Single-Photon Storage in a Ground-State Vapor Cell Quantum Memory

Interfaced single-photon sources and quantum memories for photons together form a foundational component of quantum technology. Achieving compatibility between heterogeneous, state-of-the-art devices is a long-standing challenge. We built and successfully interfaced a heralded single-photon source based on cavity-enhanced spontaneous parametric down-conversion in ppKTP and a matched memory based on electromagnetically induced transparency in warm $^{87}$Rb vapor. The bandwidth of the photons emitted by the source is 370 MHz, placing its speed in the technologically relevant regime while remaining well within the acceptance bandwidth of the memory. Simultaneously, the experimental complexity is kept low, with all components operating at or above room temperature. Read-out noise of the memory is considerably reduced by exploiting polarization selection rules in the hyperfine structure of spin-polarized atoms. For the first time, we demonstrate single-photon storage and retrieval in a ground-state vapor cell memory, with $g_{c,\text{ret}}^{(2)}=0.177(23)$ demonstrating the single-photon character of the retrieved light. Our platform of single-photon source and atomic memory is attractive for future experiments on room-temperature quantum networks operating at high bandwidth.


I. INTRODUCTION
Quantum memories combined with single photons from high quality sources are versatile and indispensable building blocks across the fields of quantum communication and information. They are at the heart of each node and interconnect in visions of a quantum internet [1,2], and central to the standard paradigm of quantum repeaters [3][4][5]. They can be used to synchronize probabilistic gate operations and sources [6,7], and can even improve the indistinguishability of photons emitted by quantum dots through filtering [8]. Further prospective applications include linear optical quantum computing, metrology, and photon detection [9,10]. These applications put different requirements on a memory, calling for a quantitative assessment of memory performance with numerous figures of merit [11], including fidelity, efficiency, storage time, bandwidth, and various compatibility parameters.
Memories implemented in the ground state of roomtemperature atomic vapors perform well in terms of fidelity, efficiency, storage times, and bandwidth [12][13][14][15]. Moreover, they are compatible with high quality singlephoton sources based on spontaneous parametric downconversion [15,16] or semiconductor quantum dots [17][18][19][20]. Together with their technological simplicity, this renders atomic vapor cells a promising memory system for quantum networks, potentially even ones deployed in space [21,22]. However, a long-standing problem of warm atomic vapor memories is read-out noise arising from four-wave mixing [23,24] and collisional fluorescence [25,26], which degrades the quality of the retrieved * gianni.buser@unibas.ch photons. Consequently, such memories are commonly tested with laser pulses attenuated to the single-photon level, circumventing the stricter requirements on memory noise imposed by real single photon sources with imperfect efficiencies. Readout noise can be suppressed in cold atom systems [27][28][29][30], or with excited-state storage schemes [31,32], but these approaches come at the price of much higher experimental complexity, or fundamentally limited storage times, respectively. Demonstrating storage and retrieval of single photons in ground-state vapor cell memories, as characterized by non-classical photon number statistics of the retrieved light, has so far remained elusive [12,15,33,34].
Here we report the storage and retrieval of single photons in a ground-state atomic vapor cell quantum memory. Our memory scheme suppresses readout noise by exploiting polarization selection rules in the atomic hyperfine structure and by operating at a bandwidth much higher than the excited state's radiative decay rate. We interface the atomic memory with a single photon source based on cavity-enhanced spontaneous parametric downconversion (SPDC), which we built for this purpose with improved operation and performance characteristics compared to our earlier work [16]. Single photons from this source are stored in the atomic memory and retrieved with decidedly non-classical photon number statistics, opening up many further possibilities for quantum networking experiments at high bandwidth in a room-temperature system.

