Photon storage in Lambda-type optically dense atomic media. IV. Optimal control using gradient ascent

We use the numerical gradient ascent method from optimal control theory to
extend efficient photon storage in Lambda-type media to previously inaccessible
regimes and to provide simple intuitive explanations for our optimization
techniques. In particular, by using gradient ascent to shape classical control
pulses used to mediate photon storage, we open up the possibility of high
efficiency photon storage in the non-adiabatic limit, in which analytical
solutions to the equations of motion do not exist. This control shaping
technique enables an order-of-magnitude increase in the bandwidth of the
memory. We also demonstrate that the often discussed connection between time
reversal and optimality in photon storage follows naturally from gradient
ascent. Finally, we discuss the optimization of controlled reversible
inhomogeneous broadening.