Detecting dark solitons using persistent homology

This preprint has made available a large collection of labelled images of BECs containing 0, 1 or multiple dark solitons. The authors of that study trained a convolutional neural network to distinguish these three classes of images. Single dark solitons could be detected with an accuracy of about 90\%. On 2014 MacBook Pro each image took 2.3s to classify using the neural network. Our aim here is to develop a persistent-homology based approach with superior performance (both in accuracy and run-time). Fast and accurate machine learning-based identification of solitons would enable high-throughput experimental study of their dynamics by eliminating the time-consuming and at times error-prone manual identification of the solitons in the experimentally-obtained images.

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Edit (3/8/21): I have a more recent post discussing the finished manuscript resulting from this project.

Scarry quantum systems

There are various classes of non-equilibrium dynamics supported by isolated many-body quantum systems. In systems obeying the eigenstate thermalization hypothesis, initially-ordered states evolve into states that appear to be in thermal equilibrium with a fictitious bath. On the other hand, many-body localised systems retain memory of the initial state indefinitely via a set of emergent local conserved quantities. Recently peculiar quantum phases hosting co-existing thermal and athermal states with similar energy densities have been discovered. The athermal (or non-ergodic) eigenstates embedded within a chaotic spectrum are dubbed "quantum many-body scars".

Interest in this topic appears to have been sparked by a 2017 experiment using a 1D chain of 51 trapped Rydberg atoms, where long-lived interaction-induced oscillations of the atomic states were observed. A subsequent theory paper analyzed this behaviour using a relatively simple effective model, where strong interactions constrain the dynamics of certain initial states to a small subset of the full Hilbert space. Remarkably, the set of anomalous non-ergodic eigenstates is not necessarily limited to a small fraction of the full spectrum; models with confining interaction potentials or geometrical frustration can exhibit a fragmentation of the spectrum into an exponentially large number of disconnected sectors of various sizes!

One motivation for studying many-body quantum scars is that their long-lived coherent dynamics may be useful as a means of storing and manipulating quantum information. However, we still need to better understand what precise model features give rise to this non-ergodicity, and how to control and maximise the lifetime of the coherent many-body dynamics, such as by optimising longer-range interactions. Experiments using arrays of 200 Rydberg atoms published last month have demonstrated the importance of the underlying lattice geometry (persistent coherent dynamics were only observed in bipartite lattices) as well as the ability to stabilise the many-body scars using periodic driving. In the future I think it will be important to come up with more flexible ways to identify and measure the quantum many-body scarring and Hilbert space fragmentation, in particular to quantify its robustness to various perturbations.