The interaction of a two-level atom with two light pulses which have different carrier frequencies and propagate in opposite directions is studied in the adiabatic approximation. It is shown that when there is a delay between the light pulses, the momentum of the atom changes, as a result of the interaction with the laser field, by a definite amount that depends on the amplitude of the light pulses and on the difference of their carrier frequencies. It is predicted that the momentum transfer to the atom is a step function of the amplitude of the light pulses.
We report what we call co- and counter propagating slow-light systems based on the high nonlinearity in Si lattice-shifted
photonic crystal waveguides (LSPCWs). The intense slow-light pulse, as a control pulse, efficiently generates
two-photon absorption and carrier plasma effects, which tunes the dispersion characteristics of the LSPCWs and
spectrum of copropagating or counter-propagating slow-light pulse, as a signal pulse. Using the control pulse, we
succeeded in experimentally demonstrating adiabatic wavelength conversion and its enhancement, delay tuning of up to
10 ps with a response time <10 ps, and temporal pulse compression of factor 9.9 in the signal pulse. Furthermore, we
discussed theoretically the collision and reflection of the signal pulse counterpropagating against the control pulse
through the photonic-bandgap shift, resulting in a large Doppler shift. Considering the detail of these phenomena, we
clarified the relation and difference between the adiabatic wavelength conversion, cross-phase modulation, and Doppler
shift, which have been unclear so far.
We investigate the behavior of the light pulse in $\ensuremath{\Lambda}$-type cold-atom gases with two counter-propagating control lights with equal strength by directly simulating the dynamic equations and exploring the dispersion relation. Our analysis shows that, depending on the length
L0 of the stored wave packet and the decay rate $\ensuremath{\gamma}$ of ground-spin coherence, the recreated light can behave differently. For long
L0 and/or large $\ensuremath{\gamma}$, a stationary light pulse is produced, while two propagating light pulses appear for short
L0 and/or small $\ensuremath{\gamma}$. In the $\ensuremath{\gamma}\ensuremath{\rightarrow}0$ limit, the light always splits into two propagating pulses for a sufficiently long time. This scenario agrees with a recent experiment [Y.-W. Lin et al., Phys. Rev. Lett. 102, 213601 (2009)] where two propagating light pulses are generated in laser-cooled cold-atom ensembles.