II. MEMORY SCHEME
An overview of the single-photon source and quantum memory setup is shown in Fig. 1. The memory oper- (c) Energy level scheme for the atomic memory. Optical pumping and selection rules are used to isolate a four-level lambda system on the 87 Rb D1 line. The σ − polarized signal is detuned by ∆ from the F = 2 → F = 1 transition and the σ + polarized control is equally detuned from F = 1 → F = 1. Photons can thus be stored as a spin wave excitation between the initially prepared ground state |g and the storage state |s via the excited states |e1 and |e2 .
ates on the 87 Rb D 1 line at 795 nm in a hot atomic vapor. We initially prepare the atoms in the stretched Zeeman ground state |g = |F = 2, m F = 2 by optical pumping. This allows us to exploit polarization selection rules to isolate a four-level lambda system formed by the two ground states |g and |s = |F = 1, m F = 0 and the excited states |e 1 = |F = 1, m F = 1 and |e 2 = |F = 2, m F = 1 as shown in Fig. 1 (c). In the storage process, a circularly polarized (σ − ) signal, that is the single photon to be stored, is reversibly mapped to an atomic ground-state superposition between |g and |s by the (σ + ) control laser. Applying the control laser pulse again after the storage time recreates the photon in the signal mode [35].
Our scheme overcomes two significant limitations of lambda-scheme atomic memories that do not control the Zeeman state, namely their susceptibility to four-wave mixing noise [15,23,24] and the presence of parasitic single-photon transitions [33]. The former arises from off-resonant coupling of the strong control laser to the initially prepared atomic state. The latter occur when the signal is absorbed on a transition that would require a selection-rule forbidden mapping to the storage state by the control. In hyperfine lambda-schemes using πpolarized light this can occur with atoms initially in the m F = 0 state [36]. Both of these problems are addressed simultaneously by controlling the Zeeman state of the atoms and exploiting polarization selection rules [37].
Since the two storage pathways involving |e 1 and |e 2 interfere destructively [38], this approach only works if the detuning of signal and control light is lower or comparable to the excited state splitting, and not in between the states, so that one of the transitions dominates. This interference leads to an effective reduction in the optical depth of the ensemble, but not to absorption without storage. Therefore detunings within a GHz range red from F = 1 or blue from F = 2 can be considered and optimized for signal-to-noise ratio (SNR) and efficiency. The final working point used, ∆ = −2π × 700 MHz, is the result of empirical optimization, and the exact value is less crucial than minimizing the two-photon detuning between the signal and control.
We operate our memory in the technologically relevant regime of large bandwidths, typically several hundred MHz, much larger than the excited-state radiative decay rate of the 87 Rb D 1 line of 2π × 5.75 MHz. This allows us to also significantly suppress noise due to collisional fluorescence [25,26] by time-gating the signal. Overall, our memory scheme thus eliminates several main limitations of previous attempts to store single photons in the ground-state of atomic vapors.

III. MEMORY SETUP
The implementation of the memory is further detailed in Fig. 2. The atomic vapor cell at the heart of the memory is a commercial 75 mm long quartz cylinder with 19 mm outer diameter and wedged windows, which contains enriched 87 Rb (< 1 % 85 Rb specified), 5 Torr of N 2 buffer gas, and paraffin coating on the walls. It is housed inside a 4-layer magnetic shield (Twinleaf MS-1L). A simple heater maintains an atomic temperature of 50(1)°C, yielding an optical depth on the signal transition of about 25. The atomic state preparation is performed with 1 mm e −2 diameter, circularly polarized laser beams, pumping on the 87 Rb D 1 hyperfine transition |F = 2, m F → |F = 2, m F = m F + 1 and repumping on the 87 Rb D 2 hyperfine transition |F = 1, m F → |F , m F = m F + 1 , with around 20 mW and 10 mW CW power, respectively. The effectiveness of the state preparation was characterized at an atomic temperature of 70°C with pump-probe measurements to exclude concerns of radiation trapping at high density [39], and is estimated to be > 98 % initially, decaying exponentially with τ = 5(1) µs.
