Single-photon synchronization with a room-temperature atomic quantum memory

Multi-photon states are an important resource for photonic quantum information processing, with potential applications in quantum computation, communication, and metrology [1, 2, 3, 4]. It is beneficial that these photons interact coherently with atomic ensembles, to enable the implementation of deterministic two-photon gates [5] and quantum repeaters for long-distance communication [6]. Efficient, well-established, room-temperature platforms for generating such photons are based on parametric processes such as spontaneous parametric down-conversion (SPDC) and four-wave mixing (FWM) [7]. These processes give rise to stochastic emission of photon pairs and are therefore utilized as heralded single-photon sources [8, 9, 10, 11]. However, they are probabilistic, rendering the construction of larger multi-photon states exponentially slow [12]. At present, the demonstrated rate for generating a 12-photon entangled state from six stochastic emission events is one per hour [13].

The exponential scaling of the rate with the number of photons $N$ can be mitigated by using quantum memories to synchronize the probabilistically generated photons [12]. Particularly, the quantum memory can support a time-multiplexing scheme, generating a string of quasi-deterministic photons at pre-determined clock cycles [14, 15, 16]. Alternatively, $N$ stochastic photon sources with $N-1$ memories can be used to generate a synchronous $N$-photon state [12, 17]. Most works focus on $N=2$, and we do so as well.

For $N=2$, we identify several key metrics. The first is the rate enhancement factor $\zeta={R_{\mathrm{sync}}}/{R_{\mathrm{stoc}}}$, which is the accomplishment of the synchronization, the ratio between the detection rate of photon pairs after the synchronization ${R_{\mathrm{sync}}}$ compared to the stochastic (accidental) pair detection rate before synchronization ${R_{\mathrm{stoc}}}$. The second is ${R_{\mathrm{sync}}}$, which should be high for practical applications. A third metric is the anti-bunching of the synchronized photons ${g^{(2)}_{\mathrm{h}}}$, which is the normalized autocorrelation of the retrieved signal field conditioned on heralding. Ideally, ${g^{(2)}_{\mathrm{h}}}=0$, and any undesired multi-photon component, e.g., due to noise, increases ${g^{(2)}_{\mathrm{h}}}$.

There are two types of memories: those containing an internal source [18, 19, 20], and input-output memories accepting photons from outside [21, 22, 23]. The natural advantage of input-output memories is that they can be used to synchronize and delay photons that have already undergone some processing, including photons that are part of larger entangled states. Photon synchronization has been demonstrated with cold [24, 25, 26, 27] and hot [28] atomic ensembles, employing internal-source memories [24, 25, 26, 28] and input-output memories [27]. However, all these demonstrations suffer from a low photon-pair synchronization rate [${R_{\mathrm{sync}}}<1$ counts per second (cps)] and moderate photon antibunching (${g^{(2)}_{\mathrm{h}}}>0.15$). For a comparison of different experiments, see Supplemental Material (SM).

A successful, competing approach to atomic memories uses all-optical setups, namely cavities [29, 30] and storage loops [14, 15, 17, 16, 31, 32, 33]. Cavity systems have achieved good performance with narrowband photons, $\zeta=25$ and ${R_{\mathrm{sync}}}=90$ cps [30], but these are internal-source systems. Storage loops, which are input-output systems, have reached $\zeta=30$ and ${R_{\mathrm{sync}}}=450$ cps with broadband SPDC photons [17, 16, 32] but inferior performance with narrowband photons [31]. Notably, interfacing the broadband photons generated from SPDC with atomic ensembles remains an outstanding challenge.

Here we demonstrate for the first time single-photon synchronization using an input-output memory that combines substantial rate enhancement $10\leq\zeta\leq 30$, high pair detection rates ${R_{\mathrm{sync}}}\leq 1200$ cps, low-noise operation with ${g^{(2)}_{\mathrm{h}}}=0.023$, and compatibility with atomic ensembles. We achieve these at room temperature by employing the ladder orbital scheme $|5S_{1/2}\rangle\rightarrow|5P_{3/2}\rangle\rightarrow|5D_{5/2}\rangle$ in rubidium vapor for the photon source [34, 35, 36] and for the quantum memory [37, 38]. This scheme has three main benefits. First, the all-orbital fast ladder memory (FLAME) provides high-bandwidth operation, low noise, and high end-to-end memory efficiency [39, 37, 38] which are key for high-rate single-photon synchronization. Second, the small wavelength mismatch within the two-photon transition enables a nearly Doppler-free operation and thus a long coherence time between the ground and doubly-excited state. This provides a memory lifetime of over $100$ ns [38] and single-photon generation with high rate and low noise [34, 35, 36]. Third, by employing the same level scheme for the photon source and quantum memory, the generated photons are inherently compatible with the memory, enabling an end-to-end memory efficiency of ${\eta_{\mathrm{e2e}}}=25\%$. This also maintains the indistinguishability of the synchronized photons, as quantified by the Hong-Ou-Mandel (HOM) interference visibility $V_{\text{sync}}=76\%$.

