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D. M. Whittaker

Publications and source records attributed to D. M. Whittaker.

At least 19 recordsLinked to original sources
arXiv2026

Observation of a Topological Phase Transition in Random Coaxial Cable Structures with Chiral Symmetry

We report an experimental study of the disordered Su-Schrieffer-Heeger (SSH) model, implemented in a system of coaxial cables, whose radio frequency properties map on to the SSH Hamiltonian. By measuring multiple chains with random hopping terms, we demonstrate the presence of a topologically protected state, with frequency variation of less than 0.2% over the ensemble. Connecting the ends of the chains to form loops, we observe a topological phase transition, characterised by the closure of the band gap and the appearance of states which are delocalised, despite the strong disorder.

cond-mat.dis-nn↗
arXiv2025

Sequential topology: iterative topological phase transitions in finite chiral structures

We present theoretical and experimental results probing the rich topological structure of arbitrarily disordered finite tight binding Hamiltonians with chiral symmetry. We extend the known classification by considering the topological properties of phase boundaries themselves. That is, can Hamiltonians that are confined to being topologically marginal, also have distinct topological phases? For chiral structures, we answer this in the affirmative, where we define topological phase boundaries as having an unavoidable increase in the degeneracy of real space zero modes. By iterating this question, and considering how to enforce a Hamiltonian to a phase boundary, we give a protocol to find the largest dimension subspace of a disordered parameter space that has a certain order degeneracy of zero energy states, which we call \textit{sequential topology}. We show such degeneracy alters localisation and transport properties of zero modes, allowing us to experimentally corroborate our theory using a state-of-the-art coaxial cable platform. Our theory applies to systems with an arbitrary underlying connectivity or disorder, and so can be calculated for any finite chiral structure. Technological and theoretical applications of our work are discussed.

cond-mat.mes-hall↗
arXiv2024

A Topological Classification of Finite Chiral Structures using Complete Matchings

We present the theory and experimental demonstration of a topological classification of finite tight binding Hamiltonians with chiral symmetry. Using the graph-theoretic notion of complete matchings, we show that many chiral tight binding structures can be divided into a number of sections, each of which has independent topological phases. Hence the overall classification is $N\mathbb{Z}_2$, corresponding to $2^N$ distinct phases, where $N$ is the number of sections with a non-trivial $\mathbb{Z}_2$ classification. In our classification, distinct topological phases are separated by exact closures in the energy spectrum of the Hamiltonian, with degenerate pairs of zero energy states. We show that that these zero energy states have an unusual localisation across distinct regions of the structure, determined by the manner in which the sections are connected together. We use this localisation to provide an experimental demonstration of the validity of the classification, through radio frequency measurements on a coaxial cable network which maps onto a tight binding system. The structure we investigate is a cable analogue of an ideal graphene ribbon, which divides into four sections and has a $4\mathbb{Z}_2$ topological classification.

cond-mat.mes-hall↗
arXiv2022

Engineering strong chiral light-matter interactions in a waveguide-coupled nanocavity

Spin-dependent, directional light-matter interactions form the basis of chiral quantum networks. In the solid state, quantum emitters commonly possess circularly polarised optical transitions with spin-dependent handedness. We demonstrate numerically that spin-dependent chiral coupling can be realised by embedding such an emitter in a waveguide-coupled nanocavity, which supports two near-degenerate, orthogonally-polarised cavity modes. The chiral behaviour arises due to direction-dependent interference between the cavity modes upon coupling to two single-mode output waveguides. Notably, an experimentally realistic cavity design simultaneously supports near-unity chiral contrast, efficient ($β> 0.95$) waveguide coupling and enhanced light-matter interaction strength (Purcell factor $F_P > 70$). In combination, these parameters could enable the development of highly coherent spin-photon interfaces, ready for integration into nanophotonic circuits.

physics.optics↗
arXiv2021

Topological Protection in Disordered Photonic Multilayers and Transmission Lines

The Su-Schrieffer-Heeger (SSH) model is the simplest example of a lattice with non-trivial topology. It supports mid-gap topologically protected states, whose energies are unaffected by disorder. We show that photonic multilayer structures provide an exact implementation of an SSH lattice, provided each layer has the same propagation thickness. From this, it follows that the cavity mode in a conventional semiconductor microcavity is a protected SSH mid-gap state. We demonstrate this experimentally using controlled disorder in a mathematically equivalent system, a radio frequency transmission line made from sections of coaxial cable with high and low impedances. We also show theoretically that transmission lines connected to form networks map onto topologically interesting lattices in in higher dimensions.

