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

One-dimensional description of a Bose-Einstein condensate in a rotating closed-loop waveguide

We propose a general procedure for reducing the three-dimensional Schrodinger equation for atoms moving along a strongly confining atomic waveguide to an effective one-dimensional equation. This procedure is applied to the case of a rotating closed-loop waveguide. The possibility of including mean-field atomic interactions is presented. Application of the general theory to characterize a new concept of atomic waveguide based on optical tweezers is finally discussed

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

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

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

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

Ground state fidelity and quantum phase transitions in free Fermi systems

We compute the fidelity between the ground states of general quadratic fermionic hamiltonians and analyze its connections with quantum phase transitions. Each of these systems is characterized by a $L\times L$ real matrix whose polar decomposition, into a non-negative $\Lambda$ and a unitary $T$, contains all the relevant ground state (GS) information. The boundaries between different regions in the GS phase diagram are given by the points of, possibly asymptotic, singularity of $\Lambda$. This latter in turn implies a critical drop of the fidelity function. We present general results as well as their exemplification by a model of fermions on a totally connected graph.Comment: 4 pages, 2 figure

Evaluating a radiotherapy deep learning synthetic CT algorithm for PET-MR attenuation correction in the pelvis

\ua9 2024, The Author(s). Background: Positron emission tomography–magnetic resonance (PET-MR) attenuation correction is challenging because the MR signal does not represent tissue density and conventional MR sequences cannot image bone. A novel zero echo time (ZTE) MR sequence has been previously developed which generates signal from cortical bone with images acquired in 65 s. This has been combined with a deep learning model to generate a synthetic computed tomography (sCT) for MR-only radiotherapy. This study aimed to evaluate this algorithm for PET-MR attenuation correction in the pelvis. Methods: Ten patients being treated with ano-rectal radiotherapy received a 18 F-FDG-PET-MR in the radiotherapy position. Attenuation maps were generated from ZTE-based sCT (sCTAC) and the standard vendor-supplied MRAC. The radiotherapy planning CT scan was rigidly registered and cropped to generate a gold standard attenuation map (CTAC). PET images were reconstructed using each attenuation map and compared for standard uptake value (SUV) measurement, automatic thresholded gross tumour volume (GTV) delineation and GTV metabolic parameter measurement. The last was assessed for clinical equivalence to CTAC using two one-sided paired t tests with a significance level corrected for multiple testing of p≤ 0.05 / 7 = 0.007 . Equivalence margins of \ub1 3.5 % were used. Results: Mean whole-image SUV differences were −0.02% (sCTAC) compared to −3.0% (MRAC), with larger differences in the bone regions (−0.5% to −16.3%). There was no difference in thresholded GTVs, with Dice similarity coefficients ≥ 0.987 . However, there were larger differences in GTV metabolic parameters. Mean differences to CTAC in SUV max were 1.0 \ub1 0.8 % (\ub1 standard error, sCTAC) and - 4.6 \ub1 0.9 % (MRAC), and 1.0 \ub1 0.7 % (sCTAC) and - 4.3 \ub1 0.8 % (MRAC) in SUV mean . The sCTAC was statistically equivalent to CTAC within a \ub1 3.5 % equivalence margin for SUV max and SUV mean (p= 0.007 and p= 0.002), whereas the MRAC was not (p= 0.88 and p= 0.83). Conclusion: Attenuation correction using this radiotherapy ZTE-based sCT algorithm was substantially more accurate than current MRAC methods with only a 40 s increase in MR acquisition time. This did not impact tumour delineation but did significantly improve the accuracy of whole-image and tumour SUV measurements, which were clinically equivalent to CTAC. This suggests PET images reconstructed with sCTAC would enable accurate quantitative PET images to be acquired on a PET-MR scanner