Direct Generation of Narrow-band Hyperentangled Photons

In quantum communication and photonic quantum information processing, the requirement of quantum repeaters and quantum memory often imposes a strict bandwidth prerequisite for the entangled photons. At the same time, there is ever more increasing demand for entangling more degrees of freedom, i.e., hyperentanglement, for a photon pair. In this Letter, we report the direct generation of narrow-band orbital angular momentum (OAM) and polarization hyperentangled photons from cold atoms. The narrow-band photon pair is naturally entangled in polarization and OAM, in addition to time-frequency, degrees of freedom due to spin and orbital angular momentum conservation conditions in the spontaneous four-wave mixing process in a cold atom ensemble. The narrow-band hyperentangled photon pair source reported here is expected to play important roles in quantum memory-based long-distance quantum communication.

Figure 1

System schematics. (a) Experimental setup for creation and detection of the hyperentangled state. WP is the wave plate, PBS is the polarization beam splitter, VPP is the vortex phase plate, FP is the Fabry-Perot cavity, SPD is the single-photon detector, and TCSPC is the time-correlated single-photon counting module. Coupler is the combination of objective lens and single mode fiber. In the inset, we show the phase pattern of the VPPs. Pa, Pb, Pc, and Pd are in sequence used to measure $|G⟩$, $|R⟩$, $1/\sqrt{2}(|G⟩+|R⟩)$ and $1/\sqrt{2}(|G⟩-i|R⟩)$ modes, see text for details. (b) The energy level diagram for SFWM.

Figure 2

Energy level diagrams and transition paths at different polarization configurations in SFWM when coupling and pump beam are with the polarization ${\sigma }^{+}$ and ${\sigma }^{-}$, respectively. (a) For ${\sigma }^{-}$ polarized Stokes and ${\sigma }^{+}$ polarized anti-Stokes photons. (b) For ${\sigma }^{+}$ polarized Stokes and ${\sigma }^{-}$ polarized anti-Stokes photons. Solid, double solid, dashed, and double dashed lines are transitions for the pump, coupling, Stokes photon, and anti-Stokes photons, respectively.

Figure 3

Reconstructed two-photon polarization state ${\rho }_1$. The real and imaginary parts are shown in (a) and (b), respectively.

Figure 4

Reconstructed two-photon OAM state ${\rho }_2$. The real and imaginary parts are shown in (a) and (b), respectively.