arXiv subjects

E. Taylor

Publications and source records attributed to E. Taylor.

29 records · Page 2Linked to original sources

arXiv2010

Second sound and the density response function in uniform superfluid atomic gases

Recently there has been renewed interest in second sound in superfluid Bose and Fermi gases. By using two-fluid hydrodynamic theory, we review the density response $χ_{nn}(\bq,ω)$ of these systems as a tool to identify second sound in experiments based on density probes. Our work generalizes the well-known studies of the dynamic structure factor $S(\bq,ω)$ in superfluid $^4$He in the critical region. We show that, in the unitary limit of uniform superfluid Fermi gases, the relative weight of second vs. first sound in the compressibility sum rule is given by the Landau--Placzek ratio $\lp\equiv (\bar{c}_p-\bar{c}_v)/\bar{c}_v$ for all temperatures below $T_c$. In contrast to superfluid $^4$He, $\lp$ is much larger in strongly interacting Fermi gases, being already of order unity for $T \sim 0.8 T_c$, thereby providing promising opportunities to excite second sound with density probes. The relative weights of first and second sound are quite different in $S(\bq,ω)$ (measured in pulse propagation studies) as compared to $\mathrm{Im}χ_{nn}(\bq,ω)$ (measured in two-photon Bragg scattering). We show that first and second sound in $S(\bq,ω)$ in a strongly interacting Bose-condensed gas are similar to those in a Fermi gas at unitarity. However, in a weakly interacting Bose gas, first and second sound are mainly uncoupled oscillations of the thermal cloud and condensate, respectively, and second sound has most of the spectral weight in $S(\bq,ω)$. We also discuss the behaviour of the superfluid and normal fluid velocity fields involved in first and second sound.

cond-mat.quant-gas↗

arXiv2009

First and second sound in a strongly interacting Fermi gas

Using a variational approach, we solve the equations of two-fluid hydrodynamics for a uniform and trapped Fermi gas at unitarity. In the uniform case, we find that the first and second sound modes are remarkably similar to those in superfluid Helium, a consequence of strong interactions. In the presence of harmonic trapping, first and second sound become degenerate at certain temperatures. At these points, second sound hybridizes with first sound and is strongly coupled with density fluctuations, giving a promising way of observing second sound. We also discuss the possibility of exciting second sound by generating local heat perturbations.

cond-mat.quant-gas↗

arXiv2009

Critical Behaviour in Trapped Strongly Interacting Fermi Gases

We investigate the width of the Ginzburg critical region and experimental signatures of critical behavior in strongly interacting trapped Fermi gases close to unitarity, where the s-wave scattering length diverges. Despite the fact that the width of the critical region is of the order unity, evidence of critical behavior in the bulk thermodynamics of trapped gases is strongly suppressed by their inhomogeneity. The specific heat of a harmonically confined gas, for instance, is \textit{linear} in the reduced temperature $t = (T-T_{\mathrm{c}})/T_{\mathrm{c}}$ above $T_{\mathrm{c}}$. We also discuss the prospects of observing critical behavior in the local compressibility from measurements of the density profile.

cond-mat.stat-mech↗

arXiv2008

Quantum phases of a Two-Dimensional Dipolar Fermi Gas

We examine the superfluid and collapse instabilities of a quasi two-dimensional gas of dipolar fermions aligned by an orientable external field. It is shown that the interplay between the anisotropy of the dipolar interaction, the geometry of the system, and the p-wave symmetry of the superfluid order parameter means that the effective interaction for pairing can be made very large without the system collapsing. This leads to a broad region in the phase diagram where the system forms a stable superfluid. Analyzing the superfluid transition at finite temperatures, we calculate the Berezinskii--Kosterlitz--Thouless temperature as a function of the dipole angle.

