Quantum Storage of Heralded Polarization Qubits in Birefringent and Anisotropically Absorbing Materials

Storage of quantum information encoded into heralded single photons is an essential constituent of long-distance quantum communication based on quantum repeaters and of optical quantum information processing. The storage of photonic polarization qubits is, however, difficult because many materials are birefringent and have polarization-dependent absorption. Here we present a simple scheme that eliminates these polarization effects, and we demonstrate it by storing heralded polarization qubits into a solid-state quantum memory. The quantum memory is implemented with a biaxial yttrium orthosilicate (${\mathrm{Y}}_2{\mathrm{SiO}}_5$) crystal doped with rare-earth ions. Heralded single photons generated from a filtered spontaneous parametric down-conversion source are stored, and quantum state tomography of the retrieved polarization state reveals an average fidelity of $97.5\pm 0.4\%$, which is significantly higher than what is achievable with a measure-and-prepare strategy.

Figure 1

Scheme for compensating birefringence and absorption anisotropy using two identical quantum memories $M_A$ and $M_B$. (a) Light propagates along $+z$. The principal axes of the index of refraction $D_1$ and $D_2$ of each memory are orthogonal to $z$, and $M_B$ is rotated 90° around $z$ with respect to $M_A$. This arrangement creates a quantum memory that is polarization preserving and has a constant efficiency for all input polarization states. (b) Alternatively, a wave plate can be inserted between $M_A$ and $M_B$. (c) Light intensity and (d) accumulated optical phase along the two-memory arrangement for light polarized along $D_1$ or $D_2$. The total transmission and phase are the same for both components, and hence for any linear combination.

Figure 2

Measurements of (a) optical depth and (b) memory efficiency of two ${\mathrm{Nd}}^{3+}\mathrm{\text{:}}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystals without (●) and with (□) compensation scheme. Incident light is linearly polarized, and the $x$-axis indicates the angle of the polarization with respect to the $D_1$ axis of the crystals. (a) Without compensation the optical depth varies between 2.70(1) and 0.99(1), corresponding to propagation along the two optical extinction axes. With compensation the peak-to-peak variation is reduced to 16% of the mean optical depth. Lines are fits to Eq. (1). (b) Efficiency of 50 ns storage measured using laser pulses. With compensation the efficiency is almost independent of polarization.

Figure 3

Experimental setup for polarization qubit tomography. Pairs of photons are generated by spontaneous parametric down-conversion in a periodically poled KTP waveguide pumped with 4 mW of light from a continuous-wave laser at 532 nm, separated by a dichroic mirror (DM) and strongly filtered. The detection of a photon at 1338 nm on a superconducting nanowire single-photon detector heralds the presence of a single photon at 883 nm. The latter is in resonance with the crystal quantum memories $M_A$ and $M_B$ (where $M_A$ is placed above $M_B$ inside the same cryostat) and acts as a polarization qubit. The initial state of the qubit is prepared using a fiber-based polarization controller (PC) and two wave plates ($\lambda /2$ and $\lambda /4$). A half-wave plate compensates for their anisotropy. Finally, the polarization state of the retrieved photon is analyzed using two more wave plates ($\lambda /4$ and $\lambda /2$) and a polarizing beam splitter (PBS) with a silicon avalanche photo diode at each output. Another polarization controller is used to ensure that the quantum memory is always prepared with the same polarization.