Time reversal constraint limits unidirectional photon emission in slow-light photonic crystals

Photonic crystal waveguides are known to support C-points - point-like polarisation singularities with local chirality. Such points can couple with dipole-like emitters to produce highly directional emission, from which spin-photon entanglers can be built. Much is made of the promise of using slow-light modes to enhance this light-matter coupling. Here we explore the transition from travelling to standing waves for two different photonic crystal waveguide designs. We find that time-reversal symmetry and the reciprocal nature of light places constraints on using C-points in the slow-light regime. We observe two distinctly different mechanisms through which this condition is satisfied in the two waveguides. In the waveguide designs we consider, a modest group-velocity of $v_g \approx c/10$ is found to be the optimum for slow-light coupling to the C-points.Comment: 16 pages, 4 figure

Optimised chiral light-matter interactions at polarisation singularities for quantum photonics

Photonic crystal waveguides support chiral-point polarisation singularities which give rise to local chirality even in the absence of a global chiral symmetry. Placing a quantum dot at such a C-point gives rise to a uni-directional emission dependent on the electron spin – ideal for applications in quantum information as it entangles the spin direction of electrons on the quantum dot (static qubits) to the path in the waveguide (flying qubits). Here we discuss the optimisation of this chiral light-matter interaction using slow-light waveguides, and show designs with 8.6 times enhancement of the local density of optical states at a C-point

Stabilisation of an optical transition energy via nuclear Zeno dynamics in quantum dot-cavity systems

We investigate the effect of nuclear spins on the phase shift and polarisation rotation of photons scattered off a quantum dot-cavity system. We show that as the phase shift depends strongly on the resonance energy of an electronic transition in the quantum dot, it can provide a sensitive probe of the quantum state of nuclear spins that broaden this transition energy. By including the electron-nuclear spin coupling at a Hamiltonian level within an extended input-output formalism, we show how a photon scattering event acts as a nuclear spin measurement, which when rapidly applied leads to an inhibition of the nuclear spin dynamics via the quantum Zeno effect, and a corresponding stabilisation of the optical resonance. We show how such an effect manifests in the intensity autocorrelation $g^{(2)}(\tau)$ of scattered photons, whose long-time bunching behaviour changes from quadratic decay for low photon scattering rates (weak laser intensities), to ever slower exponential decay for increasing laser intensities as optical measurements impede the nuclear spin evolution.Comment: 8 pages, 3 figure

Reflection by two level system: phase singularities on the Poincaré hypersphere

We consider the reflection of a photon by a two-level system in a quasi-one-dimensional waveguide. The waveguide polarisation at the location of the two-level system and the transition dipole are key determinants of the physics, controlling of the phase and amplitude of the scattered light in both directions. In most cases full control is possible by tuning only one of these two degrees of freedom. In reverse, this enables unique characterisation of the dipole from measurements of the scattered light. Phase singularities occur where the reflection coefficient is zero, with the (hyper-)spherical parameter space determining the dynamics of these singularities

Design principles for >90% efficiency and >99% indistinguishability broadband quantum dot cavities

Quantum dots have the potential to be the brightest deterministic single photon source with plausible high end applications in quantum computing and cluster state generation. In this work, we re-examine the design of simple micropillars by meticulously examining the structural effects of the decay into leaky channels beyond the atom-like cavity estimation. We show that precise control of the side losses with the diameter and avoidance of propagating Bloch modes in the DBR structure can result in easy to manufacture broadband (Q$\approx750-2500$) micropillars and demonstrate extremely high internal efficiency ($90.5\%-96.4\%$). We also demonstrate that such cavities naturally decouple from the phonon sideband, with the phonon sideband reducing by a factor of $5-33$ allowing us to predict that the photons should show $99.2\%-99.8\%$ indistinguishability

Stability of polarization singularities in disordered photonic crystal waveguides

The effects of short-range disorder on the polarization characteristics of light in photonic crystal waveguides were investigated using finite-difference time-domain simulations with a view to investigating the stability of polarization singularities. It was found that points of local circular polarization (C points) and contours of linear polarization (L lines) continued to appear even in the presence of high levels of disorder, and that they remained close to their positions in the ordered crystal. These results are a promising indication that devices exploiting polarization in these structures are viable given current fabrication standards

Transfer of arbitrary quantum emitter states to near-field photon superpositions in nanocavities

We present a method to analyze the suitability of particular photonic cavity designs for information exchange between arbitrary superposition states of a quantum emitter and the near-field photonic cavity mode. As an illustrative example, we consider whether quantum dot emitters embedded in "L3" and "H1" photonic crystal cavities are able to transfer a spin superposition state to a confined photonic superposition state for use in quantum information transfer. Using an established dyadic Green's function (DGF) analysis, we describe methods to calculate coupling to arbitrary quantum emitter positions and orientations using the modified local density of states (LDOS) calculated using numerical finite-difference time-domain (FDTD) simulations. We find that while superposition states are not supported in L3 cavities, the double degeneracy of the H1 cavities supports superposition states of the two orthogonal modes that may be described as states on a Poincar\'{e}-like sphere. Methods are developed to comprehensively analyze the confined superposition state generated from an arbitrary emitter position and emitter dipole orientation.Comment: 22 pages, 9 figure

Polarization engineering in photonic crystal waveguides for spin-photon entanglers

By performing a full analysis of the projected local density of states (LDOS) in a photonic crystal waveguide, we show that phase plays a crucial role in the symmetry of the light-matter interaction. By considering a quantum dot (QD) spin coupled to a photonic crystal waveguide (PCW) mode, we demonstrate that the light-matter interaction can be asymmetric, leading to unidirectional emission and a deterministic entangled photon source. Further we show that understanding the phase associated with both the LDOS and the QD spin is essential for a range of devices that that can be realised with a QD in a PCW. We also show how quantum entanglement can completely reverse photon propagation direction, and highlight a fundamental breakdown of the semiclassical dipole approximation for describing light-matter interactions in these spin dependent systems.Comment: Updated version fixes some errors. The main changes have come in the second half of the paper, with a more in depth treatment of the scattering from dipoles inside the PC