physics.optics↗
arXiv2018

Effect of photonic spin-orbit coupling on the topological edge modes of a Su-Schrieffer-Heeger chain

We study the effect of photonic spin-orbit coupling (SOC) in micropillar lattices on the topological edge states of a one-dimensional chain with a zigzag geometry, corresponding to the Su-Schrieffer-Heeger model equipped with an additional internal degree of freedom. The system combines the strong hopping anisotropy of the $p$-type pillar modes with the large TE-TM splitting in Bragg microcavities. By resolving the photoluminescence emission in energy and polarization we probe the effects of the resulting SOC on the spatial and spectral properties of the edge modes. We find that the edge modes feature a fine structure of states that penetrate by different amounts into the bulk of the chain, depending on the strength of the SOC terms present, thereby opening a route to manipulation of the topological states in the system.

physics.optics↗
arXiv2018

Exciton Polaritons in a Two-Dimensional Lieb Lattice with Spin-Orbit Coupling

We study exciton-polaritons in a two-dimensional Lieb lattice of micropillars. The energy spectrum of the system features two flat bands formed from $S$ and $P_{x,y}$ photonic orbitals, into which we trigger bosonic condensation under high power excitation. The symmetry of the orbital wave functions combined with photonic spin-orbit coupling gives rise to emission patterns with pseudospin texture in the flat band condensates. Our work shows the potential of polariton lattices for emulating flat band Hamiltonians with spin-orbit coupling, orbital degrees of freedom and interactions.

cond-mat.mes-hall↗
arXiv2017

Polariton pattern formation and photon statistics of the associated emission

We report on the formation of a diverse family of transverse spatial polygon patterns in a microcavity polariton fluid under coherent driving by a blue-detuned pump. Patterns emerge spontaneously as a result of energy-degenerate polariton-polariton scattering from the pump state to interfering high order vortex and antivortex modes, breaking azimuthal symmetry. The interplay between a multimode parametric instability and intrinsic optical bistability leads to a sharp spike in the value of second order coherence $g^{(2)}(0)$ of the emitted light, which we attribute to the strongly superlinear kinetics of the underlying scattering processes driving the formation of patterns. We show numerically by means of a linear stability analysis how the growth of parametric instabilities in our system can lead to spontaneous symmetry breaking, predicting the formation and competition of different pattern states in good agreement with experimental observations.

cond-mat.mes-hall↗
arXiv2016

Optical source of individual pairs of color-conjugated photons

We demonstrate that Kerr nonlinearity in optical circuits can lead to both resonant four-wave mixing and photon blockade, which can be used for high-yield generation of high-fidelity individual photon pairs with conjugated frequencies. We propose an optical circuit, which, in the optimal pulsed-drive regime, would produce photon pairs at the rate up to $10^5s^{-1}$ (0.5 pairs per pulse) with $g^{(2)}<10^{-2}$ for one of the conjugated frequencies. We show that such a scheme can be utilised to generate color-entangled photons.

quant-ph↗
arXiv2015

Spin Textures of Polariton Condensates in a Tunable Microcavity with Strong Spin-Orbit Interaction

We report an extended family of spin textures in coexisting modes of zero-dimensional polariton condensates spatially confined in tunable open microcavity structures. The coupling between photon spin and angular momentum, which is enhanced in the open cavity structures, leads to new eigenstates of the polariton condensates carrying quantised spin vortices. Depending on the strength and anisotropy of the cavity confinement potential and the strength of the spin-orbit coupling, which can be tuned via the excitonic/photonic fractions, the condensate emissions exhibit either spin-vortex-like patterns or linear polarization, in good agreement with theoretical modelling.

cond-mat.mes-hall↗
arXiv2013

Effect of Interactions on Vortices in a Non-equilibrium Polariton Condensate

We demonstrate the creation of vortices in a macroscopically occupied polariton state formed in a semiconductor microcavity. A weak external laser beam carrying orbital angular momentum (OAM) is used to imprint a vortex on the condensate arising from the polariton optical parametric oscillator (OPO). The vortex core radius is found to decrease with increasing pump power, and is determined by polariton-polariton interactions. As a result of OAM conservation in the parametric scattering process, the excitation consists of a vortex in the signal and a corresponding anti-vortex in the idler of the OPO. The experimental results are in good agreement with a theoretical model of a vortex in the polariton OPO.

