Engineering Biphoton Wave Packets with an Electromagnetically Induced Grating

We propose to shape biphoton wave packets with an electromagnetically induced grating in a four-level double-$\mathrm{\Lambda }$ cold atomic system. We show that the induced hybrid grating plays an essential role in directing the new fields into different angular positions, especially to the zeroth-order diffraction. A number of interesting features appear in the shaped two-photon waveforms. For example, broadening or narrowing the spectrum would be possible in the proposed scheme even without the use of a cavity.