A perennial mystery of nature is how order can exist amidst chaos. Familiar systems such as the clock pendulum exhibit regular periodic motion. This ordered behaviour, however, is fragile. For example, interactions between particles rapidly lead to chaos, forcing the system to thermalise and "forget" its initial state. This can be visualised as an ice cream that melts away and never finds its way back to the frozen state. "Quantum scars" refer to the surprising behaviour that defies such common intuition: for special initial states, the ice cream periodically melts away and then freezes up again. Recent experiments on ultracold Rydberg atoms have found evidence of similar behaviour where the atoms were able to return to their initial state many times during the measurement. Our recent work [Nature Physics 14, 745 (2018)] has proposed the first theoretical explanation for this phenomenon and named it "quantum many- body scars". At this point, the origins of quantum many-body scars largely remain a mystery. Your project will develop a computer simulation of quantum many-body scars in two-dimensional lattices of Rydberg atoms, with the goal of predicting future experiments on these systems that may unlock a range of applications in the emerging quantum technologies.
Recent state-of-the-art experiments on a quantum simulator built from strongly-correlated Rydberg atoms [H. Bernien et al., Nature 551, 579 (2017)] have discovered a remarkable dynamical phenomenon that challenged the conventional notion of how quantum systems reach thermal equilibrium. We have recently proposed the first theoretical explanation for this phenomenon and named it "quantum many-body scars" [Nature Physics 14, 745 (2018]. Following the surge of international interest in this topic, including popular articles in the press [see: https://www.quantamagazine.org/quantum-
scarring-appears-to- defy-universes-push-for-disorder-20190320/], this project will contribute to the on-going quest to understand the mathematical origins of quantum many-body scars and their unusual dynamical properties. The practical benefits of this research will be new computational techniques for simulating non-ergodic many-body dynamics and phases of matter, and their potential use as a platform for robust quantum technology that could operate at arbitrarily high temperatures.
The initial phase of the project will focus on: (i) learning about quantum dynamics, thermalisation, and related phenomena (integrability, many-body localisation), and (ii) learning how to numerically simulate quantum many-body systems (e.g., using Python, C++, or any preferred language). In particular, you will learn how to apply quantum information concepts to characterise dynamics and thermalisation (e.g., entanglement entropy and spectrum). You will apply all these tools to investigate in the detail the toy model of a 1D Rydberg atom chain, then extend the known results by investigating various physical perturbations to the model.
Desired student background: We seek talented and highly-motivated physics students to pursue this project in the general area of quantum many-body physics, which is at the interface of quantum information and condensed matter physics. The necessary theoretical background will be obtained through the CDT courses within the MRes programme. A significant component of the project is numerical modelling of quantum many-body systems via exact diagonalisation and related techniques (e.g., matrix product states, DMRG, etc.), thus the project is particularly suitable for those with strong interest in computational physics and numerical simulations.