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Quantum simulation of transport properties in arbitrary shaped potential landscapes with ultracold bosonic atoms

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

Transport experiments are among the most important experimental probes in solid state physics to investigate the properties of different phases of matter. Among the most intriguing effects recently discovered are high-Tc superconductors and fractional-quantum Hall insulators. In both cases interactions between charge carriers play a significant role, which makes the development of suitable theoretical models challenging, in parts because numerical studies are computationally costly. An alternative solution consists in analog quantum simulations, e.g. with ultracold atoms. These systems constitute very clean and highly controllable environments whose parameters, such as dimensionality and interactions, can be adjusted externally and in many cases even varied dynamically. Most recent technical achievements enabled the engineering of almost arbitrary trapping geometries using high-resolution imaging systems and Digital Micromirror Devices (DMDs). The research area of atomtronics in particular aims at designing and studying electronic-like circuits. Based on the new developments they can now reach unprecedented control and precision. In combination with recent success in the realization of topological quantum states, future studies of topological transport phenomena may come within reach.
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.
During this project we have established a reliable production of dense uniform quasi-2D atom clouds. Out-of-plane the atoms are confined in a tunable accordion lattice with variable confinement. The in-plane trap is provided by a DMD and a high-resolution objective to generate almost arbitrary trapping geometries (Fig. 1). We investigated the properties of the atom clouds by looking at their response to near-resonant light and by employing their coherence to study the stochastic formation of supercurrents in an annulus. The main experimental results have been presented on several international conferences and seminars and are going to be summarized in four separate publications, as described below:
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. [1].
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. [2].
[1] J. L. Ville et al., Phys. Rev. A 95, 013632 (2017)
[2] M. Aidelsburger et al., arXiv:1705.02650 (2017)
We have made several important contributions beyond the state of the art which will have a significant impact on the community. Despite being interesting in its own right, the observation and detailed theoretical description of multiple-scattering effects in dense quasi-2D atom clouds, are of direct relevance to many experiments since it affects one of the most common detection methods in cold-atom setups - absorption imaging. The successful implementation of an optical accordion potential and its detailed characterization is of interest to many teams working with 2D gases. It provides a solution to the well-known challenges associated with an efficient preparation of 2D gases with high atomic densities and large out-of-plane confinement. We have established a compact and reliable setup that can be used for different studies. We demonstrated its capabilities in a set of measurement on the merging of multiple independent condensates, combining all the previously described techniques. It enabled the first quantitative experimental study of the formation of supercurrents as a function of the number of condensates, which constitutes an important contribution to a detailed understanding of the Kibble-Zurek mechanism.
Fig.5: a) Illustration of the measurement. b) Probability distributions.
Fig.4: a) Optical accordion setup. b) Measured lattice spacings.
Fig.3: a) Fluorescence image. b) Radial profile of the fluorescense signal.
Fig.2: a) Typical image of the atoms. b) Density-dependent transmission.
Fig.1: Atoms loaded into optical traps tailored with a DMD.