arXiv subjects

Stephen Hughes

Publications and source records attributed to Stephen Hughes.

At least 73 records · Page 4Linked to original sources

arXiv2021

Inverse design of broadband and lossless topological photonic crystal waveguide modes

Topological photonic crystal waveguides can create edge states that may be more robust against fabrication disorder, and can yield propagation modes below the light line. We present a fully three-dimensional method to modify state-of-the-art designs to achieve a significant bandwidth improvement for lossless propagation. Starting from an initial design with a normalized bandwidth of 7.5% (13.4 THz), the modification gives more than 100% bandwidth improvement to 16.2% (28.0 THz). This new design is obtained using automatic differentiation enabled inverse design and a guided mode expansion technique to efficiently calculate the band structure and edge state modes.

physics.optics↗

arXiv2021

Quasinormal modes and Purcell factors of coupled loss-gain resonators and index-modulated ring resonators near exceptional points

We first present a quasinormal mode (QNM) theory for coupled loss-gain resonators working near an exceptional point. Assuming linear media, which can be fully quantified using the complex pole properties of the QNMs, we show how the QNMs yield a quantitatively good model to a full dipole spontaneous emission response in Maxwell's equations at various spatial positions and frequencies (linear response). We also develop a highly accurate and intuitive QNM coupled-mode theory, which can be used to rigorously model such systems using only the QNMs of the bare resonators, where the hybrid QNMs of the complete system are automatically obtained. Near a lossy exceptional point, we analytically show how the QNMs yield a Lorentzian-like and a Lorentzian-squared-like response for the spontaneous emission lineshape, consistent with other works. However, using rigorous analytical and numerical solutions for microdisk resonators, we demonstrate that the general lineshapes are far richer than what has been previously predicted. Indeed, the classical picture of spontaneous emission can take on a wide range of positive and negative Purcell factors from the hybrid modes of the coupled loss-gain system. These negative Purcell factors are unphysical and signal a clear breakdown of the classical dipole picture of spontaneous emission in such media, though the negative local density of states is correct. We also show the rich spectral features of the Green function propagators, which can be used to model various physical observables. Second, we present a QNM approach to model index modulated ring resonators working near an exceptional point and show unusual chiral power flow from linearly polarized emitters, in agreement with recent experiments, which is quantitatively explained without invoking the interpretation of a missing dimension (the Jordan vector) and a decoupling from the cavity eigenmodes.

physics.optics↗

arXiv2021

High-resolution spectroscopy of a quantum dot driven bichromatically by two strong coherent fields

We present spectroscopic experiments and theory of a quantum dot driven bichromatically by two strong coherent lasers. In particular, we explore the regime where the drive strengths are substantial enough to merit a general non-perturbative analysis, resulting in a rich higher-order Floquet dressed-state energy structure. We show high resolution spectroscopy measurements with a variety of laser detunings performed on a single InGaAs quantum dot, with the resulting features well explained with a time-dependent quantum master equation and Floquet analysis. Notably, driving the quantum dot resonance and one of the subsequent Mollow triplet sidepeaks, we observe the disappearance and subsequent reappearance of the central transition and transition resonant with detuned-laser at high detuned-laser pump strengths and additional higher-order effects, e.g. emission triplets at higher harmonics and signatures of higher order Floquet states. For a similar excitation condition but with an off-resonant primary laser, we observe similar spectral features but with an enhanced inherent spectral asymmetry.

quant-ph↗

arXiv2020

Space-Time Computation and Visualization of the Electromagnetic Fields and Potentials Generated by Moving Point Charges

We present a computational methodology to directly calculate and visualize the directional components of the Coulomb, radiation, and total electromagnetic fields, as well as the scalar and vector potentials, generated by moving point charges in arbitrary motion with varying speeds. Our method explicitly calculates the retarded time of the point charge along a discretized grid which is then used to determine the fields and potentials. The computational approach, implemented in Python, provides an intuitive understanding of the electromagnetic waves generated by moving point charges and can be used as a pedagogical tool for undergraduate and graduate-level electromagnetic theory courses. Our computer code, freely available for download, can also approximate complicated time-varying continuous charge and current densities, and can be used in conjunction with grid-based numerical modeling methods to solve real-world computational electromagnetics problems, such as experiments with high-energy electron sources. We simulate and discuss several interesting example applications and lab experiments including electric and magnetic dipoles, oscillating and linear accelerating point charges, synchrotron radiation, and Bremsstrahlung.

physics.comp-ph↗

arXiv2020

Modelling quantum light-matter interactions in waveguide-QED with retardation and a time-delayed feedback: matrix product states versus a space-discretized waveguide model