The laser setup for pumping and control is schematically shown in Fig. 2. The pumping beams are generated by CW external cavity diode lasers seeding fiberintegrated semiconductor optical amplifiers (SOAs) for fast switching via the SOA current in response to a herald trigger. They are combined on a dichroic mirror, then fiber coupled and overlapped with the control beam under a small angle of 2.95(15) mrad. The Gaussian control pulses are generated on demand with a fiber-integrated electro-optical amplitude modulator (Jenoptik AM785), controlled by a fast arbitrary pulse generator (PicoQuant PPG512). The FWHM of these pulses measured before the vapor cell is 3.77(4) ns. These pulses are am-FIG. 2. Experimental setup: ECDL external cavity diode laser, PC Pockels cell, ppKTP monolithic periodically poled potassium titanyl phosphate cavity, LP optical longpass, PBS polarizing beamsplitter, IF interference filter, SPAD single photon avalanche diode, DL 60 m fiber delay line, DDG digital delay generator, AWG arbitrary waveform generator, SOA semiconductor optical amplifier (fiber connections omitted), DM dichroic mirror, EOM electro-optic modulator (fiber connections omitted), TA tapered amplifier, CP calcite polarizing prism, λ/2 half-wave plate, λ/4 quarter-wave plate, µMS 4layer mu-metal magnetic shield, HBT Hanbury Brown and Twiss configured single photon detectors, M fiber connection for monitoring the control. The labels S, P, and C represent the fiber connections of the signal, pump, and control to the memory respectively. plified with a tapered amplifier (TA), then spectrally filtered to remove the background of amplified spontaneous emission of the TA with two narrowband interference filters (IFs, 0.5 nm FWHM specified by manufacturer at 795 nm) and two monolithic etalons (550(10) MHz bandwidth, 25.5(4) GHz free spectral range), and finally fiber coupled to bring them to the memory with a maximum possible peak power on the atoms around 680(40) mW.
In the experiments detailed below the power is adjusted to yield a peak Rabi frequency of Ω = 2π × 400(30) MHz on the |s → |e 1 transition.
Control and signal are initially in orthogonal linear polarizations, and are thus combined on a single calcite prism. Then a quarter-wave plate prepares the required circular polarizations. The signal (control) is focused to a e −2 diameter of 480(6) µm (520(6) µm) in the center of the vapor cell by the fiber outcoupling lenses. After the cell further waveplates linearize and align the polarizations, then a second calcite prism separates the signal from the control with a polarization extinction ra-tio of > 80 dB (characterization limited by detection) after which it is fiber coupled to a spectral filtering stage. These spectral filters consist of three monolithic etalons (550(10) MHz bandwidth, 25.5(4) GHz free spectral range) in series, temperature tuned to the signal frequency. For CW light at the control frequency each of these etalons delivers −26 dB reduction in intensity. Including the polarization filtering, this results in a total CW control suppression in the signal channel by more than 160 dB. Finally, another fiber coupling after the etalons sends the signal to the detection system consisting of two single photon avalanche diodes (SPADs, Excelitas SPCM-AQRH-16) arranged in Hanbury Brown and Twiss configuration. Despite the meticulous control filtration, the total transmission of a strong CW probe at the signal frequency from the fiber input of the memory to this output, leaving the atoms warm and unpumped, is T = 30(3) %.

IV. SPDC SOURCE
The single photon source is based on cavity-enhanced SPDC, which provides heralded single photons with high quality, high efficiency, and tunable bandwidth [40][41][42]. The source is an evolution of the one described in [16,43] with improved reliability and performance. It is carefully tailored to emit signal photons compatible with the atomic memory, at a wavelength of 795 nm fine-tuned to the 87 Rb D 1 line and a bandwidth of ∼ 370 MHz matching the acceptance bandwidth of the memory.
