From retrodiction to Bayesian quantum imaging

We employ quantum retrodiction to develop a robust Bayesian algorithm for reconstructing the intensity values of an image from sparse photocount data, while also accounting for detector noise in the form of dark counts. This method yields not only a reconstructed image but also provides the full probability distribution function for the intensity at each pixel. We use simulated as well as real data to illustrate both the applications of the algorithm and the analysis options that are only available when the full probability distribution functions are known. These include calculating Bayesian credible regions for each pixel intensity, allowing an objective assessment of the reliability of the reconstructed image intensity values

Gamma Ray Bursts: Cosmic Rulers for the High-Redshift Universe?

The desire to extend the Hubble Diagram to higher redshifts than the range of current Type Ia Supernovae observations has prompted investigation into spectral correlations in Gamma Ray Bursts, in the hope that standard candle-like properties can be identified. In this paper we discuss the potential of these new `cosmic rulers' and highlight their limitations by investigating the constraints that current data can place on an alternative Cosmological model in the form of Conformal Gravity. By fitting current Type 1a Supernovae and Gamma Ray Burst (GRB) data to the predicted luminosity distance redshift relation of both the standard Concordance Model and Conformal Gravity, we show that currently \emph{neither} model is strongly favoured at high redshift. The scatter in the current GRB data testifies to the further work required if GRBs are to cement their place as effective probes of the cosmological distance scale.Comment: 2 pages, 1 figure (black & white, colour available). To be published in "Phil. Trans. of the Royal Society" as proceedings from Discussion Meeting on Gamma Ray Burst

Optical angular momentum in a rotating frame

It is well established that light carrying orbital angular momentum (OAM) can be used to induce a mechanical torque causing an object to spin. We consider the complementary scenario: will an observer spinning relative to the beam axis measure a change in OAM as a result of their rotational velocity? Remarkably, although a linear Doppler shift changes the linear momentum of a photon, the angular Doppler shift induces no change in the angular momentum. Further, we examine the rotational Doppler shift in frequency imparted to the incident light due to the relative motion of the beam with respect to the observer and consider what must happen to the measured wavelength if the speed of light c is to remain constant. We show specifically that the OAM of the incident beam is not affected by the rotating observer and that the measured wavelength is shifted by a factor equal and opposite to that of the frequency shift induced by the rotational Doppler effect

Detection of a spinning object using light's orbital angular momentum

The linear Doppler shift is widely used to infer the velocity of approaching objects, but this shift does not detect rotation. By analyzing the orbital angular momentum of the light scattered from a spinning object, we observed a frequency shift proportional to product of the rotation frequency of the object and the orbital angular momentum of the light. This rotational frequency shift was still present when the angular momentum vector was parallel to the observation direction. The multiplicative enhancement of the frequency shift may have applications for the remote detection of rotating bodies in both terrestrial and astronomical settings

Investigating the properties of gamma ray bursts and gravitational wave standard sirens as high redshift distance indicators

In a discipline commonly faulted for ad hoc assumptions and models with very little discriminating observational evidence, cosmologists are continually trying, and in many cases succeeding, to improve both the data and models. However, the desire to support currently favoured models often dominates research and may lead to a systematic bias being introduced in favour of a model before a strong body of supporting evidence has been accumulated. This is perhaps most evident in literature supporting the viability of Gamma Ray Bursts as cosmological distance indicators, where aside from subjective data-selection, the basic statistical methods are at best questionable and at worst incorrect. To this end, we construct a simple cosmology-independent illustration of the effect that the application of these methods has on parameter estimation and discuss the correct method to apply to current data. We also investigate the constraints potential future Gamma Ray Burst data may place on alternatives to the status quo Concordance Model in the shape of Conformal Gravity and Unified Dark Matter through a widely applicable and transferable Bayesian model comparison technique and the development of a representative mock data set. Finally, we investigate gravitational wave standard sirens as an alternative high-redshift distance indicator. We first illustrate their strong diagnostic potential through a Bayesian model comparison between the standard Unified Dark Matter model and a variant in which the dark component is redshift dependent. By drawing mock data from a known cosmological model, thus fixing the expected values of the model parameters, we find that while 182 Type 1a Supernovae are readily confused between constant and evolving models, just 2 standard sirens are able to successfully identify the correct model. Having established standard sirens as an effective tool in cosmological model comparison, we then address the potential confusion of models with dynamical dark energy and intrinsic curvature. We show that currently used distance indicators - Type 1a Supernovae, Baryon Acoustic Oscillations and the Cosmic Microwave Background Radiation - are not reliable enough to identify a small amount of intrinsic curvature, which partly justifies the common practice of assuming flat space in order to reduce the number of free parameters. However, we show that the addition of even a small number of standard sirens greatly reduces this problem. The addition of just two sirens offers a slight improvement, while adding ten sirens to the aforementioned list of indicators halves the range over which there is uncertainty between models

