Context. The prototypical low-mass young stellar object, T Tauri, is a well-studied multiple system with at least three components. Aims. We aim to explore the T Tau system with the highest spatial resolution, study the time evolution of the known components, and re-determine the orbital parameters of the stars. Methods. Near-infrared classical imaging and integral field spectrograph observations were obtained during the Science Verification of SPHERE, the new high-contrast imaging facility at the VLT. The obtained FWHM of the primary star varies between 0.050 and 0.059, making these the highest spatial resolution near-infrared images of the T Tauri system obtained to date. Results. Our near-infrared images confirm the presence of extended emission south of T Tau Sa, reported in the literature. New narrow-band images show, for the first time, that this feature shows strong emission in both the Br-{gamma} and H2 1-0 S(1) lines. Broadband imaging at 2.27 {mu}m shows that T Tau Sa is 0.92 mag brighter than T Tau Sb, which is in contrast to observations from Jan. 2014 (when T Tau Sa was fainter than Sb), and demonstrates that T Tau Sa has entered a new period of high variability. The newly obtained astrometric positions of T Tau Sa and Sb agree with orbital fits from previous works. The orbit of T Tau S (the center of gravity of Sa and Sb) around T Tau N is poorly constrained by the available observations and can be fit with a range of orbits ranging from a nearly circular orbit with a period of 475 years to highly eccentric orbits with periods up to 2.7*10^4 years. We also detected a feature south of T Tau N, at a distance of $144 pm 3$ mas, which shows the properties of a new companion.
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