We present two different methods for modelling non-Markovian quantum light-matter interactions in waveguide QED systems, using matrix product states (MPSs) and a space-discretized waveguide (SDW) model. After describing the general theory and implementation of both approaches, we compare and contrast these methods directly on three topical problems of interest in waveguide-QED, including (i) a two-level system (TLS) coupled to an infinite (one-dimensional) waveguide, (ii) a TLS coupled to a terminated waveguide with a time-delayed coherent feedback, and (iii) two spatially separated TLSs coupled within an infinite waveguide. Both approaches are shown to efficiently model multi-photon nonlinear dynamics in highly non-Markovian regimes, and we highlight the advantages and disadvantages of these methods for modelling waveguide QED interactions, including their implementation in Python, computational run times, and ease of conceptual understanding. We explore both vacuum dynamics as well as regimes of strong optical pumping, where a weak excitation approximation cannot be applied. The MPS approach scales better when modelling multi-photon dynamics and long delay times, and explicitly includes non-Markovian memory effects. In contrast, the SDW model accounts for non-Markovian effects through space discretization, and solves Markovian equations of motion, yet rigorously includes the effects of retardation. The SDW model, based on an extension of recent collisional pictures in quantum optics, is solved through quantum trajectory techniques, and can more easily add in additional dissipation processes, including off-chip decay and TLS pure dephasing. The impact of these processes is shown directly on feedback-induced population trapping and TLS entanglement between spatially separated TLSs.

quant-ph↗

arXiv2020

Quasinormal mode theory of elastic Purcell factors and Fano resonances of optomechanical beams

We introduce a quasinormal mode theory of mechanical open-cavity modes for optomechanical resonators, and demonstrate the importance of using a generalized (complex) effective mode volume and the phase of the quasinormal mode. We first generalize and fix the normal mode theories of the elastic Purcell factor, and then show a striking example of coupled quasinormal modes yielding a pronounced Fano resonance. Our theory is exemplified and confirmed by full three-dimensional calculations on optomechanical beams, but the general findings apply to a wide range of mechanical cavity modes. This quasinormal mechanical mode formalism, when also coupled with a quasinormal theory of optical cavities, offers a unified framework for describing a wide range of optomechanical structures where dissipation is an inherent part of the resonator modes.

physics.optics↗

arXiv2020

Theory of intrinsic propagation losses in topological edge states of planar photonic crystals

Using a semi-analytic guided-mode expansion technique, we present theory and analysis of intrinsic propagation losses for topological photonic crystal slab waveguide structures with modified honeycomb lattices of circular or triangular holes. Although conventional photonic crystal waveguide structures, such as the W1 waveguide, have been designed to have lossless propagation modes, they are prone to disorder-induced losses and backscattering. Topological structures have been proposed to help mitigate this effect as their photonic edge states may allow for topological protection. However, the intrinsic propagation losses of these structures are not well understood and the concept of the light line can become blurred. For four example topological edge state structures, photonic band diagrams, loss parameters, and electromagnetic fields of the guided modes are computed. Two of these structures, based on armchair edge states, are found to have significant intrinsic losses for modes inside the photonic band gap, more than 100 dB/cm, which is comparable to or larger than typical disorder-induced losses using slow-light modes in conventional photonic crystal waveguides, while the other two structures, using the valley Hall effect and inversion symmetry, are found to have a good bandwidth for exploiting lossless propagation modes below the light line.

physics.optics↗

arXiv2020

Quantized quasinormal mode description of non-linear cavity QED effects from coupled resonators with a Fano-like resonance

We employ a recently developed quantization scheme for quasinormal modes (QNMs) to study a nonperturbative open cavity-QED system consisting of a hybrid metal-dielectric resonator coupled to a quantum emitter. This hybrid cavity system allows one to explore the complex coupling between a low $Q$ (quality factor) resonance and a high $Q$ resonance, manifesting in a striking Fano resonance, an effect that is not captured by traditional quantization schemes using normal modes or a Jaynes-Cummings (JC) type model. The QNM quantization approach rigorously includes dissipative coupling between the QNMs, and is supplemented with generalized input-output relations for the output electric field operator for multiple modes in the system, and correlation functions outside the system. The role of the dissipation-induced mode coupling is explored in the strong coupling regime between the photons and emitter beyond the first rung of the JC dressed-state ladder. Important differences in the quantum master equation and input-output relations between the QNM quantum model and phenomenological dissipative JC models are found. In a second step, numerical results for the Fock distributions and system as well as output correlation functions obtained from the quantized QNM model for the hybrid structure are compared with results from a phenomenological approach. We demonstrate explicitly how the quantized QNM model manifests in multiphoton quantum correlations beyond what is predicted by the usual JC models.

