Superfluidity in two-dimensional ultra-cold atom clouds

• Applicant: Professor Dr. Ludwig Mathey
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2014 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 262440178

We will study superfluidity in ultra-cold atom systems. This intriguing phenomenon has continued to puzzle, intrigue and inspire scientists since its first discovery. With the realization of Bose Einstein condensation (BEC) in cold atomic gases, a new experimental environment has been created in which the properties of superfluidity can be studied in a well-defined and tunable setup. In a recent experiment by the Dalibard group at the ENS, Paris, a two-dimensional condensate was stirred with a laser and the superfluid properties of the system were measured. In this project we will complement this on-going experimental work with a theoretical study, and expand the scope of it by investigating the superfluid properties in further regimes, such as across the Berezinskii-Kosterlitz-Thouless (BKT) transition. First, we will simulate the experiment in its current form, using a numerical implementation of the truncated Wigner approximation, to make quantitative comparisons with the experimental results. The truncated Wigner approximation includes the next order of thermal and quantum fluctuations beyond the mean-field Gross-Pitaevskii equation (GPE). While many numerical studies have investigated the dynamics of BECs within a GPE approach, here the key to understanding the system lies in the fluctuating nature of the phase. This necessitates a "post-GPE" approach. Further, the Truncated Wigner simulation will enable the understanding of the dissipation process, for example if the creation of vortices is the main mechanism. Besides the numerical approach we will investigate the dissipative mechanism of the stirring experiment analytically. We will first use a Bogoliubov approach, and then include beyond-Bogoliubov terms. In the next stage, we will investigate the stirring process close to the BKT transition. Besides the numerical simulation, we will employ a real-time renormalization group approach, which is a novel method to study critical dynamics analytically. We thus expect to gain insight into the interplay between superfluidity and critical phenomena. In addition to studying stirring experiments, we will study the coherence properties of 2D Bose gases via the density correlations of the expanding cloud in time-of-flight. Initially, the atoms are held in a trap. Then, the trap is turned off, and the atoms expand freely. After an expansion time, the correlations of the density are measured. This correlation function contains information about the coherence properties of the initial system, in particular, the phase fluctuations translate into density fluctuations during time-of-flight. We will calculate the correlations of these fluctuations both in real space and in momentum space, and will derive analytic expressions for these correlations where possible. We will directly work with experimental groups. In particular, we will address if the measurement of these correlations can be used to distinguish the condensed and the thermal phase.

• DFG Programme: Research Grants