Crossover from 2D to 3D in a weakly interacting Fermi gas

We have studied the transition from two to three dimensions in a low temperature weakly interacting $^6$Li Fermi gas. Below a critical atom number, $N_{2D}$, only the lowest transverse vibrational state of a highly anisotropic oblate trapping potential is occupied and the gas is two-dimensional. Above $N_{2D}$ the Fermi gas enters the quasi-2D regime where shell structure associated with the filling of individual transverse oscillator states is apparent. This dimensional crossover is demonstrated through measurements of the cloud size and aspect ratio versus atom number.Comment: Replaced with published manuscrip

Quantum anomaly and 2D-3D crossover in strongly interacting Fermi gases

We present an experimental investigation of collective oscillations in harmonically trapped Fermi gases through the crossover from two to three dimensions. Specifically, we measure the frequency of the radial monopole or breathing mode as a function of dimensionality in Fermi gases with tunable interactions. The frequency of this mode is set by the adiabatic compressibility and probes the thermodynamic equation of state. In 2D, a dynamical scaling symmetry for atoms interacting via a {\delta}-potential predicts the breathing mode to occur at exactly twice the harmonic confinement frequency. However, a renormalized quantum treatment introduces a new length scale which breaks this classical scale invariance resulting in a so-called quantum anomaly. Our measurements deep in the 2D regime lie above the scale-invariant prediction for a range of interaction strengths indicating the breakdown of a {\delta}-potential model for atomic interactions. As the dimensionality is tuned from 2D to 3D we see the breathing oscillation frequency evolve smoothly towards the 3D limit.Comment: 5 pages, 3 figure

Robust Upward Dispersion of the Neutron Spin Resonance in the Heavy Fermion Superconductor Ce1−x_{1-x}Ybx_{x}CoIn5_5

The neutron spin resonance is a collective magnetic excitation that appears in copper oxide, iron pnictide, and heavy fermion unconventional superconductors. Although the resonance is commonly associated with a spin-exciton due to the $d$($s^{\pm}$)-wave symmetry of the superconducting order parameter, it has also been proposed to be a magnon-like excitation appearing in the superconducting state. Here we use inelastic neutron scattering to demonstrate that the resonance in the heavy fermion superconductor Ce$_{1-x}$Yb$_{x}$CoIn$_5$ with $x=0,0.05,0.3$ has a ring-like upward dispersion that is robust against Yb-doping. By comparing our experimental data with random phase approximation calculation using the electronic structure and the momentum dependence of the $d_{x^2-y^2}$-wave superconducting gap determined from scanning tunneling microscopy for CeCoIn$_5$, we conclude the robust upward dispersing resonance mode in Ce$_{1-x}$Yb$_{x}$CoIn$_5$ is inconsistent with the downward dispersion predicted within the spin-exciton scenario.Comment: Supplementary Information available upon reques

A new method for the solution of the Schrodinger equation

We present a new method for the solution of the Schrodinger equation applicable to problems of non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: An asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wave function and, finally, a short distance scale, in which the wave function is sizable. The key feature of our method is the introduction of an arbitrary parameter in the last two scales, which is then used to optimize a perturbative expansion in a suitable parameter. We apply the method to the quantum anharmonic oscillator and find excellent results.Comment: 4 pages, 4 figures, RevTex

A self-interacting partially directed walk subject to a force

We consider a directed walk model of a homopolymer (in two dimensions) which is self-interacting and can undergo a collapse transition, subject to an applied tensile force. We review and interpret all the results already in the literature concerning the case where this force is in the preferred direction of the walk. We consider the force extension curves at different temperatures as well as the critical-force temperature curve. We demonstrate that this model can be analysed rigorously for all key quantities of interest even when there may not be explicit expressions for these quantities available. We show which of the techniques available can be extended to the full model, where the force has components in the preferred direction and the direction perpendicular to this. Whilst the solution of the generating function is available, its analysis is far more complicated and not all the rigorous techniques are available. However, many results can be extracted including the location of the critical point which gives the general critical-force temperature curve. Lastly, we generalise the model to a three-dimensional analogue and show that several key properties can be analysed if the force is restricted to the plane of preferred directions.Comment: 35 pages, 14 figure

Asymptotic analysis for singularly perturbed convection-diffusion equations with a turning point

Turning points occur in many circumstances in fluid mechanics. When the viscosity is small, very complex phenomena can occur near turning points, which are not yet well understood. A model problem, corresponding to a linear convection-diffusion equation (e.g., suitable linearization of the Navier-Stokes or B́nard convection equations) is considered. Our analysis shows the diversity and complexity of behaviors and boundary or interior layers which already appear for our equations simpler than the Navier-Stokes or B́nard convection equations. Of course the diversity and complexity of these structures will have to be taken into consideration for the study of the nonlinear problems. In our case, at this stage, the full theoretical (asymptotic) analysis is provided. This study is totally new to the best of our knowledge. Numerical treatment and more complex problems will be considered elsewhere.open91

Calculation of valence electron momentum densities using the projector augmented-wave method

We present valence electron Compton profiles calculated within the density-functional theory using the all-electron full-potential projector augmented-wave method (PAW). Our results for covalent (Si), metallic (Li, Al) and hydrogen-bonded ((H_2O)_2) systems agree well with experiments and computational results obtained with other band-structure and basis set schemes. The PAW basis set describes the high-momentum Fourier components of the valence wave functions accurately when compared with other basis set schemes and previous all-electron calculations.Comment: Submitted to Journal of Physics and Chemistry of Solids on September 17 2004. Revised version submitted on December 13 200

Higgs oscillations in a unitary Fermi superfluid

Symmetry-breaking phase transitions are central to our understanding of states of matter. When a continuous symmetry is spontaneously broken, new excitations appear that are tied to fluctuations of the order parameter. In superconductors and fermionic superfluids, the phase and amplitude can fluctuate independently, giving rise to two distinct collective branches. However, amplitude fluctuations are difficult to both generate and measure, as they do not couple directly to the density of fermions and have only been observed indirectly to date. Here, we excite amplitude oscillations in an atomic Fermi gas with resonant interactions by an interaction quench. Exploiting the sensitivity of Bragg spectroscopy to the amplitude of the order parameter, we measure the time-resolved response of the atom cloud, directly revealing amplitude oscillations at twice the frequency of the gap. The magnitude of the oscillatory response shows a strong temperature dependence, and the oscillations appear to decay faster than predicted by time-dependent BCS theory applied to our experimental setup