Synchronization scheme.— The synchronization experiment comprises a spatially-multiplexed single-photon source, a quantum memory, and electronic triggering of the memory operation, as shown schematically in Fig. 1. The photon source is based on FWM in rubidium vapor with two continuous-wave pump fields [35, 36]. The pump fields, at wavelengths of 780 nm and 776 nm, counter-propagate through an isotopically purified ${}^{87}\text{Rb}$ vapor cell and excite the $|5S_{1/2},F=2\rangle\rightarrow|5P_{3/2},F=3\rangle$ and $|5P_{3/2},F=3\rangle\rightarrow|5D_{5/2},F=4\rangle$ transitions, respectively. The detection of a spontaneously emitted idler photon heralds the generation of a collective state comprising a single $|5P_{3/2}\rangle$ excitation that is shared among all atoms, and the signal photon emission to the ground state is thus collectively enhanced into the phase-matched direction [40]. We utilize the cylindrical symmetry of the phase-matching condition to set collection channels on both sides of the optical axis, effectively realizing two sources in the same vapor cell. We denote the generated photons in channel $j$ as idler-$j$ and signal-$j$ ($j=1,2$). Additional details on the photon source are given in SM and in Refs. [35, 36].

The quantum memory is based on the FLAME scheme in ${}^{87}\text{Rb}$ vapor [37, 38]. Initially, the atoms in the memory cell are optically pumped to the maximal spin state. An input signal-1 photon, which couples to the $|5S_{1/2},F=2,m_{F}=2\rangle\rightarrow|5P_{3/2},F=3,m_{F}=3\rangle$ transition, is stored on the doubly-excited state $|5D_{5/2},F=4,m_{F}=4\rangle$ by sending the first (storage) control pulse. At a controllable time later, a second (retrieval) control pulse releases the signal-1^′ photon from the memory (1^′ marks post-memory). We use an auxiliary dressing field (not shown in Fig. 1) that weakly couples the storage state $|5D_{5/2}\rangle$ to a high-lying orbital in order to counteract the residual Doppler broadening of the two-photon transition [41] and prolong the memory lifetime [38]. The overall transmission of the memory module from the input fiber to the output fiber is $T=68\pm 2\%$ (including the 4% loss on exiting the input fiber). Further details on the memory are given in SM and in Ref. [38].

The detection of idler photons triggers digital delay generators (DDG) that set off the control pulses for the memory via free-space Pockels cells (PCs). DDG-1, triggered by idler-1, sends a control pulse that stores the heralded signal-1 in the memory. Subsequently, DDG-2, triggered by idler-2, sends a second control pulse that retrieves signal-1^′. This protocol synchronizes signal-1^′ and signal-2. We find that the memory efficiency is optimal when the control field is on resonance, indicating that signal-1 is emitted from the source on resonance, as expected [36]. As our PCs’ maximal average repetition rate is limited to $3\times 10^{5}$ operations per second, we devise a logical scheme that operates them only if idler-1 and idler-2 were both detected within a 100-ns time window, set by the memory lifetime. Details on the electronic triggering, timing sequence, and fiber routing are given in SM.

Storage and retrieval of heralded single photons.— We begin by characterizing the storage and retrieval of signal-1. Figure 2(a) shows the count histogram [signal-idler correlation $G_{\text{si}}(\tau)$] for a storage time of $t=20$ ns. We compare the histogram of signal-1 (i.e. directly after the photon source) to that of signal-1^′ (i.e. after storage and retrieval in the memory, including the overall transmission of the memory module). The 3.5-ns-long shaded areas indicate the integration windows used for calculating ${\eta_{\mathrm{e2e}}}$, ${g^{(2)}_{\mathrm{h}}}$, ${R_{\mathrm{stoc}}}$, ${R_{\mathrm{sync}}}$, and $V_{\text{sync}}$; This window captures over $95\%$ of the pulse energy.