cond-mat.other↗

arXiv2007

Spin-polarized Fermi superfluids as Bose-Fermi mixtures

In the strong-coupling BEC region where a Feshbach resonance gives rise to tightly-bound dimer molecules, we show that a spin-polarized Fermi superfluid reduces to a simple Bose-Fermi mixture of Bose-condensed dimers and the leftover unpaired fermions. Using a many-body functional integral formalism, the Gaussian fluctuations give rise to an induced dimer-dimer interaction mediated by the unpaired fermions, with the dimer-fermion vertex being given by the (mean-field) Born approximation. Treating the pairing fluctuations to quartic order, we show how the action for a spin-polarized Fermi superfluid reduces to one for a Bose-Fermi mixture. This Bose-Fermi action includes an expression for the effective dimer-unpaired fermion interaction in a spin-polarized Fermi superfluid beyond the Born approximation, in the superfluid phase at finite temperatures. In the low-density limit, we show how this dimer-fermion interaction gives the s-wave scattering length $a_{BF}=1.18a_F$ ($a_F$ is the s-wave fermion scattering length), a result first derived by Skorniakov and Ter-Martirosian in 1957 for three interacting fermions.

cond-mat.other↗

arXiv2006

Superfluid density and condensate fraction in the BCS-BEC crossover regime at finite temperatures

The superfluid density is a fundamental quantity describing the response to a rotation as well as in two-fluid collisional hydrodynamics. We present extensive calculations of the superfluid density ρ_s in the BCS-BEC crossover regime of a uniform superfluid Fermi gas at finite temperatures. We include strong-coupling or fluctuation effects on these quantities within a Gaussian approximation. We also incorporate the same fluctuation effects into the BCS single-particle excitations described by the superfluid order parameter Δand Fermi chemical potential μ, using the Nozières and Schmitt-Rink (NSR) approximation. This treatment is shown to be necessary for consistent treatment of ρ_s over the entire BCS-BEC crossover. We also calculate the condensate fraction N_c as a function of the temperature, a quantity which is quite different from the superfluid density ρ_s. We show that the mean-field expression for the condensate fraction N_c is a good approximation even in the strong-coupling BEC regime. Our numerical results show how ρ_s and N_c depend on temperature, from the weak-coupling BCS region to the BEC region of tightly-bound Cooper pair molecules. In a companion paper by the authors (cond-mat/0609187), we derive an equivalent expression for ρ_s from the thermodynamic potential, which exhibits the role of the pairing fluctuations in a more explicit manner.

cond-mat.mtrl-sci↗

arXiv2006

Pairing fluctuations and the superfluid density through the BCS-BEC crossover

We derive an expression for the superfluid density of a uniform two-component Fermi gas through the BCS-BEC crossover in terms of the thermodynamic potential in the presence of an imposed superfluid flow. Treating the pairing fluctuations in a Gaussian approximation following the approach of Nozières and Schmitt-Rink, we use this definition of $ρ_s$ to obtain an explicit result which is valid at finite temperatures and over the full BCS-BEC crossover. It is crucial that the BCS gap $Δ$, the chemical potential $μ$, and $ρ_s$ all include the effect of fluctuations at the same level in a self-consistent manner. We show that the normal fluid density $ρ_n \equiv n - ρ_s$ naturally separates into a sum of contributions from Fermi BCS quasiparticles ($ρ^F_{n}$) and Bose collective modes ($ρ^B_{n}$). The expression for $ρ^F_{n}$ is just Landau's formula for a BCS Fermi superfluid but now calculated over the BCS-BEC crossover. The expression for the Bose contribution $ρ^B_{n}$ is more complicated and only reduces to Landau's formula for a Bose superfluid in the extreme BEC limit, where all the fermions have formed stable Bose pairs and the Bogoliubov excitations of the associated molecular Bose condensate are undamped. In a companion paper, we present numerical calculations of $ρ_s$ using an expression equivalent to the one derived in this paper, over the BCS-BEC crossover, including unitarity, and at finite temperatures.

cond-mat.other↗

arXiv2006

The Space Density and Colors of Massive Galaxies at 2<z<3: the Predominance of Distant Red Galaxies

