  The faithful storage of a quantum bit of light is essential for long-distance
quantum communication, quantum networking and distributed quantum computing.
The required optical quantum memory must, first, be able to receive and
recreate the photonic qubit and, second, store an unknown quantum state of
light better than any classical device. These two requirements have so far been
met only by ensembles of material particles storing the information in
collective excitations. Recent developments, however, have paved the way for a
new approach in which the information exchange happens between single quanta of
light and matter. This single-particle approach allows one to address the
material qubit and thus has fundamental advantages for realistic
implementations: First, to combat inevitable losses and finite efficiencies, it
enables a heralding mechanism that signals the successful storage of a photon
by means of state detection. Second, it allows for individual qubit
manipulations, opening up avenues for in situ processing of the stored quantum
information. Here we demonstrate the most fundamental implementation of such a
quantum memory by mapping arbitrary polarization states of light into and out
of a single atom trapped inside an optical cavity. The memory performance is
analyzed through full quantum process tomography. The average fidelity is
measured to be 93% and low decoherence rates result in storage times exceeding
180\mu s. This makes our system a versatile quantum node with excellent
perspectives for optical quantum gates and quantum repeaters.
