Polarization control of single photon quantum orbital angular momentum states

The orbital angular momentum of photons, being defined in an infinitely dimensional discrete Hilbert space, offers a promising resource for high-dimensional quantum information protocols in quantum optics. The biggest obstacle to its wider use is presently represented by the limited set of tools available for its control and manipulation. Here, we introduce and test experimentally a series of simple optical schemes for the coherent transfer of quantum information from the polarization to the orbital angular momentum of single photons and vice versa. All our schemes exploit a newly developed optical device, the so-called "q-plate", which enables the manipulation of the photon orbital angular momentum driven by the polarization degree of freedom. By stacking several q-plates in a suitable sequence, one can also access to higher-order angular momentum subspaces. In particular, we demonstrate the control of the orbital angular momentum $m$ degree of freedom within the subspaces of $|m|=2 \hbar$ and $|m|=4\hbar$ per photon. Our experiments prove that these schemes are reliable, efficient and have a high fidelity.Comment: 9 pages, 8 figure

Non-rigid image registration to reduce beam-induced blurring of cryo-electron microscopy images

Microscopic imaging and technolog

Minimum Cost Homomorphisms to Locally Semicomplete and Quasi-Transitive Digraphs

For digraphs $G$ and $H$, a homomorphism of $G$ to $H$ is a mapping $f:\ V(G)\dom V(H)$such that$uv\in A(G)$implies$f(u)f(v)\in A(H)$. If, moreover, each vertex$u \in V(G)$is associated with costs$c_i(u), i \in V(H)$, then the cost of a homomorphism$f$is$\sum_{u\in V(G)}c_{f(u)}(u)$. For each fixed digraph$H$, the minimum cost homomorphism problem for$H$, denoted MinHOM($H$), can be formulated as follows: Given an input digraph$G$, together with costs$c_i(u)$,$u\in V(G)$,$i\in V(H)$, decide whether there exists a homomorphism of$G$to$H$ and, if one exists, to find one of minimum cost. Minimum cost homomorphism problems encompass (or are related to) many well studied optimization problems such as the minimum cost chromatic partition and repair analysis problems. We focus on the minimum cost homomorphism problem for locally semicomplete digraphs and quasi-transitive digraphs which are two well-known generalizations of tournaments. Using graph-theoretic characterization results for the two digraph classes, we obtain a full dichotomy classification of the complexity of minimum cost homomorphism problems for both classes

Sketch-a-park Study of the usability of diagrams for participatory sketching

Children’s view in participation currently gaining popularity (CABE Space and CABE Education, 2004) along with digital tools of participation based on design exploration currently known as Digital Participatory Platforms (DPPs) (Falco and Kleinhans, 2018), (Gün et al., 2020). Space Syntax Theory (SST) offers a well-proven human-centred analytic framework with applications for public engagement via digital twins (Dembski et al., 2019). Yet, as some authors argue (Baeck and Saunders, 2015), (Dembski et al., 2020), more needs to be done to improve the experiential side of these systems and empower citizens and children, in particular, to carry out their designs within these events using what is. We argue that using diagrammatic sketching as the basis of DPPs is particularly suited for SST since most SS models work out abstractions of urban morphology which can be drawn using simple diagrammatic sketches. However, this type of drawing may prove too abstract for participants and questions remain open regarding the usability of this type of drawings in a participatory environment. It is yet to be proven whether general members of the public, in particular young kids, can engage with diagrammatic sketches and what influence digital environments have on this engagement. To address these questions, we carried out two pilot studies with participants aged 10 to 11-year-old where we asked them to carry out drawings of urban proposals with different levels of information regarding diagrammatic drawings. Tests were repeated with different groups making paper drawings as well as using a bespoke digital tool at different stages of the drawing. We develop an analytic framework for drawings and carry out a comparative study of the material produced. Results from the experiment suggest that 10- to 11-year-old can easily understand the abstraction behind diagrammatic sketches and adopt this technique as a form of expression. We observe that this happens more markedly when using digital tools. This suggests diagrammatic sketches have the potential to be deployed as part of a SS driven participatory tool

Quantifying Spatiotemporal Chaos in Rayleigh-B\'enard Convection

Using large-scale parallel numerical simulations we explore spatiotemporal chaos in Rayleigh-B\'enard convection in a cylindrical domain with experimentally relevant boundary conditions. We use the variation of the spectrum of Lyapunov exponents and the leading order Lyapunov vector with system parameters to quantify states of high-dimensional chaos in fluid convection. We explore the relationship between the time dynamics of the spectrum of Lyapunov exponents and the pattern dynamics. For chaotic dynamics we find that all of the Lyapunov exponents are positively correlated with the leading order Lyapunov exponent and we quantify the details of their response to the dynamics of defects. The leading order Lyapunov vector is used to identify topological features of the fluid patterns that contribute significantly to the chaotic dynamics. Our results show a transition from boundary dominated dynamics to bulk dominated dynamics as the system size is increased. The spectrum of Lyapunov exponents is used to compute the variation of the fractal dimension with system parameters to quantify how the underlying high-dimensional strange attractor accommodates a range of different chaotic dynamics

