We present a new technique for using a quantum memory device to perform arbitrary rotations of qubits living in the two-dimensional Hilbert space spanned by the time-bin states |early〉 and |late〉. The CRIB protocol [1, 2, 3, 4] (controlled and reversible inhomogeneous broadening) allows the quantum information encoded in a photon state to be stored in the atomic coherences of a collection of rare-earth ions in a doped crystal or optical fibre. This is achieved by artificially broadening the inhomogeneous line width of an atomic transition within the medium in a reversible manner such that all Fourier components of the input light field can be absorbed. When this is the case one can show that later reversing the applied detuning (i.e. letting Δ→−Δ) and applying a phase-matching operation allows the equations of motion for a forward-propagating pulse to be transformed into a time-reversed copy of the equations of motion for a backward-moving pulse. When done correctly this causes the atomic coherences to evolve back to their initial state and the input pulse to be re-emitted in the opposite direction.

A modification to this protocol allows an input pulse in a well-defined time bin to be recalled in a superposition of |early> and |late>, or more than two different states. We have numerically simulated the Maxwell-Bloch equations describing the interaction of a classical electric field with an ensemble of two-level systems. In the modified version of the CRIB protocol we perform the rephasing operation on the absorbing medium at different times for two spatially distinct sections. This results in two output pulses. By modifying the relative size of the two spatial sections being rephased we are able to tailor the ratio of the amplitudes of the output pulses. The time difference between the pulses is easily controlled, so by associating the first (second) pulse with the early (late) time bin we have effectively rotated the initial pulse into a superposition state with coefficients that depend on the amplitudes of the output pulses.

We investigate a number of variations on this theme including different input pulse shapes and detuning profiles. We look at different coherence times and temporal separations of the output pulses, and consider output in both the forward and backward directions. In each case the recall efficiency provides a figure of merit.