A time crystal is a recently discovered dynamic state of matter where a periodic process spontaneously appears, similar to periodic arrangement of atoms in regular crystals. This periodic process lasts eternally in an ideal time crystal. This long-time coherence has proposed applications, for example, as a memory element in quantum computing. Unfortunately, time crystals are fragile when put in contact with environment. This project aims to overcome this limitation by engineering delicate interaction of a time crystal with surrounding media using an ultra-low-temperature platform provided by the superfluid phases of the 3He isotope. We will use this coupling to elucidate topologically nontrivial properties of the superfluid itself. We hope that the developed interaction protocols will enable applications of time crystals for quantum sensing and control in various systems.

Quantum computers are machines that exploit the rules of quantum mechanics to potentially outperform even the fastest supercomputers. However, due to the interferences of the chaotic external world, quantum computers corrupt easily making it difficult to perform computations accurately. This makes it important to study the phenomenon of quantum scarring where some quantum states manage to escape chaos. Mathematics of quantum scarring is mostly studied in single body systems such as billiards or flows on surfaces. The purpose of this project in Aalto is to design new tools in mathematics that give us a new fundamental understanding of how chaos manifests in mathematical models of quantum systems. Our plan is to bridge the ideas from large single body quantum systems to many body systems, which will help us discover mechanisms to escape chaos. Our methods draw ideas from the rapidly advancing theory of large networks, which are ubiquitous in the modern day world of big data.