in bulk. Scale bar is . (b) Mean square displacement of heading angle of single bacteria is plotted with time. The slope of this MSD curve is fitted with $2(1-\exp[-Dt])$, where $D$ reflects orientation fluctuation of smoothly swimming bacteria[@jain].[]{data-label="figs_diffusion"}](figureS_fluctuation.jpg)

Bacterial density measurement and image velocimetry
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To measure bacterial density, we used a mixture - 99-to-1 ratio - of two genetically modified bacteria (strain RP4979) that constitutively express fluorescent protein (either YFP or dTomato). That fluorescent labeling allows the quantitative recording of the trajectories of individual bacterial swimming in either dilute (Fig. 3 in main text) or dense suspensions (Fig. 4(a) in main text). By tracking dTomato-expressing bacteria, we can record the individual trajectories of bacteria inside collective vortical motion.

In the analysis of single bacteria and tracer particles in a suspension, they were tracked by means of a plugin of Particle Tracker 2D/3D in the Fiji(ImageJ) software. Bright-field optical imaging and video-microscopy were performed by using an inverted microscope (IX73, Olympus) with a CCD camera (DMK23G445, Imaging Source) that enables us to record bacterial collective motion at 30 frames per second. The velocity field of bacterial collective motion $\bm{v}(r,t)$ was analyzed by Particle Image Velocimetry(PIV) with Wiener filter method 