The heart of the source is a 5 mm long periodically poled potassium titanyl phosphate (ppKTP) crystal, polished and coated to form a doubly resonant hemispherical monolithic cavity, see Fig. 2. A periodic poling of 10.1 µm is chosen so that the quasi-phase-matching conditions for type-II SPDC are met for signal photons wavelength-matched with the 87 Rb D 1 line whereas the bandwidth-matching is given by the cavity linewidth. In the non-degenerate process 404 nm pump photons are down-converted to 795 nm (822 nm) signal (idler) photons, illustrated in Fig. 1 (b). We pump the crystal with 4.5 mW in a double pass configuration to reach heralding rates of 1.5 × 10 5 counts s −1 on average. The pump frequency is stabilized through a sideband-offset lock on a passively stable reference cavity, allowing for a tunable but locked laser. The orthogonally polarized signal and idler photons are split on a polarizing beam splitter cube, see Fig. 2, and coupled each into a polarization maintaining fiber. The herald is filtered with a temperaturestabilized monolithic etalon (1150(20) MHz bandwidth, 51(1) GHz free spectral range) and a narrow-band IF (0.57(5) nm FWHM, measured at 822 nm) before being detected with a SPAD.
We observe that a constant noise floor of uncorrelated photons is emitted by the photon source. In order to suppress this background during photon retrieval a fast Pockels cell acts as switch for the down-conversion pro-cess. By rotating the polarization of the pump beam by 90°the down-conversion process is highly suppressed since the phase-matching conditions are not met anymore. It takes about 140 ns upon the detection of an idler photon for this switch to turn off the source. As the pump light remains incident on the crystal no thermal drifts are induced by the switching. Furthermore, optical isolators are placed both in the signal and idler arms. They are used to prevent crosstalk from the lasers preparing the atomic state of the memory and to suppress external cavity modes in the herald path, both of which originate due to spurious back-reflections on the crystal's plane surface. Even with these additional optical elements the heralding efficiency, that is the probability of having a signal photon exiting the optical fiber to the memory upon the detection of an idler photon, is as high as η h = 40(4)% for a coincidence window of 6.48 ns. Such a high η h is crucial as even small amounts of memory read-out noise can accumulate when no photon is present most of the time [44]. We measure the conditional second-order autocorrelation of the signal photons at the memory input to be g (2) input = 4.21(2) × 10 −2 , confirming their high quality.

V. INTERFACING SOURCE AND MEMORY
Memories for heralded single photons need to react to the detection of the herald, in our case the idler photon from the SPDC source. This places stringent limits on the reaction time of all switching electronics and optics of the memory setup. The time between the detection of an idler photon and the arrival of the signal photon in the vapor cell is about 270 ns, as a 60 m optical fiber is used to route the signal photons from the source to the memory setup. In a storage and retrieval experiment the memory is first initialized by the pumping and repumping lasers for a minimum time of 2 µs to ensure that the desired atomic polarization is achieved. During this pumping stage the detection of idler photons is rejected on a hardware level. After this minimum duty cycle of the state preparation, the detection of an idler photon triggers a digital delay generator (DDG, Highland Technology T564, 21 ns insertion delay, < 35 ps RMS timing jitter) to switch off both the optical pumping and repumping beams as well as the pumping of the source until after the photon is retrieved. All this switching is prioritized to minimize noise, as the extinction ratio of the switches improves over time, and the cables are kept as short as possible. This reactive configuration ensures that the memory remains ready to accept a photon at any time after initialization. The trigger is also relayed to a second DDG for less time critical tasks, including triggering the generation of control pulses and time stamping the idler photon detection with a time-to-digital converter (qutools quTAU, timing resolution 81 ps). The typical rate of these experiments is 1.5 × 10 5 s −1 , set by the chosen heralding rate.

VI. SINGLE-PHOTON STORAGE RESULTS
Photon arrival-time histograms of the photons detected within 20 min of integration time are recorded for three scenarios and shown in Figs. 3 (a) and 4. In the first scenario repeated attempts of storing a heralded photon for 160 ns are performed, which we present as a test case for detailed analysis. In a read-out window of 6.48 ns (shaded region) and for a total of N herald = 159 752 941 storage attempts N ret = 454 030 photons are retrieved.
