No abstract

Tunnelling is one of the most paradigmatic and evocative phenomena of quantum physics, underlying processes such as photosynthesis and nuclear fusion, as well as devices ranging from SQUID magnetometers to superconducting qubits for quantum computers. The question of how long a particle takes to tunnel, however, has remained controversial since the first attempts to calculate it 1, 2 , which relied on the group delay. It is now well understood that this delay (the arrival time of the transmitted wave packet peak at the far side of the barrier) can be smaller than the barrier thickness divided by the speed of light, without violating causality. There have been a number of experiments confirming this [3][4][5][6] , and even a recent one claiming that tunnelling may take no time at all 7 . There have also been efforts to identify another timescale, which would better describe how long a given particle spends in the barrier region [8][9][10] . Here we present a direct measurement of such a time, studying Bose-condensed 87 Rb atoms tunnelling through a 1.3-µm thick optical barrier. By localizing