physics.optics↗
arXiv2012

Dipolar broadening of nuclear spin resonance under dynamical pumping

We study the polarisation dependence of the homogeneously broadened nuclear spin resonance in a crystal. We employ a combinatorial method to restrict the nuclear states to a fixed polarisation and show that the centre of the resonance is shifted linearly with the nuclear polarisation by up to the zero polarisation line width. The width shrinks from its maximum value at zero polarisation to zero at full polarisation. This suggests to use the line shape as a direct measure of nuclear polarisation reached under dynamical pumping. In the limit of single quantum of excitation above the fully ferromagnetic state, we provide an explicit solution to the problem of nuclear spin dynamics which links a bound on the fastest decay rate to the observable width of the resonance line.

cond-mat.mes-hall↗
arXiv2012

Spatial Coherence of a polariton condensate in 1D acoustic lattice

Several mechanisms are discussed which could determine the spatial coherence of a polariton condensate confined to a one dimensional wire. The mechanisms considered are polariton-polariton interactions, disorder scattering and non-equilibrium occupation of finite momentum modes. For each case, the shape of the resulting spatial coherence function g1(x) is analysed. The results are compared with the experimental data on a polariton condensate in an acoustic lattice from [E. A. Cerda-Mendez et al, Phys. Rev. Lett. 105, 116402 (2010)]. It is concluded that the shape of g1(x) can only be explained by non-equilibrium effects, and that ~10 modes are occupied in the experimental system.

cond-mat.mes-hall↗
arXiv2011

Photon blockade and nonlinear effects for a quantum dot strongly coupled to a semiconductor microcavity

Our model comprehensively simulates modern nanoscale semiconductor microcavities incorporating cavity quantum electrodynamics within both the weak and strong coupling regimes, using on-resonant laser excitation and nonresonant excitation due to a wetting layer. For weak coupling, the most significant effect is photon antibunching with nonresonant emission. We investigate how the antibunching characteristics change as the cavity finesse is increased towards the strong coupling regime. Antibunching can also be observed in a strongly coupled system with resonant excitation, using the photon blockade mechanism which has been demonstrated in atom systems. We calculate what cavity parameters are required to observe this effect. Experimentally these studies are equivalent to nonlinear pump probe measurements, where a strong pump, either resonant or nonresonant, is used to excite the coupled system, and the resulting state is characterized using a weak, resonant probe beam.

cond-mat.mtrl-sci↗
arXiv2010

Role of incoherent substrate reflections in photonic crystal spectroscopy

A method is presented for modelling the optical properties of a photonic crystal structure mounted on a substrate which is thick enough that the light reflected from the back is incoherent with reflections from the front. Transmission and reflection spectra are presented for the cases where the structure is a multilayer planar microcavity and an opal photonic crystal. The contributions from the incoherent reflections can be very large, and in the photonic crystal case, change the positions of the spectral peaks.

physics.optics↗
arXiv2010

Spontaneous and triggered vortices in polariton OPO superfluids

We study non-equilibrium polariton superfluids in the optical parametric oscillator (OPO) regime using a two-component Gross-Pitaevskii equation with pumping and decay. We identify a regime above OPO threshold, where the system undergoes spontaneous symmetry breaking and is unstable towards vortex formation without any driving rotation. Stable vortex solutions differ from metastable ones; the latter can persist in OPO superfluids but can only be triggered externally. Both spontaneous and triggered vortices are characterised by a generalised healing length, specified by the OPO parameters only.

cond-mat.mes-hall↗
arXiv2009

Coexisting Non-Equilibrium Condensates with Long-Range Spatial Coherence in Semiconductor Microcavities

Real and momentum space spectrally resolved images of microcavity polariton emission in the regime of condensation are investigated under non resonant excitation using a laser source with reduced intensity fluctuations on the timescale of the exciton lifetime. We observe that the polariton emission consists of many macroscopically occupied modes. Lower energy modes are strongly localized by the photonic potential disorder on a scale of few microns. Higher energy modes have finite k-vectors and are delocalized over 10-15 microns. All the modes exhibit long range spatial coherence comparable to their size. We provide a theoretical model describing the behavior of the system with the results of the simulations in good agreement with the experimental observations. We show that the multimode emission of the polariton condensate is a result of its nonequilibrium character, the interaction with the local photonic potential and the reduced intensity fluctuations of the excitation laser.

cond-mat.other↗