The other two scenarios represent distinct measurements of the noise performance. The source blocked scenario represents the typical readout noise estimation performed for memories, measuring the amount of noise produced when the input is physically blocked. This serves bins, and τp = 0 represents the time at which an input photon arrives at the detector if it leaks through the setup without being stored or lost. The y-axis is normalized to the peak of the no read-in curve in the retrieval window (8325 counts) to yield a proxy for the worst-case signal-to-noise ratio, and is plotted logarithmically so that small features, labeled A-F, can be identified. These illustrate the experimental sequence and are described further in the main text. Colored bars above the plot signify the time windows in terms of detection time wherein the state preparation beams and the photon source are effectively turned off.
as a comparative measure to other memories, characterizing it in isolation. When the source is blocked the number of memory induced noise counts for the same number of experiments as above is N noise, mem = 29 075. The readout noise floor is then µ mem = N noise, mem /N herald = 1.82(18) × 10 −4 . This however does not capture noise stemming either from the source itself in the form of uncorrelated photons at the signal frequency, nor from spurious back reflections of light originating from the memory setup in the source. The total noise is estimated in a measurement omitting the read-in control pulse, labeled as the no readin scenario. This induces a small systematic error as the atomic response to the read-out pulse is also influenced by the read-in pulse. The no read-in curve therefore delivers a slight overestimation of the total amount of noise present in the read-out window. The number of noise counts detected in this curve's read-out window is N noise, tot = 38 634 yielding a total noise floor of µ tot = 2.42(24) × 10 −4 . With this we calculate the end-to-end efficiency defined as to be η e2e = 1.1(2) %. Here η det is the quantum efficiency of the single photon detectors specified as 60(6) %, which is the dominant source of uncertainty. The signalto-noise ratio of the combined experiment is SNR = Nret−Nnoise,tot Nnoise,tot = 10.8 (15) which bodes well for the quality of the retrieved photons. Indeed, the conditioned autocorrelation of the retrieved photons is g (2) c, ret = 0.177 (23) confirming that the memory emission is dominated by single photons. This is the first experimental confirmation of the viability of retrieving single photons from ground-state memories in hot atomic vapor.
A measurement of the exponential 1/e lifetime of the memory is shown in Fig. 3 (b). The fit yields τ = 680(50) ns lifetime and an initial efficiency of η e2e,0 = 1.4(4) %. This lifetime is close to what is expected for a memory limited by atomic motion out of the interaction region, but may be slightly shortened by the lifetime of the initial ground state preparation which has not been exhaustively optimized for longevity. Accounting for the technical losses in the setup by dividing out the measured transmission and extrapolating to zero storage yields a total internal efficiency of η int = η e2e,0 /T = 4.7(14) %. The conditioned autocorrelation of the retrieved photons eventually increases for long storage times. For τ s = 280 ns it is still low at g (2) c, ret = 0.171 (28), but by τ s = 700 ns it increases to g (2) c, ret = 0.503(93). The lifetime could therefore also be seen as roughly the time for which g (2) c, ret ≤ 0.5.