The azimuthal component of Poynting's vector and the angular momentum of light

The usual description in basic electromagnetic theory of the linear and angular momenta of light is centred upon the identification of Poynting's vector as the linear momentum density and its cross product with position, or azimuthal component, as the angular momentum density. This seemingly reasonable approach brings with it peculiarities, however, in particular with regards to the separation of angular momentum into orbital and spin contributions, which has sometimes been regarded as contrived. In the present paper, we observe that densities are not unique, which leads us to ask whether the usual description is, in fact, the most natural choice. To answer this, we adopt a fundamental rather than heuristic approach by first identifying appropriate symmetries of Maxwell's equations and subsequently applying Noether's theorem to obtain associated conservation laws. We do not arrive at the usual description. Rather, an equally acceptable one in which the relationship between linear and angular momenta is nevertheless more subtle and in which orbital and spin contributions emerge separately and with transparent forms

On lines of constant polarisation in structured light beams

We show that Skyrmion field lines, constructed from the local Stokes parameters, trace out lines of constant optical polarisation

Rotational Doppler velocimetry to probe the angular velocity of spinning microparticles

Laser Doppler velocimetry is a technique used to measure linear velocity, ranging from that of exhaust gases to blood flow. A rotational analog of laser Doppler velocimetry was recently demonstrated, using a rotationally symmetric interference pattern to probe the angular velocity of a spinning object. In this work, we demonstrate the use of a diffraction-limited structured illumination pattern to measure the angular velocity of a micron-sized particle trapped and spinning at tens of Hz in an optical trap. The technique requires no detailed knowledge of the shape of the particle, or the distribution of scatterers within it, and is independent of the particle's chirality, transparency, and birefringence. The particle is also subjected to Brownian motion, which complicates the signal by affecting the rotation rate and the rotation axis. By careful consideration of these influences, we show how the measurement is robust to both, representing a technique with which to probe the rotational motion of microscale particles

Paraxial Skyrmionic beams

Vector vortex beams possess a topological property that derives both from the spatially varying amplitude of the field and also from its varying polarization. This property arises as a consequence of the inherent Skyrmionic nature of such beams and is quantified by the associated Skyrmion number, which embodies a topological property of the beam. We illustrate this idea for some of the simplest vector beams and discuss the physical significance of the Skyrmion number in this context.Comment: 6 pages, 6 figure

Trajectory-Based Unveiling of Angular Momentum of Photons

The Heisenberg uncertainty principle suggests that it is impossible to determine the trajectory of a quantum particle in the same way as a classical particle. However, we may still yield insight into novel behavior of photons based on the average photon trajectories (APTs). Here we explore the APTs of photons carrying spin angular momentum (SAM) and/or orbital angular momentum (OAM) under the paraxial condition. We define the helicity and differential helicity for unveiling the three-dimensional spiral structures of the APTs of photons. We clarify the novel behaviors of the APTs caused by the SAM and OAM as well as the SAM-OAM coupling. The APT concept is very helpful for profoundly understanding the motion of trapped particles and for elucidating other physical systems. Due to the presence of the helical path caused by the SAM and/or the OAM, the actual traveling distance of the photons might be much longer than the geometric distance