Sonic hedgehog (Shh) is a morphogen active during vertebrate development and tissue homeostasis in adulthood. Dysregulation of the Shh signalling pathway is known to incite carcinogenesis. Due to the highly lipophilic nature of this protein imparted by two post-translational modifications, Shh's method of transit through the aqueous extracellular milieu has been a long-standing conundrum, prompting the proposition of numerous hypotheses to explain the manner of its displacement from the surface of the producing cell. Detection of high molecular-weight complexes of Shh in the intercellular environment has indicated that the protein achieves this by accumulating into multimeric structures prior to release from producing cells. The mechanism of assembly of the multimers, however, has hitherto remained mysterious and contentious. Here, with the aid of high-resolution optical imaging and post-translational modification mutants of Shh, we show that the C-terminal cholesterol and the N-terminal palmitate adducts contribute to the assembly of large multimers and regulate their shape. Moreover, we show that small Shh multimers are produced in the absence of any lipid modifications. Based on an assessment of the distribution of various dimensional characteristics of individual Shh clusters, in parallel with deductions about the kinetics of release of the protein from the producing cells, we conclude that multimerization is driven by self-assembly underpinned by the law of mass action. We speculate that the lipid modifications augment the size of the multimolecular complexes through prolonging their association with the exoplasmic membrane.

We employ a quantum master equations approach based on a vectorial Maxwell-pseudospin model to compute the quantum evolution of the spin populations and coherences in the fundamental singlet trion transition of a negatively charged quantum dot embedded in a micropillar cavity. Excitation of the system is achieved through an ultrashort, either circularly or linearly polarised resonant pulse. By implementing a realistic micropillar cavity geometry, we numerically demonstrate a giant optical phase shift (∼ ±π/2) of a resonant circularly polarised pulse in the weak-coupling regime. The phase shift that we predict considerably exceeds the experimentally observed Kerr rotation angle (∼ 6 • ) under a continuous-wave, linearly polarised excitation. By contrast, we show that a linearly polarised pulse is rotated to a much lesser extent of a few degrees. Depending on the initial boundary conditions, this is due to either retardation or advancement in the amplitude build-up in time of the orthogonal electric field component. Unlike previous published work, the dominant spin relaxation and decoherence processes are fully accounted for in the system dynamics. Our dynamical model can be used for optimisation of the optical polarisation rotation angle for realisation of spin-photon entanglement and ultrafast polarisation switching on a chip.

We have developed a model of the nonlinear polariton dynamics in realistic 3D non-planar microcavity wires in the driven-dissipative regime. We find that the typical microcavity optical bistability evolves into multistability upon variation of the model parameters. The origin of the multistability is discussed in detail. We apply linear perturbation analysis to modulational instabilities, and identify conditions for localisation of composite multi-mode polariton solitons in the triggered parametric oscillator regime. Further, we demonstrate stable polariton soliton propagation in tilted and tapered waveguides, and determine maximum tilt angles for which solitons still exist. Additionally, we study soliton amplitude and velocity dependence on the wire width, with a view to engineering quantum photonic devices.PACS numbers: I. INTRODUCTIONSemiconductor quantum-well (QW) microcavities are 1D photonic crystal structures, specifically designed to control light-matter interactions. The strong coupling cavity-emitter regime of operation is realised when the QW exciton-cavity photon interaction exceeds any dissipative rates in the system. The eigenmodes of the system are mixed, entangled light-matter states that can be viewed as photons 'dressed' with the medium polarisation (exciton); these give rise to bosonic quasiparticles known as microcavity exciton-polaritons. Owing to their photon component, exciton polaritons are extremely light particles. As a result of their excitonic component, however, they exhibit strong repulsive inter-particle interactions, leading to strong nonlinearities nearly four orders of magnitude higher than in typical nonlinear solid-state optical media 1 . The nonlinearities arise primarily from parametric scattering of exciton-polaritons, driven by a Coulomb exchange interaction between polariton-excitonic constituents, with additional, smaller contributions originating from phase space filling 2-4 .Nonlinear self-localisation and coherent propagation phenomena with exciton polaritons in planar microcavities have been extensively studied in recent years. Formation of moving 2D self-localised, non-equilibrium polariton droplets travelling without loss at high speeds (∼ 1% of the speed of light) has been experimentally demonstrated in coherently pumped semiconductor microcavities operating in the strong-coupling regime 5 . These polaritons display collective dynamics consistent with superfluidity. When studying polariton flow around a defect, it has been demonstrated that at high flow velocities, the perturbation induced by the defect gives rise to the turbulent emission of quantised vortices, and to the nucleation of oblique, dark 'quantum hydrodynamic' solitons 6 . Accurate tracking in space and time of long-life (100 − 200 ps) polaritons reveals long-range ballistic propagation and coherent flow over macroscopic distances -from hundreds of µm to millimetres within the cavity 7-9 .It is well known that a high-density and low-temperature gas of microcavity polaritons exhibits effects pertinent t...

We investigate cavity-assisted Stimulated Raman Adiabatic passage (STIRAP) schemes in semiconductor quantum dots (QDs) embedded in an optical cavity as a route for generation of high-quality single photons with programmable waveform. This work addresses the need for high-purity, indistinguishable photons in linear quantum computing, boson sampling, and quantum communications. We develop a time-dependent Maxwellpseudospin model of single-photon generation through cavity-assisted adiabatic passage in a Λ-system isolated in a neutral InAs QD in a realistic GaAs/AlGaAs micropillar cavity. As a model Λ-system, we consider QD biexciton triplet states coupled to dark-exciton states by a circularly polarised pulse and a cavity field. Our simulations demonstrate control of the emitted single-photon pulse waveform by the driving pulse characteristics: shape, duration, intensity and detuning.