Final Report Summary - FLUX LATTICES (Quantum Hall states in ultracold atomic gases)
Executive Summary:
The general research line of the project “flux lattices” was (1) to fully understand the equilibrium properties of two-dimensional quantum gases of atoms, (2) produce these samples in novel and flexible geometries, (3) implement artificial gauge fields on these 2D gases and study the possible emergence of novel phases. This project started on April 1st 2012, and was supposed to last until March 31st, 2014. However due the fact that the Marie Curie Fellow was offered a position in Hamburg University at the beginning of 2013, the contract undergone an early termination on August 31st, 2013. Therefore only the first two items have been fully addressed during this contract.
--- Cold atoms and artificial gauge fields: a short overview ---
Cold atoms constitute a prolific platform to study quantum physics due to the exquisite experimental control and the large tunability of interactions and external potentials. They were successfully used to study the physics of electrons in a condensed matter environment, e.g. simulating the Mott insulator transition in an optical lattice. However, due to their neutrality, atoms do not couple to magnetic fields in the same way as electrons do. In order to study the intriguing physics of electrons in large magnetic fields, such as the fractional quantum Hall effects, artificial gauge fields have to be engineered. This can be done either by rotating the trap and using the formal equivalence of the Coriolis force and the Lorentz force or by engineering the phases that a particle acquires in the gauge field. Several concrete proposals have been made to produce artificial gauge fields. Some of them are based on the use of a uniform optical lattice, with boundaries set by a square-box potential. Another class of proposal consists in reducing the atom number to just a few and rotate the sample, such that the ratio of quanta of angular momentum and atom number could be on the order of unity. We have explored the first steps towards the implementation of both strategies during the duration of the contract.
--- Static two-dimensional Bose gases: superfluidity and equation of state ---
Before applying a gauge field to a 2D quantum fluid, it is of course essential to characterize as well as possible its static and dynamical properties. A detailed investigation of the superfluidity of the two-dimensional Bose gas was carried out by directly measuring its response to a moving obstacle formed by a tightly focused laser beam. When the system is in a superfluid state, there is a critical velocity below which the obstacle cannot create excitations, which shows in the absence of heating. This superfluid behavior occurs above a critical phase space density, i.e. for low temperatures and high densities. The trapped atomic gas has an inhomogeneous density, so we chose to move the obstacle in circles in order to probe at a fixed density. In this way it was possible to map out the critical phase space density and to compare it to the prediction of Monte Carlo simulations. This work was published in Nature Physics, with the fellow as Corresponding author.
Another characterization of the properties of a fluid is provided by its equation of state. We have implemented a novel method for measuring this quantity. This method fully exploits the approximate scale invariance of two-dimensional fluids and it does not require any fit of individual images. The agreement of our results with the best existing numerical predictions is excellent. These results are currently being written and the corresponding paper should be submitted soon, probably to Physical Review Letters.
--- Production of two-dimensional gases in various geometries ---
Cold atoms are usually produced and confined in harmonic potentials. For experiments based on the investigation of quasi-long range coherence, which is crucial in two dimensions, it is worth replacing this harmonic confinement by a box- shaped potential. The uniform gases that are produced in this way are particularly interesting, because they avoid the average over different densities that are present in a gas in a harmonic trap and therefore allow a more direct comparison with the predictions for the thermodynamic limit. In particular, the box trap has a different density of states than the usual harmonic trap, which changes the priority of the two competing phase transitions of Bose-Einstein-condensation and the Berezinskii-Kosterlitz-Thouless transition that are present in 2D Bose gases.
We have created these box potentials by imaging a mask onto the atoms. This allows arbitrary geometries, including two neighboring traps. The interference of the atoms released from these traps has allowed us to measure the coherence in the system. This allows new insight into the physics of two-dimensional Bose gases and exciting results are expected to follow.
A preliminary version of these results has already been presented in international conferences (in particular BEC San Feliu 2013). We are finalizing the calibration of the experiment, notably its temperature, which raises several new and subtle questions for a uniform 2D system, as compared to the usual case of harmonically trapped gas. We will then proceed with the writing of an article summarizing all our results on this topic, to be submitted to Physical Review Letters probably.
--- Towards detection of artificial gauge fields: single atom imaging ---
We mentioned above that some implementations of gauge fields are only possible for very small atom numbers. The detection of these samples requires a single-atom imaging setup, in which the atoms are fixed in a pinning lattice while they are illuminated with laser beams. The strategy was to use a near-resonant pinning lattice to keep the atoms in place while illuminating them with an optical molasses that keeps them at a temperature of around 20 µK. The molasses and the pinning lattice were installed, aligned, and independently characterized. It was found that both work independently, but that the pinning lattice compromised the proper functioning of the molasses. A careful analysis showed that a notably larger power of the pinning lattice was required. A corresponding update of the laser source was lanced but it has not been possible to implement it, due to the early termination of the project. However the progresses that have been already made will be very useful for the team in place for future research.