A Single Atom Mirror for 1D Atomic Lattice Gases

We propose a scheme utilizing quantum interference to control the transport of atoms in a 1D optical lattice by a single impurity atom. The two internal state of the impurity represent a spin-1/2 (qubit), which in one spin state is perfectly transparent to the lattice gas, and in the other spin state acts as a single atom mirror, confining the lattice gas. This allows to ``amplify'' the state of the qubit, and provides a single-shot quantum non-demolition measurement of the state of the qubit. We derive exact analytical expression for the scattering of a single atom by the impurity, and give approximate expressions for the dynamics a gas of many interacting bosonic of fermionic atoms.