Nonclassical photon pairs are standard tools to probe and exploit the quantum realm beyond classical limit. We generate the photon pairs by using spontaneous four-wave mixing(sFWM) in cold atomic ensembles. We work with 85Rb dark-line two-dimensional (2D) magneto-optical trap (MOT) to achieve large atomic density with high OD 170.

In the theoretical study, we compare the two formalisms in the interaction and Heisenberg pictures and show that in low parametric gain regime both agree well. We extend the existing theories by taking into account the non-uniformity in the atom distribution, the pump, and the coupling laser intensity distribution in the longitudinal direction of the atomic cloud. we show that the profiles of the pump and coupling laser intensities have significant effects on the biphoton waveform. By controlling the spatial profile of the driving field, we can shape the biphoton waveform in time domain. On the other hand, the time-domain waveform of the photon pairs allows us to retrieve information on the spatial profile of the pump and coupling laser beams. Following the theory, we realize the shaping of biphoton with spatially modulated pump field experimentally.

For such a large OD, we generate the narrow-band biphotons in the group delay regime, where the two-photon temporal correlation length is determined by the group delay time taug of the slow anti-Stokes photon. The group delay time taug stems from the slow light effect in electromagnetically induced transparency (EIT), and the value is determined by OD and the coupling power. To explore the longest biphoton coherence time, we study the relationship between the correlation time and coupling power while taking into account of the finite ground state dephasing rate. With optimal experimental parameters, we achieve the coherence time for narrow-band photon pairs up to 3.28 mus.

We study the mirrorless optical parametric oscillation in cold atoms. Working with backward four-wave mixing schematics, we increase the parametric gain to get into the oscillation regime. To study the transition near the oscillation, we measure the second order auto-correlation of the field to verify its photon property.