Dynamics and Interaction of Vortex Lines in an Elongated Bose-Einstein Condensate

U-net based vortex detection in Bose-Einstein condensates with automatic correction for manually mislabeled data

Quantum vortices in Bose-Einstein condensates (BECs) are essential phenomena in condensed matter physics, and precisely locating their positions, especially the vortex core, is a precondition for studying their properties. With the rise of machine learning, there is a possibility to expedite the localization process and provide accurate predictions. However, traditional machine learning requires particular considerable amount of manual data annotation, leading to uncontrollable accuracy. In this paper, we utilize the U-Net method to detect vortex positions accurately at the pixel level and propose an Automatic Correction Labeling (ACL) approach to optimize the acquisition of data sets for vortex localization in BECs. This approach addresses inaccuracies in the labeled vortex positions and improves the accuracy of vortex localization, especially the vortex core positions, while enhancing the tolerance for human mislabeling. The main process involves Rough Labeling [Formula: see text] Machine Learning [Formula: see text] Probability Region Search [Formula: see text] Data Relabeling [Formula: see text] Machine Learning again. The objective of ACL is to secure more accurate labeled data for model retraining. Through vortex localization experiments conducted in a two-dimensional Bose-Einstein condensate, our results establish the following: 1. Even under conditions of biased and missing manual annotations, U-Net can still accurately locate vortex positions; 2. Vortices exhibit certain regularities, and training U-Net with a small number of samples yields excellent predictive consequences; 3. The machine learning vortex locator based on the ACL method effectively corrects errors in manually annotated data, significantly improving the model's performance metrics, thus enhancing the precision and metrics of vortex localization. This substantial advancement in the application of machine learning in vortex localization provides an effective way for vortex dynamics localization. Furthermore, this method of obtaining more accurate positions of approximate human labels through machine learning offers new insights for machine learning in other types of image recognition problems.

Weak-measurement-induced heating in Bose-Einstein condensates

Ultracold atoms are an ideal platform for understanding system-reservoir dynamics of many-body systems. Here, we study quantum back-action in atomic Bose-Einstein condensates, weakly interacting with a far-from resonant, i.e., dispersively interacting, probe laser beam. The light scattered by the atoms can be considered as a part of quantum measurement process, whereby the change in the system state derives from measurement back-action. We experimentally quantify the resulting back-action in terms of the deposited energy. We model the interaction of the system and environment with a generalized measurement process, leading to a Markovian reservoir. Further, we identify two systematic sources of heating and loss: a stray optical lattice and probe-induced light-assisted collisions (an intrinsic atomic process). The observed heating and loss rates are larger for blue detuning than for red detuning, where they are oscillatory functions of detuning with increased loss at molecular resonances and reduced loss between molecular resonances.

Casimir Force between Two Vortices in a Turbulent Bose–Einstein Condensate

We consider the Casimir force between two vortices due to the presence of density fluctuations induced by turbulent modes in a Bose–Einstein condensate. We discuss the cases of unbounded and finite condensates. Turbulence is described as a superposition of elementary excitations (phonons or BdG modes) in the medium. Expressions for the Casimir force between two identical vortex lines are derived, assuming that the vortices behave as point particles. Our analytical model of the Casimir force is confirmed by numerical simulations of the Gross–Pitaevskii equation, where the finite size of the vortices is retained. Our results are valid in the mean-field description of the turbulent medium. However, the Casimir force due to quantum fluctuations can also be estimated, assuming the particular case where the occupation number of the phonon modes in the condensed medium is reduced to zero and only zero-point fluctuations remain.

Irreversible Dynamics of Vortex Reconnections in Quantum Fluids

We statistically study vortex reconnections in quantum fluids by evolving different realizations of vortex Hopf links using the Gross-Pitaevskii model. Despite the time reversibility of the model, we report clear evidence that the dynamics of the reconnection process is time irreversible, as reconnecting vortices tend to separate faster than they approach. Thanks to a matching theory devised concurrently by Proment and Krstulovic [Phys. Rev. Fluids 5, 104701 (2020)PLFHBR2469-990X10.1103/PhysRevFluids.5.104701], we quantitatively relate the origin of this asymmetry to the generation of a sound pulse after the reconnection event. Our results have the prospect of being tested in several quantum fluid experiments and, theoretically, may shed new light on the energy transfer mechanisms in both classical and quantum turbulent fluids.

Single-shot reconstruction of the density profile of a dense atomic gas

Partial transfer absorption imaging (PTAI) of ultracold atoms allows for repeated and minimally-destructive measurements of an atomic ensemble. Here, we present a reconstruction technique based on PTAI that can be used to piece together the non-uniform spatial profile of high-density atomic samples using multiple measurements. We achieved a thirty-fold increase of the effective dynamic range of our imaging, and were able to image otherwise saturated samples with unprecedented accuracy of both low- and high-density features.

Discrete vortices on spatially nonuniform two-dimensional electric networks

Two-dimensional arrays of nonlinear electric oscillators are considered theoretically where nearest neighbors are coupled by relatively small constant but nonequal capacitors. The dynamics is approximately reduced to a weakly dissipative defocusing discrete nonlinear Schrödinger equation with translationally noninvariant linear dispersive coefficients. Behavior of quantized discrete vortices in such systems is shown to depend strongly on the spatial profile of the internode coupling as well as on the ratio between time-increasing healing length and lattice spacings. In particular, vortex clusters can be stably trapped for some initial period of time by a circular barrier in the coupling profile, but then, due to gradual dissipative broadening of vortex cores, they lose stability and suddenly start to move.