The memory efficiency ${\eta_{\mathrm{e2e}}}$ versus the storage time $t$ is shown in Fig. 2(b). Here, we directly measure the end-to-end efficiency by connecting the optical fiber of signal-1 either to the memory input fiber ($98\pm 1\%$ coupling) or directly to the detector input fiber ($92\pm 1\%$ coupling). Comparing between the detection rates of signal-1 and signal-1^′, after correcting for the different couplings, provides ${\eta_{\mathrm{e2e}}}$. Note particularly that ${\eta_{\mathrm{e2e}}}$ includes all fiber/free-space couplings. We measure ${\eta_{\mathrm{e2e}}}(t=12\text{ ns})=24.3\pm 0.8\%$. By fitting the data to a decoherence model $\eta(t)=\eta(0)e^{-t^{2}/2\tau_{\sigma}^{2}-t/\tau_{\gamma}}$ with homogeneous ($\tau_{\gamma}$) and inhomogeneous ($\tau_{\sigma}$) decoherence times, we extract the zero-time memory efficiency ${\eta_{\mathrm{e2e}}}(0)=26.2\pm 0.5\%$. The memory $1/e$ lifetime is $\tau_{s}=114\pm 2$ ns. Here the errors are 1 standard deviation (s.d.) of the fit uncertainty. Given the overall transmission $T$, the memory internal efficiency, comprising only the mapping of the light to and from the atoms, is $\eta_{\text{int}}(0)=38.4\pm 1.1\%$.

We verify that the memory preserves the quantum statistics ${g^{(2)}_{\mathrm{h}}}\ll 1$ of the stored single photons, as shown in Fig. 2(c). For $t=20$ ns, the multi-photon component of signal-1^′ is ${g^{(2)}_{\mathrm{h}}}=0.023\pm 0.001$, which is higher than ${g^{(2)}_{\mathrm{h}}}=0.0126\pm 0.0002$ of signal-1 but still at the few-percent level.

The increase in ${g^{(2)}_{\mathrm{h}}}$ is due to noise photons originating in either the memory or the source. In our system, the former is negligible: the memory generates only $\nu=(1.7\pm 0.2)\times 10^{-5}$ noise photons per operation. These photons govern the short-time signal-to-noise ratio $\text{SNR}=\eta_{\text{h}}{\eta_{\mathrm{e2e}}}(0)/\nu=3100\pm 400$, where $\eta_{\text{h}}=20\%$ is the heralding efficiency of the source, and indeed $\text{SNR}^{-1}\ll{g^{(2)}_{\mathrm{h}}}$. Therefore, we attribute the increase in ${g^{(2)}_{\mathrm{h}}}$ predominantly to noise photons arriving from the source at the time of retrieval and detected in coincidence with signal-1^′. The dominant contribution comes from photons that scatter directly from the continuous, off-resonant, 780-nm pump field, which are transmitted well through the memory module. Further increase of ${g^{(2)}_{\mathrm{h}}}(t)$ at larger $t$ is explained solely by the decrease of ${\eta_{\mathrm{e2e}}}(t)$. Our model of this mechanism, shown in Fig. 2(c) and detailed in SM, agrees well with the data.

Photon synchronization.— We now turn to demonstrate the synchronization of photon pairs using the memory. Figure 3(a) shows temporal profiles of the retrieved signal-1^′ photons (signal-1^′-idler-2 correlation conditioned on memory operation, $G_{\text{s}{1^{\prime}}\text{i}2}$) in comparison to the profile of signal-2 (signal-2-idler-2 correlation, $G_{\text{s2i2}}$) for varying timing settings. Note that the data do not correspond to a specific memory time $t$ but rather represent an average over $0<t\leq 100$ ns, stochastically ‘sampled’ by the regular operation of the synchronization protocol. We control the exact relative timing $\Delta t$ between signal-1^′ and signal-2 by electronically tuning the trigger delay, which controls the memory retrieval time. Figure 3(a) demonstrates, for arbitrary 500-ps intervals, our capability of on-demand, continuous tuning of the retrieval time.

To optimize the relative timing and to characterize the fidelity of the synchronized photons, we perform HOM interference measurements [42]. These measurements attest to the indistinguishability of the synchronized photon pair. Figure 3(b) shows the HOM correlation of signal-1^′ and signal-2 for varying triggering delays. The HOM visibility (the interference contrast), quantifying the indistinguishability, is $V_{\text{sync}}=76\pm 2\%$. We use the position of the minimum to define $\Delta t=0$ and to set the optimal delays in the system. For reference, we show in Fig. 3(b) the HOM measurement of accidental pairs without the memory, exhibiting $V_{\text{stoc}}=88\pm 2$%. Notably, the acquisition time per data point for synchronized pairs is 100 times shorter than for accidental pairs, illustrating the importance of synchronization for efficiently manipulating multi-photon states.