cond-mat.mes-hall↗

arXiv2020

Fluctuation-dissipation theorem and fundamental photon commutation relations in lossy nanostructures using quasinormal modes

We provide theory and formal insight on the Green function quantization method for absorptive and dispersive spatial-inhomogeneous media in the context of dielectric media. We show that a fundamental Green function identity, which appears, e.g., in the fundamental commutation relation of the electromagnetic fields, is also valid in the limit of non-absorbing media. We also demonstrate how the zero-point field fluctuations yields a non-vanishing surface term in configurations without absorption, when using a more formal procedure of the Green function quantization method. We then apply the presented method to a recently developed theory of photon quantization using quasinormal modes [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)] for finite nanostructures embedded in a lossless background medium. We discuss the strict dielectric limit of the commutation relations of the quasinormal mode operators and present different methods to obtain them, connected to the radiative loss for non-absorptive but open resonators. We show exemplary calculations of a fully three-dimensional photonic crystal beam cavity, including the lossless limit, which supports a single quasinormal mode and discuss the limits of the commutation relation for vanishing damping (no material loss and no radiative loss).

cond-mat.mes-hall↗

arXiv2020

Gauge Principle and Gauge Invariance in Quantum Two-Level Systems

The quantum Rabi model is a widespread description for the coupling between a two-level system and a quantized single mode of an electromagnetic resonator. Issues about this model's gauge invariance have been raised. These issues become evident when the light-matter interaction reaches the so-called ultrastrong coupling regime. Recently, a modified quantum Rabi model able to provide gauge-invariant physical results in any interaction regime was introduced [Nature Physics 15, 803 (2019)]. Here we provide an alternative derivation of this result, based on the implementation in two-state systems of the gauge principle, which is the principle from which all the fundamental interactions in quantum field theory are derived. The adopted procedure can be regarded as the two-site version of the general method used to implement the gauge principle in lattice gauge theories. Applying this method, we also obtain the gauge-invariant quantum Rabi model for asymmetric two-state systems, and the multi-mode gauge-invariant quantum Rabi model beyond the dipole approximation.

quant-ph↗

arXiv2020

Screening of the quantum dot Förster coupling at small distances

We study the near-field energy transfer rates between two finite size quantum dot disks, generalizing the result of Förster coupling between two point dipoles. In particular, we derive analytical results for the envelope of the electronic wavefunction for model potentials at the boundaries of quantum dot disks and demonstrate how the Förster interaction is screened as the size of the dots becomes comparable to the dot-dot separation.

physics.optics↗

arXiv2020

Gauge freedom, quantum measurements, and time-dependent interactions in cavity and circuit QED

The interaction between the electromagnetic field inside a cavity and natural or artificial atoms has played a crucial role in developing our understanding of light-matter interaction, and is central to various quantum technologies. Recently, new regimes beyond the weak and strong light-matter coupling have been explored in several settings. These regimes, where the interaction strength is comparable (ultrastrong) or even higher (deep-strong) than the transition frequencies in the system, can give rise to new physical effects and applications. At the same time, they challenge our understanding of cavity QED. When the interaction strength is so high, fundamental issues like the proper definition of subsystems and of their quantum measurements, the structure of light-matter ground states, or the analysis of time-dependent interactions are subject to ambiguities leading to even qualitatively distinct predictions. The resolution of these ambiguities is also important for understanding and designing next-generation quantum devices that will exploit the ultrastrong coupling regime. Here we discuss and provide solutions to these issues.

quant-ph↗

arXiv2019

Efficient near-field to far-field transformations for quasinormal modes of optical cavities and plasmonic resonators

We describe an efficient near-field to far-field transformation for optical quasinormal modes, which are the dissipative modes of open cavities and plasmonic resonators with complex eigenfrequencies. As an application of the theory, we show how one can compute the reservoir modes (or regularized quasinormal modes) outside the resonator, which are essential to use in both classical and quantum optics. We subsequently demonstrate how to efficiently compute the quantum optical parameters necessary in the theory of quantized quasinormal modes [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)]. To confirm the accuracy of our technique, we directly compare with a Dyson equation approach currently used in the literature (in regimes where this is possible), and demonstrate several order of magnitude improvement for the calculation run times. We also introduce an efficient pole approximation for computing the quantized quasinormal mode parameters, since they require an integration over a range of frequencies. Using this approach, we show how to compute regularized quasinormal modes and quantum optical parameters for a full 3D metal dimer in under one minute on a standard desktop computer. Our technique is exemplified by studying the quasinormal modes of metal dimers and a hybrid structure consisting of a gold dimer on top of a photonic crystal beam. In the latter example, we show how to compute the quantum optical parameters that describe a pronounced Fano resonance, using structural geometries that cannot practically be solved using a Dyson equation approach. All calculations for the spontaneous emission rates are confirmed with full-dipole calculations in Maxwell's equations and are shown to be in excellent agreement.

