Controlling, evading, and maximising quantum thermalisation

Quantum thermalisation is the process by which generic interacting many-body systems evolve such that local observables relax to their thermal equilibrium values, regardless of the system’s initial state. While progress has been made through the Eigenstate Thermalisation Hypothesis – a powerful conjecture describing thermalisation in closed quantum systems – practical methods to control or exploit this process remain elusive. This is a crucial challenge if we aim to use interacting many-body systems as a foundation for quantum technologies. After providing introduction to quantum thermalisation and many-body chaos in Chapters 1-2, the core of this thesis explores theoretical frameworks for controlling quantum thermalisation using tunable quantum systems, with a strong emphasis on experimental realisability. In Chapter 3, we introduce a chiral spin-chain model and demonstrate that, when tuned to the appropriate coupling regime, it exhibits maximally thermalising behaviour, similar to the well-known Sachdev-Ye-Kitaev model. Leveraging this property, we implement the Hayden–Preskill teleportation protocol, showing that maximal scrambling can improve the protocol’s timescales. In Chapter 4, we step back and introduce quantum many-body scarring as a mechanism for evading thermalisation. We showcase how the PXP model – a limit of the experimentally realised Rydberg atom platform – allows for tunable quantum many-body scars by means of varying the detuning or chemical potential. This approach unveils a continuous family of scarred initial states that extends beyond low-entangled product states. Finally, in Chapter 5, we investigate a distinct information-scrambling process – “Gaussification”. In this process, which bears some resemblance to thermalisation, the states which are initially interacting, i.e., possess non-Gaussian correlations and violate Wick’s theorem, progressively evolve into Gaussian ones. We demonstrate that Rydberg atom arrays can retain non-Gaussian correlations after a quantum quench in a way that is robust against experimental errors. Our conclusions are presented in Chapter 6 where we argue that the results presented in this thesis challenge the notion that thermalisation is an inevitable destructive force by offering several strategies to both resist it and harness it for applications in quantum-information processing.