Deep-learning-based quantum vortex detection in atomic Bose–Einstein condensates

Abstract

Quantum vortices naturally emerge in rotating Bose–Einstein condensates (BECs) and, similarly to their classical counterparts, allow the study of a range of interesting out-of-equilibrium phenomena, such as turbulence and chaos. However, the study of such phenomena requires the determination of the precise location of each vortex within a BEC, which becomes challenging when either only the density of the condensate is available or sources of noise are present, as is typically the case in experimental settings. Here, we introduce a machine-learning-based vortex detector motivated by state-of-the-art object detection methods that can accurately locate vortices in simulated BEC density images. Our model allows for robust and real-time detection in noisy and non-equilibrium configurations. Furthermore, the network can distinguish between vortices and anti-vortices if the phase profile of the condensate is also available. We anticipate that our vortex detector will be advantageous for both experimental and theoretical studies of the static and dynamic properties of vortex configurations in BECs.

A method for the dynamics of vortices in a Bose-Einstein condensate: analytical equations of the trajectories of phase singularities

“…Other research problem which can be approached with this method is to study initial conditions with many singularities at random positions; we note that this last case will require to determine its locations numerically (which as commented requires a dedicated numerical method as [63,64]). And also it will require to solve a large set of equations even in the non-interacting case.…”

“…For a large enough number of singularities it may require sophisticated methods, see e.g. [63,64] but in our case we used a simple method. The analytically calculated merging time is tm = 1.9 a.u.…”

Observing phase jumps of solitons in Bose-Einstein condensates

“…the phase jump factor or the interference density ratio is maximum within a certain region, even if the soliton is no longer present. This difficulty could be removed by using the machine learning techniques to trace the structure of solitons [24,25]. It will be interesting and useful to apply the machine learning technique to analyze the density and interference density ratio profile for understanding the soliton dynamics in BESs breakdown into vortices at nonzero temperatures.…”

Deep learning based quantum vortex detection in atomic Bose-Einstein condensates

“…The trained models from the main text as well as the code used for training and evaluating the network will be available at [66]. The training data is available from the corresponding authors on reasonable request.…”