Superfluidity in two-dimensional ultra-cold atom clouds
Final Report Abstract
We have performed a comprehensive study of advanced static and dynamical features of two-dimensional Bose-Einstein condensates. In two dimensions, the condensation phase transition is a Kosterlitz-Thouless transition. This subtle and intriguing phase transition is defined by a change from algebraic scaling below the phase transition to exponential scaling above the critical point. As a first project, we have proposed a method to detect the phase transition and the power-law scaling of two-dimensional condensates. We propose to measure the noise correlations of time-of-flight images after a short expansion time, and demonstrate that it provides both the qualitative and the quantitative insight into the state of the system. We have collaborated with the group of Prof. Henning Moritz on the realization of this proposal. The experimental results indeed support the validity of the method under realistic conditions. Due to a heating process of the experimental setup, whose origin was unclear at the time, the Moritz group decided not to publish the data. As the second project, we have analyzed and achieved a quantitative understanding of the laser stirring experiment by the Dalibard group. In this experiment, a two-dimensional condensate was stirred with a tightly focused laser beam to probe the superfluid properties across the Kosterlitz-Thouless transition. The experiment reported a discrepancy of the critical point, compared to its predicted value. We have identified the origin of this discrepancy. It derives from the slow thermalization across the phase boundary of the condensate and the surrounding thermal cloud. This result is both of conceptual importance, because it points out a pre-thermalized state in a system with non-uniform order, as well as of direct and wide experimental importance, because it shows that a widely used method of thermometry in cold atom systems does not detect the temperature of the condensate but only of the thermal cloud, which are, in general, not in thermal equilibrium. As a third project, we have performed an in-depth study of first and second sound of two-dimensional condensates. This study was in part motivated by an experiment of the Dalibard group reported in 2018, for which we provide a quantitative interpretation. As a central result, we point out that there are two regimes regarding the velocity hierarchy of the two sound modes. In the weak-coupling regime, the Bogoliubov mode is slower than the non-Bogoliubov mode, in the strong-coupling regime, the Bogoliubov mode is faster than the non-Bogoliubov mode. While the strong-coupling regime has been discussed in the literature within a hydrodynamic description, we here emphasize the existence of a second regime, which is not compatible with hydrodynamics. We propose an experiment to excite both modes simultaneously, which would detect our scenario experimentally. With these three projects, centered around two-dimensional condensates, we have advanced the understanding the dynamics and correlations of these systems. We have developed an understanding of experimental findings by one of the most eminent groups of experimental AMO research, which is the group of Prof. Dalibard. Furthermore, we have pointed out the underlying principles of these findings, and developed proposals to further advance this field, with results that will have a broad and invigorating impact on the community.
Publications
- Noise correlations of two-dimensional Bose gases, Phys. Rev. A 89, 053612 (2014)
Vijay Pal Singh and L. Mathey
(See online at https://doi.org/10.1103/PhysRevA.89.053612) - Superfluidity and relaxation dynamics of a laser-stirred 2D Bose gas, Phys. Rev. A 95, 043631 (2017)
V. Singh, C. Weitenberg, J. Dalibard, and Ludwig Mathey
(See online at https://doi.org/10.1103/PhysRevA.95.043631) - Sound propagation in a two-dimensional Bose gas across the superfluid transition
Vijay Pal Singh and Ludwig Mathey
(See online at https://doi.org/10.1103/PhysRevResearch.2.023336)
