Single-Port Homodyne Detection in a Squeezed-State Interferometry with Optimal Data Processing

Performing homodyne detection at a single output port of a squeezed-state light interferometer and then separating the measurement quadrature into several bins can realize superresolving and supersensitive phase measurements. However, the phase resolution and the achievable phase sensitivity depend on the bin size that is adopted in the data processing. By maximizing classical Fisher information, we analytically derive an optimal value of the bin size and the associated best sensitivity for the case of three bins, which can be regarded as a three-outcome measurement. Our results indicate that both the resolution and the achievable sensitivity are better than that of the previous binary–outcome case. Finally, we present an approximate maximum Likelihood estimator to asymptotically saturate the ultimate lower bound of the phase sensitivity.

Phase Resolution of Heterozygous Sites in Diploid Genomes is Important to Phylogenomic Analysis under the Multispecies Coalescent Model

Genome sequencing projects routinely generate haploid consensus sequences from diploid genomes, which are effectively chimeric sequences with the phase at heterozygous sites resolved at random. The impact of phasing errors on phylogenomic analyses under the multispecies coalescent (MSC) model is largely unknown. Here we conduct a computer simulation to evaluate the performance of four phase-resolution strategies (the true phase resolution, the diploid analytical integration algorithm which averages over all phase resolutions, computational phase resolution using the program PHASE, and random resolution) on estimation of the species tree and evolutionary parameters in analysis of multi-locus genomic data under the MSC model. We found that species tree estimation is robust to phasing errors when species divergences were much older than average coalescent times but may be affected by phasing errors when the species tree is shallow. Estimation of parameters under the MSC model with and without introgression is affected by phasing errors. In particular, random phase resolution causes serious overestimation of population sizes for modern species and biased estimation of cross-species introgression probability. In general the impact of phasing errors is greater when the mutation rate is higher, the data include more samples per species, and the species tree is shallower with recent divergences. Use of phased sequences inferred by the PHASE program produced small biases in parameter estimates. We analyze two real datasets, one of East Asian brown frogs and another of Rocky Mountains chipmunks, to demonstrate that heterozygote phase-resolution strategies have similar impacts on practical data analyses. We suggest that genome sequencing projects should produce unphased diploid genotype sequences if fully phased data are too challenging to generate, and avoid haploid consensus sequences, which have heterozygous sites phased at random. In case the analytical integration algorithm is computationally unfeasible, computational phasing prior to population genomic analyses is an acceptable alternative.

The Relativistic Binary Programme on MeerKAT: Science objectives and first results

We describe the ongoing Relativistic Binary programme (RelBin), a part of the MeerTime large survey project with the MeerKAT radio telescope. RelBin is primarily focused on observations of relativistic effects in binary pulsars to enable measurements of neutron star masses and tests of theories of gravity. We selected 25 pulsars as an initial high priority list of targets based on their characteristics and observational history with other telescopes. In this paper, we provide an outline of the programme, present polarisation calibrated pulse profiles for all selected pulsars as a reference catalogue along with updated dispersion measures. We report Faraday rotation measures for 24 pulsars, twelve of which have been measured for the first time. More than a third of our selected pulsars show a flat position angle swing confirming earlier observations. We demonstrate the ability of the Rotating Vector Model (RVM), fitted here to seven binary pulsars, including the Double Pulsar (PSR J0737−3039A), to obtain information about the orbital inclination angle. We present a high time resolution light curve of the eclipse of PSR J0737−3039A by the companion’s magnetosphere, a high-phase resolution position angle swing for PSR J1141−6545, an improved detection of the Shapiro delay of PSR J1811−2405, and pulse scattering measurements for PSRs J1227−6208, J1757−1854, and J1811−1736. Finally, we demonstrate that timing observations with MeerKAT improve on existing data sets by a factor of, typically, 2–3, sometimes by an order of magnitude.