Narrowband biphotons with polarization-frequency-coupled entanglement

We demonstrate the generation of narrowband biphotons with polarization-frequency-coupled entanglement from spontaneous four-wave mixing in cold atoms. The coupling between polarization and frequency is realized through a frequency shifter and linear optics. When the polarization-frequency degrees of freedom are decoupled, it is robust to create polarization and frequency Bell states, confirmed by the polarization quantum-state tomography and the two-photon temporal quantum beating. Making use of the polarization-frequency coupling to transfer polarization phase retardation to the entangled frequency modes, we produce a frequency Bell state with tunable phase difference between its two bases.

Figure 1

(a) Experimental schematic of narrowband biphotons generation and detection with polarization-frequency-coupled entanglement. The photon pairs are produced from SFWM in cold ${}^{85}\mathrm{Rb}$ atoms. (b) ${}^{85}\mathrm{Rb}$ atomic energy level diagram. (c) Two-photon coincidence counts before the BS as a function of relative time delay between the ports 1 and 2.

Figure 2

Polarization entanglement under the decoupled condition $\delta =0$. (a) Polarization correlation between the paired photons. The coincidence counts are integrated over a 90 ns coincidence window that covers the entire biphoton wave packet. The polarization angles of the linear polarizer $P_3$ are fixed at $0^{\circ }$ and $-{45}^{\circ }$ to the horizontal axis for the circular (red) and square (blue) experimental data, respectively. (b) Real and imaginary parts of the polarization state density matrix reconstructed from the polarization quantum-state tomography.

Figure 3

Frequency entanglement under the decoupled condition $P_1=P_2=P_0$. (a) Biphotons wave form before the BS. (b) Two-photon interference coincidence counts measured at the output ports 3 and 4 of the BS. (c) Normalized two-photon beating signal.

Figure 4

Two-photon beating for varying phase difference $\theta$ of the frequency-entangled state $\frac{1}{\sqrt{2}}\left(|{\omega }_s+\delta ,{\omega }_{as}\rangle +e^{i\theta }|{\omega }_s,{\omega }_{as}+\delta \rangle \right)$: (a) $\theta =0$, (b) $\theta =\pi /2$, (c) $\theta =\pi$, and (d) $\theta =3\pi /2$.