physics.optics↗

arXiv2019

Efficient Pulse-Excitation Techniques for Single Photon Sources from Quantum Dots in Cavities

We present rigorous and intuitive master equation models to study on-demand single photon sources from pulse-excited quantum dots coupled to cavities. We consider three methods of source excitation: resonant pi-pulse, off-resonant phonon-assisted inversion, and two-photon excitation of a biexciton-exciton cascade, and investigate the effect of the pulse excitation process on the quantum indistinguishability, efficiency, and purity of emitted photons. By explicitly modelling the time-dependent pulsed excitation process in a manner which captures non-Markovian effects associated with coupling to photon and phonon reservoirs, we find that photons of near-unity indistinguishability can be emitted with over 90% efficiency for all these schemes, with the off-resonant schemes not necessarily requiring polarization filtering due to the frequency separation of the excitation pulse, and allowing for very high single photon purities. Furthermore, the off-resonant methods are shown to be robust over certain parameter regimes, with less stringent requirements on the excitation pulse duration in particular. We also derive a semi-analytical simplification of our master equation for the off-resonant drive, which gives insight into the important role that exciton-phonon decoupling for a strong drive plays in the off-resonant phonon-assisted inversion process

quant-ph↗

arXiv2019

Molecular optomechanics in the anharmonic cavity-QED regime using hybrid metal-dielectric cavity modes

Using carefully designed hybrid metal-dielectric resonators, we study molecular optomechanics in the strong coupling regime ($g_{\rm }^2/ω_m {>} κ$), which manifests in anharmonic emission lines in the sideband-resolved region of the cavity-emitted spectrum ($κ{<}ω_m$). This nonlinear optomechanical strong coupling regime is enabled through a metal-dielectric cavity system that yields not only deep sub-wavelength plasmonic confinement, but also dielectric-like confinement times that are more than two orders of magnitude larger than those from typical localized plasmon modes. These hybrid metal-dielectric cavity modes enable one to study new avenues of quantum plasmonics for single molecule Raman scattering.

cond-mat.mes-hall↗

arXiv2019

Quantum trajectory theory of few photon cavity-QED systems with a time-delayed coherent feedback

We describe an efficient approach to modelling cavity quantum electrodynamics (QED) with a time-delayed coherent feedback using quantum trajectory simulations. An analytical set of equations is derived to exploit the advantages of trajectories in the presence of the non-Markovian dynamics, where adjustments to the standard stochastic dynamics are discussed. In the weak excitation regime, we first verify that our approach recovers known results obtained with other simulation methods and demonstrate how a coherent feedback loop can increase the photon lifetime in typical cavity-QED systems. We then explore the nonlinear few-photon regime of cavity-QED, under the restriction of at most one photon at a time in the feedback loop. In particular, we show how feedback affects the cavity photoluminescence (populations versus laser detuning), and describe how one must account for conditioning in the presence of feedback, specifically the system observables must be conditioned on no photon detections at the feedback output channel occurring.

quant-ph↗

arXiv2019

Dissipative modes, Purcell factors and directional beta factors in gold bowtie nanoantenna structures

We present a detailed quasinormal mode analysis of gold bowtie nanoantennas, and highlight the unusual role of the substrate and the onset of multi-mode behaviour. In particular, we show and explain why the directional radiatiave beta factor is completely dominated by emission into the substrate, and explain how the beta factors and quenching depend on the underlying mode properties. We also quantitatively explain the generalized Purcell factors and explore the role of gap size and substrate in detail. These rich modal features are essential to understand for future applications such as sensing, lasing, and quantum information processing, for example in the design of efficient single photon emitters.

physics.comp-ph↗

arXiv2019

Accessing the bath information in open quantum systems with the stochastic c-number Langevin equation method

In traditional open quantum systems, the baths are usually traced out so that only the system information is left in the equations of motion. However, recent studies reveal that using only the system degrees of freedom can be insufficient. In this work, we develop a stochastic c-number Langevin equation method which can conveniently access the bath information. In our method, the studied quantities are the expectation values of operators which can contain both system operators and bath operators. The dynamics of the operators of interest is formally divided into separate system and bath parts, with auxiliary stochastic fields. After solving the independent stochastic dynamics of the system part and the bath part, we can recombine them by taking the average over these stochastic fields to obtain the desired quantities. Several applications of the theory are highlighted, including the pure dephasing model, the spin-boson model, and an optically excited quantum dot coupled to a bath of phonons.

quant-ph↗