Investigating non-equilibrium physics and universality using two-dimensional quantum gases

Lead Research Organisation: University of Oxford
Department Name: Oxford Physics


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.

Planned Impact

The most direct technological output is the refinement of techniques for trapping atoms with combined RF and static magnetic fields that are already being used for quantum technology applications. RF-dressed potentials for ultracold atoms are very good for long-term operation since they do not require alignment of laser beams as for optical dipole trapping. RF sources are extremely stable both in amplitude at the position of the atoms and in frequency. Moreover, time averaging makes atoms in RF-dressed potentials insensitive to noise at frequencies below the applied RF; this useful property is closely related to the decoherence-free subspaces used for quantum information processing.

We use RF-dressed magnetic potentials for fundamental science research but others working on quantum technology will profit from our innovations. Microwave and RF techniques are used for prototype atomic clocks on atom chips (Ramsey interferometry of internal states) and for gyroscopes (matter-wave interferometry with spatially-separated wave packets). Experimental work on gyroscopes for inertial navigation is being conducted by Prof. Thomas Fernholz at the University of Nottingham within the auspices of the national Quantum Hub on Quantum Sensors; this also involves theoretical work by Prof. Barry Garraway and coworkers at the University of Sussex. Professor Foot is not a member of any of the Hubs but our experimental and theoretical results on multiple-RF dressed potentials (as discussed in the Track Record) promise new ideas for future devices. For example, the double-well potential could be extended to form a double ring-shaped trap, with one ring stacked above the other. This configuration allows counter-propagating wave packets, in the two different rings, to circulate many times without colliding before a final recombination to observe interference. This is just one example of the benefits of improved techniques for manipulating cold atoms arising from this project. With more RF sources we can make more potential wells and a range of interesting phenomena have been predicted for 3 and 4 wells.

Beyond these near-term applications, there are major gains from having a better understanding of non-equilibrium (NEQ) systems. For example, the ground state of many-body quantum systems can be found by adiabatic quantum annealing and this is used as method of quantum computation to solve important optimisation problems (although the extent to which this is currently realised by the existing commercial cryogenic solid-states device is debated). Clearly, it is desirable to change the control parameters rapidly whilst maintaining quasi-equilibrium during the simulated annealing. Minimising operation time requires quantifying the non-adiabaticity and corresponding fidelity; in this context, it is important to understand the relaxation mechanism of any NEQ component of the system that arises.
Description The apparatus was constructed and operated extremely well to produce matter-wave interference fringes. Extensive data taking and analysis were carried out over the final year of the grant. This was made possible by a 12 month extension of time that was granted to account for the Covid lockdown period in early 2020 when the graduate students were not allowed in the lab as well as the research time lost by individuals quarantining. This enabled the original objectives to be obtained within the project period. Important results on the 'Observation of the Berezinskii-Kosterlitz-Thouless transition in a 2D Bose gas via matter-wave interferometry' were published in Physical Review Letters. The interference of matter waves provides information about the phase of the wave function of the many-body system and this, together with the measured amplitude, provides very detailed information about the evolution of quantum systems. This technique works especially well for 2D systems and enables the investigation of non-equilibrium effects associated with phase transitions. A paper on the 'Universal Scaling of the Dynamic BKT Transition in Quenched 2D Bose Gases' was written in close collaboration with the theoretical group at the University of Hannover led by Prof. Ludwig Mathey. This work elucidated the application of renormalization group theory to universal non-equilibrium behaviour (whereas it was previously established for equilibrium situations). We measured the non-equilibrium dynamics triggered by a quench from superfluid to normal phase across the Berezinskii-Kosterlitz-Thouless transition in a 2D Bose gas. The quench was implemented by splitting the 2D gas in two. We then probed the relaxation dynamics by measuring the phase correlation function and vortex density via matter-wave interferometry. In this way we demonstrated universal scaling laws for the algebraic exponents and vortex density, supported by classical-field simulations, and show their agreement with the real-time RG theory
Exploitation Route The technique for manipulating dressed atoms with RF fields that we have developed as a powerful tool for the study of non-equilbrium systems by atom interferometry can also be applied to other types of interferometer such as gyroscopes.
Sectors Aerospace

Defence and Marine


Description This grant has not yet finished but we have developed close collaborations with two research groups that have carryied out theoretical work to interpret and illuminate our results. This combined experimental and theoretical programme will contribute to the detailed understanding of non-equilbrium physics in many-body quantum systems.
First Year Of Impact 2022
Sector Education