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We demonstrate the use of a ring-shaped Bose-Einstein condensate as a rotation sensor by measuring the interference between two counter-propagating phonon modes imprinted azimuthally around the ring. We observe rapid decay of the excitations, quantified by quality factors of at most $Q \approx 27$. We numerically model our experiment using the c-field methodology, allowing us to estimate the parameters that maximise the performance of our sensor. We explore the damping mechanisms underlying the observed phonon decay, and identify two distinct Landau scattering processes that each dominate at different driving amplitudes and temperatures. Our simulations reveal that $Q$ is limited by strong damping of phonons even in the zero temperature limit. We perform an experimental proof-of-principle rotation measurement using persistent currents imprinted around the ring. We demonstrate a rotation sensitivity of up to $\Delta \Omega \approx 0.3$ rad/s from a single image, with a theoretically achievable value of $\Delta \Omega \approx 0.04$ rad/s in the atomic shot-noise limit. This is a significant improvement over the shot-noise-limited $\Delta \Omega \approx 1$ rad/s sensitivity obtained by Marti et al. [Phys. Rev. A 91, 013602 (2015)] for a similar setup., Comment: 22 pages, 10 figures

We consider the situation where a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as a piecewise linear function of time with an unknown number of change-points. We develop a Bayesian approach to infer the joint posterior distribution of the number and position of change-points as well as the unknown mean parameters. A-priori, the proposed model uses an overfitting number of mean parameters but, conditionally on a set of change-points, only a subset of them influences the likelihood. An exponentially decreasing prior distribution on the number of change-points gives rise to a posterior distribution concentrating on sparse representations of the underlying sequence. A Metropolis-Hastings Markov chain Monte Carlo (MCMC) sampler is constructed for approximating the posterior distribution. Our method is benchmarked using simulated data and is applied to uncover differences in the dynamics of fungal growth from imaging time course data collected from different strains. The source code is available on CRAN., Comment: Accepted to International Journal of Biostatistics

We present a unified view of the frequency dependence of the various scattering processes involved when a neutral hydrogen atom interacts with a monochromatic, linearly-polarized photon. A computational approach is employed of the atom trapped by a finite-sized-box due to a finite basis-set expansion, which generates a set of transition matrix elements between $E<0$ eigenstates and $E>0$ pseudostates. We introduce a general computational methodology that enables the computation of the frequency-dependent dipole transition polarizability with one real and two different imaginary contributions. These dipole transition polarizabilities are related to the cross-sections of one-photon photoionization, Rayleigh, Raman, and Compton scattering. Our numerical calculations reveal individual Raman scattering cross-sections above threshold that can rapidly vanish and revive. Furthermore, our numerical Compton cross-sections do not overtly suffer from the infra-red divergence problem, and are three orders-of-magnitude higher than previous analytic-based Compton scattering cross-sections. Our total photon-hydrogen scattering cross-sections thus resolve the discrepancies between these previous calculations and those in the N.I.S.T. `FFAST' database.

A relativistic description of the structure of heavy alkali atoms and alkali-like ions using S-spinors and L-spinors has been developed. The core wavefunction is defined by a Dirac-Fock calculation using an S-spinors basis. The S-spinor basis is then supplemented by a large set of L-spinors for the calculation of the valence wavefunction in a frozen-core model. The numerical stability of the L-spinor approach is demonstrated by computing the energies and decay rates of several low-lying hydrogen eigenstates, along with the polarizabilities of a $Z=60$ hydrogenic ion. The approach is then applied to calculate the dynamic polarizabilities of the $5s$, $4d$ and $5p$ states of Sr$^+$. The magic wavelengths at which the Stark shifts between different pairs of transitions are zero are computed. Determination of the magic wavelengths for the $5s \to 4d_{\frac32}$ and $5s \to 4d_{\frac52}$ transitions near $417$~nm (near the wavelength for the $5s \to 5p_j$ transitions) would allow a determination of the oscillator strength ratio for the $5s \to 5p_{\frac12}$ and $5s \to 5p_{\frac32}$ transitions., Comment: 2 figures, 23 pages

Interferometric measurements with matter waves are established techniques for sensitive gravimetry, rotation sensing, and measurement of surface interactions, but compact interferometers will require techniques based on trapped geometries. In a step towards the realization of matter wave interferometers in toroidal geometries, we produce a large, smooth ring trap for Bose-Einstein condensates using rapidly scanned time-averaged dipole potentials. The trap potential is smoothed by using the atom distribution as input to an optical intensity correction algorithm. Smooth rings with a diameter up to 300 $\mu$m are demonstrated. We experimentally observe and simulate the dispersion of condensed atoms in the resulting potential, with good agreement serving as an indication of trap smoothness. Under time of flight expansion we observe low energy excitations in the ring, which serves to constrain the lower frequency limit of the scanned potential technique. The resulting ring potential will have applications as a waveguide for atom interferometry and studies of superfluidity.

We present a model of a spin-squeezed rotation sensor utilising the Sagnac effect in a spin-1 Bose-Einstein condensate in a ring trap. The two input states for the interferometer are seeded using Raman pulses with Laguerre-Gauss beams and are amplified by the bosonic enhancement of spin-exchange collisions, resulting in spin-squeezing and potential quantum enhancement in the interferometry. The ring geometry has an advantage over separated beam path atomic rotation sensors due to the uniform condensate density. We model the interferometer both analytically and numerically for realistic experimental parameters and find that significant quantum enhancement is possible, but this enhancement is partially degraded when working in a regime with strong atomic interactions., Comment: 13 pages, 9 figures