DRAWSCAPES: Study of the effectiveness of online diagrammatic sketching in participatory design

The increased user-friendliness of Space Syntax (SS) packages and their improved compatibility with popular 3D modelling software has pushed the use of Space Syntax Theory (SST) into the professional realm, making it approachable, not just by dedicated researchers, but also to an increasing number of practitioners. We argue that the applicability of SST can even go further if we use sketching as a form of interaction with the software, potentially opening up its use to general members of the public as part of a wider participatory process. We present a study that tries to understand whether the diagrams required for this form of engagement are easy to produce by non-professionals and once they are produced, see whether they have an impact on the planning process. We propose an experiment using an online design tool that allows participants to make drawings of urban proposals by drafting simple diagrams, beginning with connective paths followed by urban blocks using thicker versions of the same pen tool. We develop bespoke analytic methods to extract general patterns emerging from data, identify trends across different user groups, and study user interaction, design quality and user engagement. We take the expansion of UCL East as a case study and test our tool with several participant groups from the general staff and student population as well as external design professionals. Some of these professionals carry out the exercise after reviewing the design from UCL members. We obtained 700 drawings from 400 participants and carry out comparative studies across groups. The study concludes that general members of the public can understand the type of drawing exercise requested and produce designs of an adequate standard. We can also see that planners and architects observe positively the information coming from general members of the public and are willing to incorporate it into their designs

Shining a light on Dar es Salaam - 1992 to 2020: utilizing nightlight intensity data as a tool for modelling rapid urban growth patterns

This paper utilizes remotely-sensed nightlight intensity (NLI) data to construct and evaluate a multi-temporal urban growth model for Dar es Salaam, Tanzania, between 1992 and 2020. This contributes towards the creation of effective, globally-available modelling and monitoring tools to support urban planners, policy-makers and communities in contexts of data-sparsity and rapid urban growth: a duality often found in the global south. Findings reveal that multi-temporal NLI models can offer new, systematic insights into patterns of urban growth at multiple intra-city scales. For instance, this NLI model identifies and tracks parts of the city which are likely to have experienced different patterns of spatial and/or socio-economic development between 1992 and 2020

LOCV calculations for polarized liquid 3He^3{He} with the spin-dependent correlation

We have used the lowest order constrained variational (LOCV) method to calculate some ground state properties of polarized liquid $^{3}He$ at zero temperature with the spin-dependent correlation function employing the Lennard-Jones and Aziz pair potentials. We have seen that the total energy of polarized liquid $^{3}He$ increases by increasing polarization. For all polarizations, it is shown that the total energy in the spin-dependent case is lower than the spin-independent case. We have seen that the difference between the energies of spin-dependent and spin-independent cases decreases by increasing polarization. We have shown that the main contribution of the potential energy comes from the spin-triplet state.Comment: 14 pages, 5 figures. Int. J. Mod. Phys. B (2008) in pres

Photon Self-Induced Spin to Orbital Conversion in TGG crystal at high laser power

In this paper, we present experimental evidence of a newly discovered third-order nonlinear optical process Self-Induced Spin-to-Orbital Conversion (SISTOC) of the photon angular momentum. This effect is the physical mechanism at the origin of the depolarization of very intense laser beams propagating in isotropic materials. The SISTOC process, like self-focusing, is triggered by laser heating leading to a radial temperature gradient in the medium. In this work we tested the occurrence of SISTOC in a terbium gallium garnet (TGG) rod for an impinging laser power of about 100~W. To study the SISTOC process we used different techniques: polarization analysis, interferometry and tomography of the photon orbital angular momentum. Our results confirm, in particular, that the apparent depolarization of the beam is due to the occurrence of maximal entanglement between the spin and orbital angular momentum of the photons undergoing the SISTOC process. This explanation of the true nature of the depolarization mechanism could be of some help in finding novel methods to reduce or to compensate for this usually unwanted depolarization effect in all cases where very high laser power and good beam quality are required.Comment: 6 pages, 10 figures, submitte

Transverse spectral functions and Dzyaloshinskii-Moriya interactions in XXZ spin chains

Recently much progress has been made in applying field theory methods, first developed to study X-ray edge singularities, to interacting one dimensional systems in order to include band curvature effects and study edge singularities at arbitrary momentum. Finding experimental confirmations of this theory remains an open challenge. Here we point out that spin chains with uniform Dzyaloshinskii-Moriya (DM) interactions provide an opportunity to test these theories since these interactions may be exactly eliminated by a gauge transformation which shifts the momentum. However, this requires an extension of these X-ray edge methods to the transverse spectral function of the xxz spin chain in a magnetic field, which we provide