Single-atom mirror for one-dimensional atomic lattice gases

We propose a scheme utilizing quantum interference to control the transport of atoms in a one-dimensional 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 one to ``amplify'' the state of the qubit, and provides a single-shot quantum nondemolition 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 of a gas of many interacting bosonic or fermionic atoms.