Atomic-resonance-enhanced nonlinear optical frequency conversion with entangled photon pairs

We theoretically study nonlinear optical frequency conversion with time-frequency entangled paired photons whose sum frequency is on two-photon resonance of an atomic ensemble. Assisted by a strong coupling laser, two paired photons with wide spectrum are converted into a single monochromatic photon. The on-resonance nonlinear process is made possible due to the electromagnetically induced transparency that not only eliminates the on-resonance absorption but also enhances the nonlinear interaction between the single photons and atoms. Compared to this quantum-nonlinear conversion, the classical corresponding single-photon counts from accidental two-photon coincidence has a wide spectrum and experiences large absorption. As a result, the system can be used as an efficient two-photon quantum correlator in which the classical accidental coincidences can be suppressed. We perform numerical simulations basing on a Rb atomic vapor cell with realistic operating parameters.

Figure 1

Schematics of nonlinear frequency conversion with entangled photons. With a monochromatic pump laser beam (${\omega }_p$), time-frequency entangled signal (${\omega }_s$) and idle (${\omega }_i$) photons are generated through spontaneous parametric down-conversion (SPDC) from a nonlinear medium (crystal), and enter a four-level atomic ensemble on two-photon resonance (${\omega }_s+{\omega }_i={\omega }_{21}$). Driven by a strong coupling laser (${\omega }_c$), the two entangled photons are converted to a single photon (${\omega }_d$) that is on resonance with the transition $|1\rangle \to |3\rangle$.

Figure 2

Rb energy level diagram for numerical simulation with degenerate signal and idle photons at 778 nm. The coupling laser is at 761 nm. The generated photons are at 795 nm.

Figure 3

(a) EIT transmission and phase matching spectrum and (b) single-photon and two-photon classical spectrum. The single-photon power spectrum has a Gaussian shape with a FWHM bandwidth of 1 THz.

Figure 4

Normalized two-photon correlation functions measured by (a) ultra-fast electronic single-photon counters and (b) the proposed nonlinear frequency convertor. The single-photon power spectrum has a Gaussian shape with a FWHM bandwidth of 1 THz. The SPDC source is operated at an output rate of 10${}^{12}$ pairs/s.

Figure 5

Quantum-to-classical ratio (QCR) of the two-photon correlation as a function of the photon pair rate. The dashed curve is for using the conventional single-photon counters and the solid curve for using the proposed technique.

Figure 6

Square-shaped normalized two-photon correlation functions measured by (a) ultra-fast electronic single-photon counters and (b) the proposed nonlinear frequency convertor. The photons have a correlation time length of 5 ps and bandwidth of 200 GHz. The SPDC source is operated at a generation rate of 10${}^{12}$ pairs/s.