Storage of polarization-entangled THz-bandwidth photons in a diamond quantum memory

Bulk diamond phonons have been shown to be a versatile platform for the generation, storage, and manipulation of high-bandwidth quantum states of light. Here we demonstrate a diamond quantum memory that stores, and releases on demand, an arbitrarily polarized $\sim 250$ fs duration photonic qubit. The single-mode nature of the memory is overcome by mapping the two degrees of polarization of the qubit, via Raman transitions, onto two spatially distinct optical phonon modes located in the same diamond crystal. The two modes are coherently recombined upon retrieval and quantum process tomography confirms that the memory faithfully reproduces the input state with average fidelity $0.784\pm 0.004$ with a total memory efficiency of $(0.76\pm 0.03)\%$. In an additional demonstration, one photon of a polarization-entangled pair is stored in the memory. We report that entanglement persists in the retrieved state for up to 1.3 ps of storage time. These results demonstrate that the diamond phonon platform can be used in concert with polarization qubits, a key requirement for polarization-encoded photonic processing.

Figure 1

(a) Experimental setup. Pulses for the read, write, and photon source pump originate from a Ti:sapphire oscillator. Photon pairs (signal, herald) are generated via SPDC pumped by the second harmonic (SHG) of the laser and spatially filtered in single-mode fiber (SMF). A polarization qubit is prepared in the signal arm (blue), and separated into spatial modes, $|0\rangle$ and $|1\rangle$, by a polarizing beam displacer (PBD) and sent to the memory. (For entangled photon storage the signal preparation step is removed.) Read and write pulses are prepared in displaced Mach–Zehnder and Michelson interferometers (not shown), and are overlapped with $|0\rangle$ and $|1\rangle$ modes on a dichroic mirror (DC). After retrieval, half-wave plates (HWPs) and quarter-wave plates (QWPs) in each mode correct polarization, the two spatial modes are recombined by using a second beam displacer, and phase rotations are corrected with a QWP-HWP-QWP combination. The polarization is analyzed by a HWP, a QWP, and polarizing beam splitter (PBS). After an interference filter (IF) coincident detections with the herald mode are counted. (b) $\mathrm{\Lambda }$-level diagram for memory process in diamond. Input and write fields transition the crystal from its ground state $|\text{g}\rangle$ to the optical phonon level $|\text{s}\rangle$; read and output fields drive the reverse transition. Both frequencies are far detuned from the conduction band $|\text{c}\rangle$. (c) A polarization qubit $\rho$ is converted to spatial modes $|0\rangle$ and $|1\rangle$ by a beam displacer. Each mode is focused onto the diamond and stored for time $\tau$ in the diamond memory. After retrieval the two modes are recombined to form a polarization qubit.

Figure 2

(a) Measured herald-signal (blue) coincidences after retrieval, where the input state is $|\text{0}\rangle$ and the output is projected onto $|\text{0}\rangle$. Error bars show one standard deviation assuming Poissonian noise. Coincidences due to noise photons (red), i.e., when there is no input signal, are also shown. An exponential decay function $a+b{e}^{-\tau /{\tau }_{\text{m}}}$ (dashed) is fit to the data yielding a decay time of ${\tau }_{\text{m}}=3.5$ ps. (b) Average fidelity of the memory as a function of storage time. Error bars, estimated using Monte Carlo simulations, are too small to be seen on this scale. The memory operates above the $2/3$ bound for 3 ps, over 11 durations of the 270 fs input photon (shown for reference). The average fidelity for the memory model, $[1+p(\tau \left)\right]/2$, is also plotted (dashed).

Figure 3

Real and imaginary parts of ${\chi }_M$, the reconstructed process matrix for the memory in the Pauli operator basis $\{\mathbb{1},X,Y,Z\}$. Red (blue) corresponds to positive (negative) values. The process fidelity [23, 24] with the ideal memory (dashed black) is $0.677\pm 0.006$ at its peak, corresponding to an average fidelity of $0.784\pm 0.004$.

Figure 4

Real parts of the reconstructed (a) input and (b) output two-qubit density matrices. The input state has $0.939\pm 0.001$ fidelity with $|{\mathrm{\Phi }}^{+}\rangle$, whereas the state output from the quantum memory has $0.562\pm 0.007$ fidelity with $|{\mathrm{\Phi }}^{+}\rangle$ and $0.764\pm 0.005$ with the input state. (c) Fidelity of the output state with $|{\mathrm{\Phi }}^{+}\rangle$ (blue dots, left axis), and with the input state (red dots, right axis), as a function of storage time. (d) Concurrence of the output state (dots) and for a Werner state (dashed) as a function of storage time. Entanglement persists for up to 1.3 ps of storage.