Shai Ronen

The 2dF Galaxy Redshift Survey: spectral types and luminosity functions

We describe the 2dF Galaxy Redshift Survey (2dFGRS), and the current status of the observations. In this exploratory paper, we apply a Principal Component Analysis to a preliminary sample of 5869 galaxy spectra and use the two most significant components to split the sample into five spectral classes. These classes are defined by considering visual classifications of a subset of the 2dF spectra, and also by comparing to high quality spectra of local galaxies. We calculate a luminosity function for each of the different classes and find that later-type galaxies have a fainter characteristic magnitude, and a steeper faint-end slope. For the whole sample we find M ⋆ = 19.7 (for =1,H0=100kms 1 Mpc 1 ), � = 1.3, � ⋆ = 0.017. For class 1 (‘early-type’) we find M ⋆ = 19.6, � = 0.7, while for class 5 (‘late-type’) we find M ⋆ = 19.0, � = 1.7. The derived 2dF luminosity functions agree well with other recent luminosity function estimates.

Bragg Spectroscopy of a Strongly Interacting 85Rb Bose-Einstein Condensate

We report on measurements of the excitation spectrum of a strongly interacting Bose-Einstein condensate. A magnetic-field Feshbach resonance is used to tune atom-atom interactions in the condensate and to reach a regime where quantum depletion and beyond mean-field corrections to the condensate chemical potential are significant. We use two-photon Bragg spectroscopy to probe the condensate excitation spectrum; our results demonstrate the onset of beyond mean-field effects in a gaseous Bose-Einstein condensate.

Principal component analysis of synthetic galaxy spectra

We analyse synthetic galaxy spectra from the evolutionary models of Bruzual & Charlot and Fioc & Rocca-Volmerange using the method of principal component analysis (PCA). We explore synthetic spectra with different ages, star formation histories and metallicities, and identify the principal components (PCs) of variance in the spectra resulting from these different model parameters. The PCA provides a more objective and informative alternative to diagnostics by individual spectral lines. We discuss how the PCs can be used to estimate the input model parameters, and explore the impact of dust and noise in this inverse problem. We also discuss how changing the sampling of the ages and other model parameters affects the resulting PCs. Our first two synthetic PCs agree with a similar analysis on observed spectra obtained by Kennicutt and the 2dF redshift survey. We conclude that with a good enough signal-to-noise ratio (S/N>> 10) it is possible to derive age, star formation history and metallicity from observed galaxy spectra using PCA.

Bogoliubov modes of a dipolar condensate in a cylindrical trap

The calculation of properties of Bose-Einstein condensates with dipolar interactions has proven a computationally intensive problem due to the long range nature of the interactions, limiting the scope of applications. In particular, the lowest lying Bogoliubov excitations in three-dimensional harmonic trap with cylindrical symmetry were so far computed in an indirect way, by Fourier analysis of time-dependent perturbations, or by approximate variational methods. We have developed a very fast and accurate numerical algorithm based on the Hankel transform for calculating properties of dipolar Bose-Einstein condensates in cylindrically symmetric traps. As an application, we are able to compute many excitation modes by directly solving the Bogoliubov-De Gennes equations. We explore the behavior of the excited modes in different trap geometries. We use these results to calculate the quantum depletion of the condensate by a combination of a computation of the exact modes and the use of a local density approximation.

Scattering Length Instability in Dipolar Bose-Einstein Condensates

We characterize zero-temperature dipolar Bose gases under external spherical confinement as a function of the dipole strength using the essentially exact many-body diffusion Monte Carlo (DMC) technique. We show that the DMC energies are reproduced accurately within a mean-field framework if the variation of the s-wave scattering length with the dipole strength is accounted for properly. Our calculations suggest stability diagrams and collapse mechanisms of dipolar Bose gases that differ significantly from those previously proposed in the literature.

Dipolar Bose-Einstein condensates with dipole-dependent scattering length

We consider a Bose-Einstein condensate of polar molecules in a harmonic trap, where the effective dipole may be tuned by an external field. We demonstrate that taking into account the dependence of the scattering length on the dipole moment is essential to reproducing the correct energies and for predicting the stability of the condensate. We do this by comparing Gross-Pitaevskii calculations with diffusion Monte Carlo calculations. We find very good agreement between the results obtained by these two approaches once the dipole dependence of the scattering length is taken into account. We also examine the behavior of the condensate in nonisotropic traps.

Critical Superfluid Velocity in a Trapped Dipolar Gas

We investigate the superfluid properties of a dipolar Bose-Einstein condensate (BEC) in a fully three-dimensional trap. Specifically, we estimate a superfluid critical velocity for this system by applying the Landau criterion to its discrete quasiparticle spectrum. We test this critical velocity by direct numerical simulation of condensate depletion as a blue-detuned laser moves through the condensate. In both cases, the presence of the roton in the spectrum serves to lower the critical velocity beyond a critical particle number. Since the shape of the dispersion, and hence the roton minimum, is tunable as a function of particle number, we thereby propose an experiment that can simultaneously measure the Landau critical velocity of a dipolar BEC and demonstrate the presence of the roton in this system.

Stability and excitations of a dipolar Bose-Einstein condensate with a vortex

We study the stability of singly and doubly quantized vortex states of harmonically trapped dipolar BoseEinstein condensates BECs by calculating the low-lying excitations of these condensates. We map the dynamical stability of these vortices as functions of the dipole-dipole interaction strength and trap geometry by finding where their excitations have purely real energy eigenvalues. In contrast to BECs with purely contact interactions, we find that dipolar BECs in singly quantized vortex states go unstable to modes with an increasing number of angular and radial nodes for more oblate trap aspect ratios, corresponding to local collapse that occurs on a characteristic length scale. Additionally, we find that dipolar BECs in doubly quantized vortex states are unstable to decay into a different topological state with two singly quantized vortices for all interaction strengths when the trap geometry is sufficiently prolate to make the dipoles attractive, and in windows of interaction strength when the trap geometry is sufficiently oblate to make the dipoles repulsive.

Dipolar Bose-Einstein condensates at finite temperature

We study a Bose-Einstein condensate of a dilute gas with dipolar interactions, at finite temperature, using the Hartree-Fock-Bogoliubov theory within the Popov approximation. An additional approximation involving the dipolar exchange interaction is made to facilitate the computation. We calculate the temperature dependence of the condensate fraction of a condensate confined in a cylindrically symmetric harmonic trap. We show that the biconcave-shaped condensates found in [Ronen et al. Phys. Rev. Lett. 98, 30406 (2007)] in certain pancake traps at zero temperature are also stable at finite temperature. Surprisingly, the dip in the central density of these structured condensates is actually enhanced at low finite temperatures. We explain this effect.

The dispersion relation of a Bose gas in the intermediate- and high-momentum regimes

The well-known Bogoliubov expression for the spectrum of a weakly interacting dilute Bose gas becomes inadequate when the density or interactions strength is increased. The corrections to the spectrum due to stronger interactions were first considered by Beliaev (1958 Sov. Phys.—JETP 7 289). We revisit Beliaevs theory and consider its application to a dilute gas with van der Waals interactions, where the scattering length may be tuned via a Fano–Feshbach resonance. We numerically evaluate Beliaevs expression for the excitation spectrum in the intermediate-momentum regime, and we also examine the consequences of the momentum dependence of the two-body scattering amplitude. These results are relevant to the interpretation of a recent Bragg spectroscopy experiment of a strongly interacting Bose gas.