title: The X-like shaped spatiotemporal structure of the biphoton entangled state in a cold two-level atomic ensemble.
abstract: We study the spatiotemporal structure of the biphoton entangled state generated by the four-wave mixing (FWM) process in a cold two-level atomic ensemble. We analyze, for the first time, the X-like shaped structure of the biphoton entangled state and the geometry of the biphoton correlation for different lengths and densities of the cold atomic ensemble. The propagation equations of the photon pairs generated from FWM process are derived in a spatiotemporal framework. By means of the input-output relations of the propagation equations, the biphoton amplitude function is obtained in a spatiotemporal domain. In the given frequency range, the biphoton amplitude displays an X-like shaped geometry, nonfactorizable in the space-time domain. Such an X-like shaped spatiotemporal structure is caused by the phase matching and the FWM gain. The former leads to the X-like shaped envelope of the biphoton correlation, while the latter gives rise to the oscillations around the X-like shaped envelope.
authors.affiliation: Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials &Devices (SIPSE), and Guangdong Provincial Key Laboratory of Quantum Engineering &Quantum Materials, South China Normal University, Guangzhou 510006, China.
authors.forename: Dasen
authors.initials: D
authors.lastname: Zhang
authors.affiliation: Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials &Devices (SIPSE), and Guangdong Provincial Key Laboratory of Quantum Engineering &Quantum Materials, South China Normal University, Guangzhou 510006, China.
authors.forename: Zhiming
authors.initials: Z
authors.lastname: Zhang