We study experimentally and numerically the dynamics of colloidal beads confined by a harmonic potential in a bath of swimming E. coli bacteria. The resulting dynamics is well approximated by a Langevin equation for an overdamped oscillator driven by the combination of a white thermal noise and an exponentially correlated active noise. This scenario leads to a simple generalization of the equipartition theorem resulting in the coexistence of two different effective temperatures that govern dynamics along the flat and the curved directions in the potential landscape.

The possibility of exploiting motile microorganisms as tiny propellers represents a fascinating strategy for the transport of colloidal cargoes. However, delivery on target sites usually requires external control fields to steer propellers and trigger cargo release. The need for a constant feedback mechanism prevents the design of compact devices where biopropellers could perform their tasks autonomously. Here we show that properly designed three-dimensional microstructures can define accumulation areas where bacteria spontaneously and efficiently store colloidal beads. The process is stochastic in nature and results from the rectifying action of an asymmetric energy landscape over the fluctuating forces arising from collisions with swimming bacteria. As a result, the concentration of colloids over target areas can be strongly increased or depleted according to the topography of the underlying structures. Besides the significance to technological applications, our experiments pose some important questions regarding the structure of stationary probability distributions in non-equilibrium systems.

Centrifugation is a widespread laboratory technique used to separate mixtures into fractions characterized by a specific size, weight or density. We demonstrate that centrifugation can be also used to separate swimming cells having different motility. To do this we study self-propelled bacteria under the influence of an external centrifugal field. Using dynamic image correlation spectroscopy we measure the spatially resolved motility of bacteria after centrifugation. A significant gradient in swimming-speeds is observed for increasing centrifugal speeds. Our results can be reproduced by a model that treats bacteria as "hot" colloidal particles having a diffusion coefficient that depends on the swimming speed.

Digital Holographic Microscopy allows to numerically retrieve three dimensional information encoded in a single 2D snapshot of the coherent superposition of a reference and a scattered beam. Since no mechanical scans are involved, holographic techniques have a superior performance in terms of achievable frame rates. Unfortunately, numerical reconstructions of scattered field by back-propagation leads to a poor axial resolution. Here we show that overlapping the three numerical reconstructions obtained by tilted red, green and blue beams results in a great improvement over the axial resolution and sectioning capabilities of holographic microscopy. A strong reduction in the coherent background noise is also observed when combining the volumetric reconstructions of the light fields at the three different wavelengths. We discuss the performance of our technique with two test objects: an array of four glass beads that are stacked along the optical axis and a freely diffusing rod shaped E.coli bacterium.