Oscillations of a Bose-Einstein condensate rotating in a harmonic plus quartic trap

We study the normal modes of a two-dimensional rotating Bose-Einstein condensate confined in a quadratic plus quartic trap. Hydrodynamic theory and sum rules are used to derive analytical predictions for the collective frequencies in the limit of high angular velocities, $\Omega$, where the vortex lattice produced by the rotation exhibits an annular structure. We predict a class of excitations with frequency $\sqrt{6} \Omega$ in the rotating frame, irrespective of the mode multipolarity $m$, as well as a class of low energy modes with frequency proportional to $|m|/\Omega$. The predictions are in good agreement with results of numerical simulations based on the 2D Gross-Pitaevskii equation. The same analysis is also carried out at even higher angular velocities, where the system enters the giant vortex regime.Comment: 4 pages, 2 figure

Fermi Gases in Slowly Rotating Traps: Superfluid vs Collisional Hydrodynamics

The dynamic behavior of a Fermi gas confined in a deformed trap rotating at low angular velocity is investigated in the framework of hydrodynamic theory. The differences exhibited by a normal gas in the collisional regime and a superfluid are discussed. Special emphasis is given to the collective oscillations excited when the deformation of the rotating trap is suddenly removed or when the rotation is suddenly stopped. The presence of vorticity in the normal phase is shown to give rise to precession and beating phenomena which are absent in the superfluid phase.Comment: 4 pages, 2 figure

Vortex signatures in annular Bose-Einstein condensates

We consider a Bose-Einstein condensate confined in a ``Mexican hat'' potential, with a quartic minus quadratic radial dependence. We find conditions under which the ground state is annular in shape, with a hole in the center of the condensate. Rotation leads to the appearance of stable multiply-quantized vortices, giving rise to a superfluid flow around the ring. The collective modes of the system are explored both numerically and analytically using the Gross-Pitaevskii and hydrodynamic equations. Potential experimental schemes to detect vorticity are proposed and evaluated, which include measuring the splitting of collective mode frequencies, observing expansion following release from the trap, and probing the momentum distribution of the condensate.Comment: 11 pages, 7 figure

Diffused vorticity approach to the oscillations of a rotating Bose-Einstein condensate confined in a harmonic plus quartic trap

The collective modes of a rotating Bose-Einstein condensate confined in an attractive quadratic plus quartic trap are investigated. Assuming the presence of a large number of vortices we apply the diffused vorticity approach to the system. We then use the sum rule technique for the calculation of collective frequencies, comparing the results with the numerical solution of the linearized hydrodynamic equations. Numerical solutions also show the existence of low-frequency multipole modes which are interpreted as vortex oscillations.Comment: 10 pages, 4 figure

Tkachenko oscillations and the compressibility of a rotating Bose gas

The elastic oscillations of the vortex lattice of a cold Bose gas (Tkachenko modes) are shown to play a crucial role in the saturation of the compressibility sum rule, as a consequence of the hybridization with the longitudinal degrees of freedom. The presence of the vortex lattice is responsible for a $q^2$ behavior of the static structure factor at small wavevectors $q$, which implies the absence of long range order in 2D configurations at zero temperature. Sum rules are used to calculate the Tkachenko frequency in the presence of harmonic trapping. Results are derived in the Thomas-Fermi regime and compared with experiments as well as with previous theoretical estimates.Comment: 4 pages, 2 figure

Emotion-based analysis of programming languages on Stack Overflow

When developing a software engineering project, selecting the most appropriate programming language is a crucial step. Most often, feeling at ease with the possible options becomes almost as relevant as the technical features of the language. Therefore, it appears to be worth analyzing the role that the emotional component plays in this process. In this article, we analyze the trend of the emotions expressed by developers in 2018 on the Stack Overflow platform in posts concerning 26 programming languages. To do so, we propose a learning model trained by distant supervision and the comparison of two different classifier architectures

A Textured Silicon Calorimetric Light Detector

We apply the standard photovoltaic technique of texturing to reduce the reflectivity of silicon cryogenic calorimetric light detectors. In the case of photons with random incidence angles, absorption is compatible with the increase in surface area. For the geometrically thin detectors studied, energy resolution from athermal phonons, dominated by position dependence, is proportional to the surface-to-volume ratio. With the CaWO4 scintillating crystal used as light source, the time constants of the calorimeter should be adapted to the relatively slow light-emission times.Comment: Submitted to Journal of Applied Physic

Generalized Coherent States as Preferred States of Open Quantum Systems

We investigate the connection between quasi-classical (pointer) states and generalized coherent states (GCSs) within an algebraic approach to Markovian quantum systems (including bosons, spins, and fermions). We establish conditions for the GCS set to become most robust by relating the rate of purity loss to an invariant measure of uncertainty derived from quantum Fisher information. We find that, for damped bosonic modes, the stability of canonical coherent states is confirmed in a variety of scenarios, while for systems described by (compact) Lie algebras stringent symmetry constraints must be obeyed for the GCS set to be preferred. The relationship between GCSs, minimum-uncertainty states, and decoherence-free subspaces is also elucidated.Comment: 5 pages, no figures; Significantly improved presentation, new derivation of invariant uncertainty measure via quantum Fisher information added

The fidelity approach to the Hubbard model

We use the fidelity approach to quantum critical points to study the zero temperature phase diagram of the one-dimensional Hubbard model. Using a variety of analytical and numerical techniques, we analyze the fidelity metric in various regions of the phase diagram, with particular care to the critical points. Specifically we show that close to the Mott transition, taking place at on-site repulsion U=0 and electron density n=1, the fidelity metric satisfies an hyper-scaling form which we calculate. This implies that in general, as one approaches the critical point U=0, n=1, the fidelity metric tends to a limit which depends on the path of approach. At half filling, the fidelity metric is expected to diverge as U^{-4} when U is sent to zero.Comment: 8 pages, 4 figures, added results on the hyper-scaling form of the fidelity metri

CdWO4 scintillating bolometer for Double Beta Decay: Light and Heat anticorrelation, light yield and quenching factors

We report the performances of a 0.51 kg CdWO4 scintillating bolometer to be used for future Double Beta Decay Experiments. The simultaneous read-out of the heat and the scintillation light allows to discriminate between different interacting particles aiming at the disentanglement and the reduction of background contribution, key issue for next generation experiments. We will describe the observed anticorrelation between the heat and the light signal and we will show how this feature can be used in order to increase the energy resolution of the bolometer over the entire energy spectrum, improving up to a factor 2.6 on the 2615 keV line of 208Tl. The detector was tested in a 433 h background measurement that permitted to estimate extremely low internal trace contaminations of 232Th and 238U. The light yield of gamma/beta, alpha and neutrons is presented. Furthermore we developed a method in order to correctly evaluate the absolute thermal quenching factor of alpha particles in scintillating bolometers.Comment: 8 pages 7 figure