Vortex knots on three-dimensional lattices of nonlinear oscillators coupled by space-varying links

Quantized vortices in a complex wave field described by a defocusing nonlinear Schrödinger equation with a space-varying dispersion coefficient are studied theoretically and compared to vortices in the Gross-Pitaevskii model with external potential. A discrete variant of the equation is used to demonstrate numerically that vortex knots in three-dimensional arrays of oscillators coupled by specially tuned weak links can exist for as long times as many as tens of typical vortex turnover periods.

Crossover from interaction to driven regimes in quantum vortex reconnections

Reconnections of coherent filamentary structures play a key role in the dynamics of fluids, redistributing energy and helicity among the length scales, triggering dissipative effects, and inducing fine-scale mixing. Unlike ordinary (classical) fluids where vorticity is a continuous field, in superfluid helium and in atomic Bose-Einstein condensates (BECs) vorticity takes the form of isolated quantized vortex lines, which are conceptually easier to study. New experimental techniques now allow visualization of individual vortex reconnections in helium and condensates. It has long being suspected that reconnections obey universal laws, particularly a universal scaling with time of the minimum distance between vortices δ. Here we perform a comprehensive analysis of this scaling across a range of scenarios relevant to superfluid helium and trapped condensates, combining our own numerical simulations with the previous results in the literature. We reveal that the scaling exhibits two distinct fundamental regimes: a [Formula: see text] scaling arising from the mutual interaction of the reconnecting strands and a [Formula: see text] scaling when extrinsic factors drive the individual vortices.

Reconnection scaling in quantum fluids

Superfluid helium exhibits topological defects in the form of line-like objects called quantum vortices. Reconnection occurs when two vortices collide and recoil by exchanging tails. We observe such a reconnection for nearly isolated conditions and find that the intervortex separation for a certain range scales closely as the square root of the time after reconnection and that the prefactor in the square-root law shows an analytical dependence on the reconnection angle. Reconnection is important because it provides a mechanism for energy dissipation which otherwise does not occur in the zero-temperature limit. The kinematics of reconnections are similar in systems of classical vortices, cosmic strings, magnetic flux tubes in plasmas, liquid crystals, and even DNA.

Fundamental to classical and quantum vortices, superconductors, magnetic flux tubes, liquid crystals, cosmic strings, and DNA is the phenomenon of reconnection of line-like singularities. We visualize reconnection of quantum vortices in superfluid ⁴He, using submicrometer frozen air tracers. Compared with previous work, the fluid was almost at rest, leading to fewer, straighter, and slower-moving vortices. For distances that are large compared with vortex diameter but small compared with those from other nonparticipating vortices and solid boundaries (called here the intermediate asymptotic region), we find a robust 1/2-power scaling of the intervortex separation with time and characterize the influence of the intervortex angle on the evolution of the recoiling vortices. The agreement of the experimental data with the analytical and numerical models suggests that the dynamics of reconnection of long straight vortices can be described by self-similar solutions of the local induction approximation or Biot–Savart equations. Reconnection dynamics for straight vortices in the intermediate asymptotic region are substantially different from those in a vortex tangle or on distances of the order of the vortex diameter.

Probing Quantum Turbulence in ^{4}He by Quantum Evaporation Measurements

Theory of superfluid ^{4}He shows that, due to strong correlations and backflow effects, the density profile of a vortex line has the character of a density modulation and it is not a simple rarefaction region as found in clouds of cold bosonic atoms. We find that the basic features of this density modulation are represented by a wave packet of cylindrical symmetry in which rotons with a positive group velocity have a dominant role: The vortex density modulation can be viewed as a cloud of virtual excitations, mainly rotons, sustained by the phase of the vortex wave function. This suggests that in a vortex reconnection some of these rotons become real so that a vortex tangle is predicted to be a source of nonthermal rotons. The presence of such vorticity induced rotons can be verified by measurements at low temperature of quantum evaporation of ^{4}He atoms. We estimate the rate of evaporation and this turns out to be detectable by current instrumentation. Additional information on the microscopic processes in the decay of quantum turbulence will be obtained if quantum evaporation by high energy phonons should be detected.

Grid superfluid turbulence and intermittency at very low temperature

Low-temperature grid-generated turbulence is investigated by using numerical simulations of the Gross-Pitaevskii equation. The statistics of regularized velocity increments are studied. Increments of the incompressible velocity are found to be skewed for turbulent states. Results are later confronted with the (quasi) homogeneous and isotropic Taylor-Green flow, revealing the universality of the statistics. For this flow, the statistics are found to be intermittent and a Kolmogorov constant close to the one of classical fluid is found for the second-order structure function.

Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation

The development and decay of a turbulent vortex tangle driven by the Gross-Pitaevskii equation is studied. Using a recently developed accurate and robust tracking algorithm, all quantized vortices are extracted from the fields. The Vinen's decay law for the total vortex length with a coefficient that is in quantitative agreement with the values measured in helium II is observed. The topology of the tangle is then investigated showing that linked rings may appear during the evolution. The tracking also allows for determining the statistics of small-scale quantities of vortex lines, exhibiting large fluctuations of curvature and torsion. Finally, the temporal evolution of the Kelvin wave spectrum is obtained providing evidence of the development of a weak-wave turbulence cascade.