Large cross-phase modulation between slow co-propagating weak pulses in 87Rb

Strong optical cross-phase modulation (XPM) for weak fields is tremendously important, e.g.~for optical quantum information processing and for all-optical switches in classical communication. Several proposals based on electromagnetically induced transparency (EIT) have been brought forward, but XPM remains experimentally challenging. One problem is to achieve equal slow group velocities (double EIT) for both signal pulses to maximize the interaction time. \\ We present a scheme that exploits the best features of previous proposals and adds some new techniques, thereby optimizing the large XPM parameter. We propose a feasible procedure to prepare the atomic initial state such that double EIT with a single atomic species can be achieved, and present a specific implementation of the scheme for $^{87}$Rb with a single pump laser and a homogeneous magnetic field. Furthermore, we study the nonlinear evolution of the two weak signal pulses and present a new upper bound on the maximal XPM phase shift achievable for two Gaussian single-photon pulses.