Two preprints

I haven't had much time for posting recently, since I've been rushing to finish several projects before the end of the year. We have two papers out on arXiv this week, with a few more hopefully ready soon!

Unravelling quantum chaos using persistent homology

We considered the application of (quantum) chaos detection techniques to a simple system, a driven-damped Kerr nonlinear oscillator. Tuning the driving frequency in this system can induce transitions between chaotic and regular dynamics, with classical chaos emerging in the limit of large amplitude coherent states. This provides a nice setting for looking at how persistent homology-based methods for detecting classical chaos can be translated to quantum dynamics. For this purpose, we treat the quantum oscillator as an open quantum system subject to random quantum jumps (photons leaking from the cavity), described by a stochastic Schrodinger equation. Despite the higher complexity of the quantum system (in terms of a larger phase space), we can still distinguish regimes of regular and chaotic dynamics by considering the topology of a time-delay embedding of the detected photon counts!

Pseudospin-2 in photonic chiral borophene

One chapter of my PhD thesis covered wave propagation at conical interactions. At the time, we were most interested in intersections with pseudospin 1/2 (corresponding to Dirac cones in systems such as graphene), and pseudospin 1 (occurring in the Lieb lattice, a topic which I spent some time studying). While I was writing up the thesis, I found the analysis of both kinds of systems could be connected nicely by generalizing the description to arbitrary pseudospin s. We included this in a review article, but didn't give much thought as to how one might go about realizing intersections with higher values of s, assuming they would be unstable and hard to make in practice.

It turns out, higher pseudospin conical intersections can be symmetry-protected (similar to the case of the Lieb lattice), and can they emerge in lattices that don't look too crazy, can be realized using optical waveguide arrays, and may even exist as stable two-dimensional electronic materials!