Using the deep multi-wavelength MUSYC, GOODS, and FIRES surveys we construct a stellar mass-limited sample of galaxies at 2 10^11 Solar masses distributed over four independent fields with a total area of almost 400 sq arcmin. The mean number density of massive galaxies in this redshift range is (2.2+-0.6) x 10^-4 Mpc^-3. We present median values and 25th and 75th percentiles for the distributions of observed R mags, observed J-K colors, and rest-frame UV continuum slopes, M/L(V) ratios, and U-V colors. The galaxies show a large range in all these properties. The ``median galaxy'' is faint in the observer's optical (R=25.9), red in the observed near-IR (J-K=2.48), has a rest-frame UV spectrum which is relatively flat (beta=-0.4), and rest-frame optical colors resembling those of nearby spiral galaxies (U-V=0.62). We determine which galaxies would be selected as Lyman break galaxies (LBGs) or Distant Red Galaxies (DRGs, having J-K>2.3) in this mass-limited sample. By number DRGs make up 69% of the sample and LBGs 20%, with a small amount of overlap. By mass DRGs make up 77% and LBGs 17%. Neither technique provides a representative sample of massive galaxies at 2<z<3 as they only sample the extremes of the population. As we show here, multi-wavelength surveys with high quality photometry are essential for an unbiased census of massive galaxies in the early Universe. The main uncertainty in this analysis is our reliance on photometric redshifts; confirmation of the results presented here requires extensive near-infrared spectroscopy of optically-faint samples.

astro-ph↗

arXiv2005

Two-fluid hydrodynamic modes in a trapped superfluid gas

In the collisional region at finite temperatures, the collective modes of superfluids are described by the Landau two-fluid hydrodynamic equations. This region can now be probed over the entire BCS-BEC crossover in trapped Fermi superfluids with a Feshbach resonance, including the unitarity region. Building on the approach initiated by Zaremba, Nikuni, and Griffin in 1999 for trapped atomic Bose gases, we present a new variational formulation of two-fluid hydrodynamic collective modes based on the work of Zilsel in 1950 developed for superfluid helium. Assuming a simple variational ansatz for the superfluid and normal fluid velocities, the frequencies of the hydrodynamic modes are given by solutions of coupled algebraic equations, with constants only involving spatial integrals over various equilibrium thermodynamic derivatives. This variational approach is both simpler and more physical than a direct attempt to solve the Landau two-fluid differential equations. Our two-fluid results are shown to reduce to those of Pitaevskii and Stringari for a pure superfluid at T=0.

cond-mat.stat-mech↗

arXiv2004

The Hubble Higher-Z Supernova Search: Supernovae to z=1.6 and Constraints on Type Ia Progenitor Models

We present results from the Hubble Higher-z Supernova Search, the first space-based open field survey for supernovae (SNe). In cooperation with the Great Observatories Origins Deep Survey, we have used the Hubble Space Telescope with the Advanced Camera for Surveys to cover 300 square arcmin in the area of the Chandra Deep Field South and the Hubble Deep Field North on five separate search epochs (separated by 45 day intervals) to a limiting magnitude of z'=26. These deep observations have allowed us to discover 42 SNe in the redshift range 0.2 < z < 1.6. As these data span a large range in redshift, they are ideal for testing the validity of Type Ia supernova progenitor models with the distribution of expected ``delay times,'' from progenitor star formation to SN Ia explosion, and the SN rates these models predict. Through a Bayesian maximum likelihood test, we determine which delay-time models best reproduce the redshift distribution of SNe Ia discovered in this survey. We find that models that require a large fraction of ``prompt'' (less than 2 Gyr) SNe Ia poorly reproduce the observed redshift distribution and are rejected at 95% confidence. We find that Gaussian models best fit the observed data for mean delay times in the range of 3 to 4 Gyr.

astro-ph↗

arXiv2003

Bogoliubov sound speed in periodically modulated Bose-Einstein condensates

We study the Bogoliubov excitations of a Bose-condensed gas in an optical lattice. Of primary interest is the long wavelength phonon dispersion for both current-free and current-carrying condensates. We obtain the dispersion relation by carrying out a systematic expansion of the Bogoliubov equations in powers of the phonon wave vector. Our result for the current-carrying case agrees with the one recently obtained by means of a hydrodynamic theory.

cond-mat.soft↗