Finally, we show the merit of synchronization in terms of the enhanced two-photon coincidence rate ${R_{\mathrm{sync}}}$ in Fig. 4(a). We study ${R_{\mathrm{sync}}}$ as a function of the heralded single-photon rate $R_{1}$, which we control by tuning the strength of the pumps in the source module. We cover the range $50<R_{1}<440$ kilo-cps (kcps), for which the accidental coincidence rates are $1.4<{R_{\mathrm{stoc}}}<115$ cps. Here, we consider an accidental coincidence if idler-1 and idler-2 are detected within $\pm 300$ ps of each other. This time interval is chosen based on the HOM correlation measurement, which exhibits $V_{\text{stoc}}\geq 75\%$ within $\pm 300$ ps around the minimum (this is a conservative choice, generous in terms of ${R_{\mathrm{stoc}}}$). As shown in Fig. 4(a), the coincidence rates after synchronization grow to $44<{R_{\mathrm{sync}}}<1200\pm 10$ cps, a substantial enhancement compared to ${R_{\mathrm{stoc}}}$.

The rate enhancement $\zeta={R_{\mathrm{sync}}}/{R_{\mathrm{stoc}}}$ is shown in Fig. 4(b). The maximal enhancement $\zeta=28.6\pm 1.8$ is obtained at low $R_{1}$. As $R_{1}$ increases, the system is triggered more often, and each triggering event is followed by $\sim 1~{}\mu$s during which the memory cannot handle additional photons (see SM for details). This leads to technical saturation of the system, which we quantify by the relative memory downtime, shown as top axes in Fig. 4. A second issue occurring at high $R_{1}$ is a moderate increase of ${g^{(2)}_{\mathrm{h}}}$ and a corresponding decrease of $V_{\text{sync}}$ (see SM). We attribute this partially to a degradation of the pulses generated by the PCs at a high triggering rate. Nevertheless, even at the highest rate, we obtain a tenfold increase in the pair coincidence rate and a non-classical HOM visibility $V_{\text{sync}}>50\%$.

The rates of accidental and synchronized photon pairs and their dependence on the rate of single photons can be calculated from the parameters of the source, memory, and electronics, all of which we have independently characterized. Our model, based solely on these parameters without fitting (see SM for details), is presented by the solid lines in Fig. 4. The model correctly predicts ${R_{\mathrm{sync}}}$ and ${R_{\mathrm{stoc}}}$ and confirms that the decrease of $\zeta$ with $R_{1}$ is due only to the memory downtime. We attribute the slight deviation of the model from the data at large $R_{1}$ to the PCs’ pulse degradation noted above.

Discussion.— There are several factors limiting the increase of the two-photon coincidence rate. The main ones are the end-to-end efficiency of the memory, the limited operation rate of the PCs, and the heralding efficiency of the photon source. All these factors can be improved.

First, as discussed in Ref. [38], practicable technical improvements of the memory module can increase the internal memory efficiency to $65$%. This, in addition to raising the setup transmission by anti-reflection coating of the optical fiber-to-free-space interfaces, will substantially raise the end-to-end efficiency. Second, the heralding efficiency of the photon source can be increased by using etalon filters to block the direct scattering of photons from the pump fields into the idler modes. Third, the PCs can be replaced by an amplitude electro-optic modulator seeding a tapered amplifier [23]. This will enable both a higher repetition rate and a higher memory efficiency by optimizing the control temporal shape to that of the signal photons [43, 44].

In conclusion, we demonstrate synchronization of single photons with a high rate and low noise using a quantum memory and a photon source, both based on a ladder-level scheme in rubidium vapor. Our synchronized photons are well-suited for quantum information protocols requiring efficient interaction with atomic ensembles, such as Rydberg-mediated deterministic two-photon gates. The scheme presented here can be used to efficiently generate synchronous few-photon states, and, with feasible improvements, larger multi-photon states.

We acknowledge financial support from the Israel Science Foundation, the US-Israel Binational Science Foundation (BSF) and US National Science Foundation (NSF), the Minerva Foundation with funding from the Federal German Ministry for Education and Research, the Estate of Louise Yasgour, and the Laboratory in Memory of Leon and Blacky Broder.

Supplementary material

The supplementary material contains the following sections:

• •

  S1. Comparison of photon synchronization experiments

• •

  S2. Experimental setup

  • –

    S2.1. Photon source

  • –

    S2.2. Memory

  • –

    S2.3. Electronics and timing

  • –

    S2.4. Optical fibers and photon detection

• •

  S3. Model for photon coincidence rate

• •

  S4. Model for ${g^{(2)}_{\mathrm{h}}}$

• •

  S5. Data analysis

• •

  S6. Additional experimental data