  We show how to capture a single photon of arbitrary temporal shape with one
atom coupled to an optical cavity. Our model applies to Raman transitions in
three-level atoms with one branch of the transition controlled by a (classical)
laser pulse, and the other coupled to the cavity. Photons impinging on the
cavity normally exhibit partial reflection, transmission, and/or absorption by
the atom. Only a control pulse of suitable temporal shape ensures impedance
matching throughout the pulse, which is necessary for complete state mapping
from photon to atom. For most possible photon shapes, we derive an unambiguous
analytic expression for the shape of this control pulse, and we discuss how
this relates to a quantum memory.
