Spectral Multiplexing for Scalable Quantum Photonics using an Atomic Frequency Comb Quantum Memory and Feed-Forward Control

Future multiphoton applications of quantum optics and quantum information science require quantum memories that simultaneously store many photon states, each encoded into a different optical mode, and enable one to select the mapping between any input and a specific retrieved mode during storage. Here we show, with the example of a quantum repeater, how to employ spectrally multiplexed states and memories with fixed storage times that allow such mapping between spectral modes. Furthermore, using a $\mathrm{Ti}:\mathrm{Tm}:{\mathrm{LiNbO}}_3$ waveguide cooled to 3 K, a phase modulator, and a spectral filter, we demonstrate storage followed by the required feed-forward-controlled frequency manipulation with time-bin qubits encoded into up to 26 multiplexed spectral modes and 97% fidelity.

Figure 1

Quantum repeater. (a) Block diagram of a section of a quantum repeater that does not employ qubit multiplexing. A source generating entangled pairs of photons (PPS) is located at the end point of each elementary link (i.e., node). One member per pair is stored in a quantum memory (QM), and the second member is sent over a “quantum channel” to the center of the link where it meets a member of an entangled pair generated at the other end of this link. The two photons’ joint state undergoes a Bell-state measurement (BSM)—comprised of a beam splitter (BS) and two single photon detectors (SPDs), and the result is communicated over a “classical channel” back to the end points to herald the establishment of entangled quantum memories by means of entanglement swapping [4, 9, 25]. Entanglement is stored until the two memories that are part of an adjacent link, are also entangled. Then, photons are recalled from neighboring memories and subjected to BSM’. This results in the establishment of entanglement across the two links, and, by continuing this procedure with other links, entanglement is established between the end points of the entire channel. (b) [(c)] Operation of a repeater node assuming temporal [spectral] multiplexing. Members of entangled photon pairs, each featuring the same spectrum [temporal profile and arrival time] but separated in time [frequency], are simultaneously stored in multimode quantum memories. A heralding (feed-forward) signal, derived from a successful BSM at the center of each elementary link indicates which of the stored photons is to be used for the remaining step of the protocol. The heralded photons are then recalled from adjacent memories such that they arrive indistinguishably at the BSM’. For temporal multiplexing, memories that allow adjusting the recall time as well as time-resolved detection are required, while for spectral multiplexing, the memories must incorporate adjustable frequency shifts (FS) and spectral filtering ($\mathrm{\text{F}}$), and the BSM must distinguish different frequency bins.

Figure 2

Simulation of spectrally multiplexed quantum repeater performance. Optimal average entanglement distribution rate as a function of total distance. We assume loss of $0.2\mathrm{dB}/\mathrm{km}$, maximally entangled photon pairs emitted with 90% probability per attempt, quantum memories with 90% efficiency and total storage bandwidth of 300 GHz, and single-photon detectors with 90% efficiency and negligible dark counts. Bicolored curves—where a change in shading indicates the addition of an elementary link—represent (a) ${10}^2$ (shown in red), (b) ${10}^3$ (shown in green), and (c) ${10}^4$ (shown in blue) spectral modes. The dotted line represents the direct transmission of members of entangled photon pairs produced at 10 GHz.

Figure 3

Schematics of the experimental setup. The output of a frequency-stabilized continuous-wave laser at 795.4 nm wavelength is amplitude modulated with an AOM and serrodyne chirped [27] over disjoint frequency intervals using a phase modulator (PM). During 5 ms the laser light creates a broadband multimode AFC (see Fig. 4) in a $\mathrm{Tm}:\mathrm{Ti}:{\mathrm{LiNbO}}_3$ waveguide located inside a 3 Kelvin cryostat and exposed to a magnetic field of 88 Gauss [11, 26]. After a 2 ms wait time, during the next 5 ms, the AOM generates, with 4 MHz repetition rate, up to 26 spectrally multiplexed pairs of 15 ns-long Gaussian-shaped pulses (pulses in the pairs are separated by 20 ns), whose relative phases and central frequencies are set using the PM. The subsequent attenuator, or beam block, reduces the mean number of photons per pulse pair to 0.5, 0.1, or zero, respectively. The resulting time-bin qubits are then sent into the waveguide, and stored for 60 ns. Frequency-selective recall is achieved by means of a second PM, combined with a monolithic cavity (MC) having 70 MHz line width [28]. Finally, the recalled photons are detected using a Si-avalanche photodiode-based single photon detector (SPD) [allowing projections onto $|e⟩$ and $|l⟩$), or a phase-stabilized Mach-Zehnder interferometer (MZI) followed by a SPD (allowing projections onto $\frac{1}{\sqrt{2}}(|e⟩\pm |l⟩)$].

Figure 4

Multimode storage and frequency selective recall. Histogram of arrival times of 26 simultaneously stored qubits, each containing 0.5 photons on average. Qubits are prepared in separate spectral modes and alternating temporal modes (i.e., $|e⟩$ and $|l⟩$), and are each recalled individually. The cavity resonance was set to 200 MHz detuning. No recall of qubits is observed in spectral modes at $\pm 150$ and $\pm 4350\mathrm{MHz}$ detunings where no AFCs were prepared. The back panel and inset show the multibinned AFC absorption profile utilized. Modulation outside of the individual combs is due to higher order effects from the phase modulation.