  Young's double-slit interference experiment is central to quantum mechanics.
While it has been demonstrated that an array of atoms can produce interference
in light, it is a fundamental question to ask whether a single atom can act as
a double slit when prepared in a superposition of two separate positions.
Cohen-Tannoudji et al. [Proceedings of the Tenth International Conference on
Laser Spectroscopy, edited by M. Ducloy, E. Giacobino, and G. Camy (World
Scientific, Singapore, 1992), pp. 3-14] showed that the cross section of the
light scattered by a single atom is independent of the spatial separation. In
this work, however, we show that when a single atom tunneling in a double well
is coupled to an optical ring cavity, the interference phenomena arise if the
tunneling rate is comparable to the cavity linewidth. Being driven by an
external laser in the dispersive regime, the field emitted by the atom into the
cavity exhibits an interference pattern when varying the double-well spacing.
Super-Poissonian bunched light can also be generated near the destructive
interference. Furthermore, we show that the atomic flux of the coherent
tunneling motion generates directional cavity emission, which oscillates for
many cycles before the decoherence of the atomic motion and the decay of the
cavity photons. Our work opens ways to manipulate photons with controllable
external states of atoms for quantum information applications and use cavity
light as nondestructive measurements for many-body states of atomic systems.
