gauge-relative

Time-dependent light-matter interactions are a widespread means by which to describe controllable experimental operations. They can be viewed as an approximation in which a third system - the control system - is treated as external within the Hamiltonian. We demonstrate that this results in non-equivalence between gauges. We provide a physical example in which each different non-equivalent model coincides with a gauge-invariant description applied in a different experimental situation. The qualitative final-time predictions obtained from these models, including entanglement and photon number, depend on the gauge within which the time-dependent coupling assumption is made. This occurs whenever the interaction switching is sufficiently strong and non-adiabatic even if the coupling vanishes at the preparation and measurement stages of the protocol, at which times the subsystems are unique and experimentally addressable.

quant-ph↗

arXiv2018

Quantum Jump Metrology

Quantum metrology exploits quantum correlations in specially prepared entangled or other non-classical states to perform measurements that exceed the standard quantum limit. Typically though, such states are hard to engineer, particularly when larger numbers of resources are desired. As an alternative, this paper aims to establish quantum jump metrology which is based on generalised sequential measurements as a general design principle for quantum metrology and discusses how to exploit open quantum systems to obtain a quantum enhancement. By analysing a simple toy model, we illustrate that parameter-dependent quantum feedback can indeed be used to exceed the standard quantum limit without the need for complex state preparation.

quant-ph↗

arXiv2018

Gauge ambiguities imply Jaynes-Cummings physics remains valid in ultrastrong coupling QED

Ultrastrong-coupling between two-level systems and radiation is important for both fundamental and applied quantum electrodynamics (QED). Such regimes are identified by the breakdown of the rotating-wave approximation, which applied to the quantum Rabi model (QRM) yields the apparently less fundamental Jaynes-Cummings model (JCM). We show that when truncating the material system to two levels, each gauge gives a different description whose predictions vary significantly for ultrastrong-coupling. QRMs are obtained through specific gauge choices, but so too is a JCM without needing the rotating-wave approximation. Analysing a circuit QED setup, we find that this JCM provides more accurate predictions than the QRM for the ground state, and often for the first excited state as well. Thus, Jaynes-Cummings physics is not restricted to light-matter coupling below the ultrastrong limit. Among the many implications is that the system's ground state is not necessarily highly entangled, which is usually considered a hallmark of ultrastrong-coupling.

quant-ph↗