Temporal Quantum-State Tomography of Narrowband Biphotons

We describe and demonstrate a quantum state tomography for measuring the complex temporal waveform of narrowband biphotons. Through six sets of two-photon interference measurements projected in different polarization subspaces, we can construct the time-frequency entangled two-photon joint amplitude and phase functions in continuous-variable time domain. For the first time, we apply this technique to experimentally determine the temporal quantum states of narrowband biphotons generated from spontaneous four-wave mixing in cold atoms, and fully confirm the theoretical predictions.