Polarization-entanglement-conserving frequency conversion of photons

Entangled photons play a pivotal role in the distribution of quantum information in quantum networks. However, the frequency bands for optimal transmission and storage of photons are often not the same. Here, we experimentally demonstrate the coherent frequency conversion of photons entangled in their polarization, a widely used degree of freedom in photonic quantum information processing. We verify the successful entanglement conversion by violating a Clauser-Horne-Shimony-Holt (CHSH) Bell inequality and fully characterize our near-perfect entanglement transfer using both state and process tomography. Our implementation is robust and flexible, making it a practical building block for future quantum networks.

Figure 1

Experimental scheme. (a) Polarization-entangled photon source. Photon pairs are created by spontaneous parametric down-conversion in a periodically poled KTiOPO${}_4$ (ppKTP) crystal, which is bidirectionally pumped by a 405-nm diode laser in a polarization-Sagnac loop [19, 20]. (b) Polarization-coherent up-conversion setup. Signal (810 nm) and pump (1550 nm) are combined with a dichroic mirror (DM) and focused into the setup with a lens (L) of $f=50$ mm. The two polarization components of the input are up-converted to 532 nm in one of two 4.3-mm-long, orthogonally oriented ppKTP crystals. The remaining 810-nm photons and 1550-nm pump light are separated from the 532-nm photons with dichroic mirrors: one in transmission and two in a z configuration for multiple reflections. Two adjustable calcite wedges (W) compensate temporal walk-off. (c) The polarization analysis (and preparation for the process tomography) is implemented with a quarter-wave plate (QWP), half-wave plate (HWP), and a polarizing element (PBS). The 532-nm photons are then coupled into a single-mode fiber and detected by a silicon avalanche photo-diode (Si-APD). The coincidences with the second 810-nm photon are identified by home-built coincidence logic.

Figure 2

Process matrix $\chi$ (Pauli-basis representation) for polarization-coherent up-conversion, characterized by an attenuated 810-nm diode laser. The different elements of $\chi$ access what kind of operation—decomposed into the Pauli operations—an input state is subject to, with the dominating element denoting the identity operation. The calculated process fidelity $\mathcal{F}$ and purity $\left(P\right)$ are $\mathcal{F}=99.23\pm 0.01\%$ and $\mathcal{P}=98.54\pm 0.01\%$. Error margins for $\mathcal{F}$ and $\left(P\right)$ are determined assuming Poissonian count statistics.

Figure 3

Reconstructed (accidental-corrected) two-qubit density matrices of entangled input states and output states. (a) Input state (810 nm, 810 nm) with a corresponding fidelity with respect to the ${\psi }^{+}$ state of ${\mathcal{F}}_{\mathrm{in}}=97.93\pm 0.03\%$. (b) Output state (810 nm, 532 nm) with ${\mathcal{F}}_{\mathrm{out}}=96.7\pm 0.2\%$. The fidelities as well as the values for the purities ($\mathcal{P}$) and tangles ($\mathcal{T}$) of the input and output states are summarized in Fig. 4. Error margins follow from Monte-Carlo simulations assuming errors assuming Poissonian count statistics.

Figure 4

Summary of the quality parameters for the accidental-corrected input states ${\rho }_{\mathrm{in}}$ (dark) and output states ${\rho }_{\mathrm{out}}$ (light): fidelities $\mathcal{F}$, purities $\mathcal{P}$, and tangle $\mathcal{T}$. Error bars were obtained from Monte-Carlo runs of the tomographic reconstruction with assumed Poissonian count statistics.