Quantum Storage of a Photonic Polarization Qubit in a Solid

We report on the quantum storage and retrieval of photonic polarization quantum bits onto and out of a solid state storage device. The qubits are implemented with weak coherent states at the single photon level, and are stored for a predetermined time of 500 ns in a praseodymium doped crystal with a storage and retrieval efficiency of 10%, using the atomic frequency comb scheme. We characterize the storage by using quantum state tomography, and find that the average conditional fidelity of the retrieved qubits exceeds 95% for a mean photon number $\mu =0.4$. This is significantly higher than a classical benchmark, taking into account the Poissonian statistics and finite memory efficiency, which proves that our crystal functions as a quantum storage device for polarization qubits. These results extend the storage capabilities of solid state quantum light matter interfaces to polarization encoding, which is widely used in quantum information science.

Figure 1

(a) Experimental setup. The preparation beam and the qubit beam are derived from the same laser at 606 nm. Both beams are amplitude and frequency modulated using an acousto-optic modulator (AOM). The polarization of the qubit beam can be set arbitrarily with a half wave plate (HWP) and a quarter wave plate (QWP). The qubit beam is attenuated down to the single photon level using neutral density filters (NDF). The two beams are recombined at a beam splitter (BS) and sent to the storage device which is composed of the crystal, two beam displacers (BD) and two HWP. The light released by the crystal is then sent to a polarization analyzer, before being detected with a single photon detector (SPD). The two mechanical shutters (S1 and S2) are used to suppress optical noise from the preparation beam and to protect the SPD. (b) Storage and retrieval of a weak $|V⟩$ qubit with duration 140 ns and $\mu =0.4$. The temporal histogram of the detection without (dotted line, through a transparency window) and with (solid line) AFC is shown. The dashed lines around the AFC echo show the detection window. Inset: Level scheme of ${\mathrm{Pr}}^{3+}\mathrm{\text{:}}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ with the dashed arrows showing the relevant transition for photon absorption and reemission.

Figure 2

(a) Measured detection probability ($p_{\det }$) as a function of the polarizer angle, for $|V⟩$ (filled circles) and $|D⟩$ (open circles) input polarization qubits, with $\mu =0.4$. The fitted raw visibilities are $(97\pm 0.5)\%$ and $(83\pm 2)\%$, respectively. (b) $p_{\det }$ as a function of polarization angle for $|R⟩$ polarization qubit input, with (filled squares, $(89\pm 2)\%$) and without (open squares, $(15\pm 3)\%$) QWP inserted before the polarizer.

Figure 3

Quantum state tomography. Reconstructed density matrices of the retrieved qubits for $|H⟩$, $|D⟩$ and $|R⟩$ input qubits, with $\mu =0.4$. No background has been subtracted.

Figure 4

Average fidelity measured as a function of the mean number of photon per pulse $\mu$. The fidelity is measured by quantum state tomography and is the average of 3 input states $|V⟩$, $|D⟩$, and $|R⟩$. Filled circles are experimental data without any background subtraction. Empty squares correspond to dark count subtracted fidelities. The error takes into account statistical uncertainty of photon counts, technical errors and standard deviation of fidelities for the 3 polarizations. The various lines correspond to classical thresholds for different situations. The horizontal line is the limit of $2/3$ for single qubits ($N=1$). The dashed-dotted line corresponds to Eq. (1) where the Poissonian distribution of photon number is taken into account. Finally, the two other lines correspond to the cases where the finite storage efficiency is taken into account. The solid line corresponds to $\eta =(10\pm 2)\%$. Measured ${\eta }_M$ are between 8 and 10% for all points. The dashed line corresponds to $\eta ={\eta }_M{\eta }_t{\eta }_D=2\%$. For $\mu >1$, an additional ND filter is placed before the detector to avoid saturation effects.