Periodic Reporting for period 1 - BosQuanTran (Quantum simulation of transport properties in arbitrary shaped potential landscapes with ultracold bosonic atoms)
Reporting period: 2016-03-01 to 2018-02-28
Within this project we are planning to investigate transport phenomena with weakly-interacting ultracold bosonic atoms. To provide the most flexible experimental setting we combine novel high-resolution imaging techniques with recently realized two-dimensional (2D) uniform trapping geometries. Another key ingredient is an optical accordion lattice with tunable lattice spacing for efficient loading of dense 2D atom clouds and tunable interaction strength. In combination with detection techniques such as partial imaging and matter-wave interference we can access important experimental observables such as correlation functions. We have implemented and characterized a reliable and flexible experimental setup, which will enable future studies in transport geometries with one-dimensional (1D) channels that support only one single-particle transport mode. We will engineer channels with lattice or disorder potentials, which are particularly useful to observe thermomechanical effects, such as the superfluid fountain effect. By reaching the truly-2D regime we will further investigate the scaling of the Berezinsky-Kosterlitz-Thouless transition and by implementing optical flux lattices we will work towards the ambitious goal of observing topological transport phenomena.
1) Typical cold-atom experiments rely on standard absorption imaging, where a resonant laser beam is sent on the atoms and the corresponding shadow is imaged with a camera. For small atomic densities the atoms can be treated independently and the extracted optical density is proportional to the atomic density. For large atomic densities, as obtained in our setup, this is no longer true and the optical response is modified by the light-induced dipole-dipole interactions between adjacent atoms. We have studied the modified transmission of near-resonant light through uniform slabs of atoms as a function of density (Fig. 2) and compared them to numerical coupled-dipole simulations. We found that the response is strongly modified due to multiple scattering of photons (in preparation).
2) Motivated by these results one may ask, how photons propagate in such a dense medium of randomly positioned scatterers. We addressed this question by exciting the atoms locally within a small region of the cloud and detected the fluorescence photons propagating outside the excitation region (Fig. 3a). From the radial profile (Fig. 3b) one can see that photons are detected several microns away from the excitation region. We studied the characteristic propagation length as a function of the cloud parameters and the detuning of the excitation light from the single-atom resonance and compared them to coupled-dipole simulations as well as to a pure diffusive model. An interesting question yet to be answered is the role of localization in this experimental setting (in preparation).
3) An important tool in our setup is the accordion lattice (Fig. 4a). It allows for a dynamical tunability of the out-of-plane confinement and therefore of the interaction strength. We performed a detailed characterization of its performance and showed that the lattice spacing can be varied by a factor of 5 (Fig. 4b), which changes the 2D interaction parameter by a factor of more than 2. We have tested that by varying the confinement dynamically we do not heat the atoms significantly. The results are summarized in Ref. .
4) Using this experimental toolset, we studied what happens, if we merge up to 12 independently prepared condensates in an annulus. The condensates are characterized by random phases, which can lead to a net phase accumulation around the ring. This in turn may lead to the generation of supercurrents (Fig. 5a) with integer winding number. Each experimental realization results in a different set of random phases and after several repetitions we were able to extract the corresponding probability distributions as a function of the initial number of condensates (Fig. 5b). These results are an important contribution to the detailed understanding of the celebrated Kibble-Zurek mechanism. A summary can be found in Ref. .
 J. L. Ville et al., Phys. Rev. A 95, 013632 (2017)
 M. Aidelsburger et al., arXiv:1705.02650 (2017)