Systems that are not in equilibrium are ubiquitous but can be complex to describe. Although systems at equilibrium are described with great success by quantum mechanics there is, as yet, no general theoretical framework for how a closed many-body quantum system evolves to such thermalised states. This project investigates the process by which non-equilibrium (NEQ) systems relax towards thermal equilibrium, which we call thermalisation. Macroscopic examples range from the cooling of a cup of coffee to the emergence of structures in the early universe. NEQ processes are also important for quantum systems including quantum computers and quantum heat engines. Our experimental techniques allow many-body quantum systems to be prepared in precisely defined NEQ situations and then track their evolution towards equilibrium in unprecedented level of detail.
The system that we will use to gain a better understanding of NEQ physics is a two-dimensional (2D) gas of atoms at temperatures of tens of nanokelvin. The properties of 2D systems are of central importance in physics and part of the Nobel prize for Physics (2016) was awarded to Kosterlitz and Thouless for their work on a phase transition in 2D quantum systems that is named after them. This transition occurs as the quantum gas is cooled and at a certain temperature changes into a superfluid, which flows without friction amongst other fascinating properties.
The ultracold atoms are trapped in extremely well-controlled conditions thus enabling us to make definitive quantitative comparisons with theoretical expectations. Quantum systems confined to 2D are especially interesting for studying NEQ processes because the fluctuations, that are an inherent part of quantum mechanics, play a large role in preventing true long-range order. This new method will provide insights into similar phase transitions in other 2D systems such as thin-film superconductors and liquid crystals, and the quantum gas acts as a quantum simulator for 2D quantum physics in general.
A cornerstone of this proposal is the double-well potential for ultracold rubidium atoms that we have created recently by an innovative use of combined radio-frequency (RF) and static magnetic fields. This technique is ideally suited for coherent splitting of a 2D quantum gas because the shape and height of the potential are controlled directly by the applied RF fields, thus exploiting the extremely high precision of RF electronics. The rate of splitting determines the energy deposited into the system to produce a chosen initial state. At a predefined time after the splitting, the two clouds are released from the double-well potential so that they expand and overlap. This permits interferometric measurements of the relative phase of the matter waves. From repeated measurements, each with the initial state prepared in the same way, we will be able to determine the probability distribution function (PDF) corresponding to the relative phase of the quantum gas for all positions in the 2D plane. PDFs represent the essence of quantum mechanics and allow a more comprehensive comparison with theoretical models than monitoring the time evolution of the expectation values of certain observables as is commonly done. This cold-atom apparatus acts as a 'quantum simulator' of many-body phases in 2D systems thus providing fresh insights relevant to long-standing research questions.