Measuring the Biphoton Temporal Wave Function with Polarization-Dependent and Time-Resolved Two-Photon Interference

We propose and demonstrate an approach to measuring the biphoton temporal wave function with polarization-dependent and time-resolved two-photon interference. Through six sets of two-photon interference measurements projected onto different polarization subspaces, we can reconstruct the amplitude and phase functions of the biphoton temporal waveform. For the first time, we apply this technique to experimentally determine the temporal quantum states of the narrow-band biphotons generated from the spontaneous four-wave mixing in cold atoms.

Figure 1

Experimental setup for measuring the temporal wave function of narrow-band biphotons generated from backward-wave SFWM in the right-angle confirmation.

Figure 2

Degenerate biphoton (${\delta }_{\omega }=0$) waveform with Rabi oscillation. (a) Two-photon coincidence counts before the BS. (b) The measured combined phase-difference function $\mathrm{\Xi }(\tau )$ for $T_l=5.8\mathrm{ns}$. (c) The reconstructed phase $\varphi (\tau )$.

Figure 3

Nondegenerate biphoton (${\delta }_{\omega }=2\pi \times 43\mathrm{MHz}$) waveform with Rabi oscillation. (a) Two-photon coincidence counts before the BS. (b) The measured combined phase-difference function $\mathrm{\Xi }(\tau )$ for $T_l=5.8\mathrm{ns}$. (c) The reconstructed phase $\varphi (\tau )$.

Figure 4

Nondegenerate biphoton (${\delta }_{\omega }=2\pi \times 43\mathrm{MHz}$) waveform with overdamped Rabi oscillation. (a) Two-photon coincidence counts before the BS. (b) The measured combined phase-difference function $\mathrm{\Xi }(\tau )$ for $T_l=5.8\mathrm{ns}$. (c) The reconstructed phase $\varphi (\tau )$.