The photon number statistics of the retrieved light depend on the photon number statistics of the signal pulse, as well as those of the noise and potentially the process at its origin too. An exact and physically simple model for the case of an incoherent admixture of noise is derived in [15]. It treats the noise as being generated independently from the storage and retrieval processes, the additional light being added to the read-out by straightforward superposition. It reads g (2) c, ret, theo = (N ret − N noise ) 2 g (2) Here, g (2) input has been established during the characterization of the source; the statistics of the noise g (2) c, noise , however, are not measured directly, as insufficient noise counts accumulate within a reasonable integration time to evaluate them meaningfully. Sources of noise for which we would expect g (2) c, noise = 1 are limited to leaked control laser light. Known possible thermal noise sources include uncorrelated SPDC photons from the source, as well as collisional fluorescence and four-wave mixing induced by the control. We distinguish these scenarios on the memory side by scanning the final filter etalon with the SPDC source blocked. We observe collisional fluorescence peaks on resonance with the natural oscillators F → F = 2 [25] which seem to constitute the entirety of the noise at the signal frequency. Scanning the etalon to the control frequency, we also observe the control laser and collisional fluorescence on F → F = 1, but these are well suppressed when the final etalon is set to the signal frequency. No further peaks are visible after the filters, in particular confirming that fourwave mixing is well suppressed by the memory scheme. We therefore expect g (2) c, noise = 2 as non-thermal noise sources are well excluded. Moreover, if the noise can be modeled incoherently this is a conservative assumption as it represents the worst case. This approach yields an expected value of g (2) c, ret, theo = 0.204 (29), which is in excellent agreement with our observed statistics. In the limits g (2) input → 0, g (2) c, noise → 2 the exact model reduces to g (2) c, ret, theo ≈ 2/(SNR + 1), illustrating the link between the statistical measure and the memory performance directly visible in the data. Note that were the memory limited by a coherent noise source such as fourwave mixing gain, incoherent models would drastically underestimate the g (2) of the retrieved light [15]. Figure 4 makes small features in the data visible yielding additional insights into the main features. The peaks at τ p = 0 and τ p = 161 ns, also displayed in Fig. 3 (a), are now revealed to be followed by exponential tails. These counts correspond to fluorescence from the atomic excited state. Due to the high bandwidth, the majority of this noise is avoided thanks to its temporal separation from the signal, highlighting an innate advantage of highspeed memories. Further labeled features correspond to steps in the experimental sequence and technical effects. In the region A (B) the herald photon has already triggered the electronics, and we see exponentially decaying fluorescence from the atoms as the pumping (repumping) beam is switched off. In the region C, after the photon is stored, the discrepancy between the storage and no read-in curves corresponds to unintentional read-out of the stored photon. The end-to-end (internal) efficiency of this unintentional read-out is 0.38(5) % (1.26(17) %).
It is caused by ringing in the EOM switching the control and its limited extinction ratio. At longer storage times the end-to-end efficiency of this read-out saturates at about 1 %. The feature present in both curves right beneath the label C at around τ p = 30 ns is due to afterpulsing of the SPADs. The steep feature labeled D corresponds to the Pockels cell switching off the SPDC source. The remaining discrepancy between the no-read and source blocked curves estimates the secondary effect of the first control pulse on the atoms. The rising feature labeled E corresponds to both pumping lasers being switched back on after the retrieval is complete. Finally, the feature labeled F marks the source switching back on.

VII. DISCUSSION AND SIMULATION
To analyze limitations of our experiment and moreover guide future development we simulate the storage and retrieval process numerically. We consider an atomic fourlevel system following the description in [45], also taking into account the transverse profile of both light fields, similar to [46]. We include both collisional broadening induced by the buffer gas and inhomogeneous Dopplerbroadening of the vapor. The latter is taken into account by introducing different velocity classes of the atoms, as shown in [47]. We focus on the scenario of forward retrieval. The storage and the retrieval processes are much faster than the mean free time between collisions of about 20 ns in the vapor cell used for this experiment. This allows us to assume that the individual atoms do not change their velocities during these processes. However, during the storage time of 160 ns we assume that the atoms rethermalize fully. The numerical simulation is implemented by solving the temporal derivatives appearing in the equations of motion with a partially implicit second-order Runge-Kutta method. For the spatial derivatives spectral collocation is used, allowing us to replace them with Chebyshev differentiation matrices as described in [46].
We use the simulation to evaluate the total efficiency as a function of the peak control Rabi frequency. Herein the temporal width of the Gaussian control pulse is fixed to 3.77 ns, and the time alignment between signal and control pulse is optimized for each simulation point. Seeking plausible routes to improvements, other experimentally controllable parameters are varied. We find that the twophoton detuning has a strong impact on the attainable performance, as can be seen in Fig. 5 (a). Minimization of the two-photon detuning intuitively corresponds to bringing the memory interaction into resonance, note however, that following the convention of [48] we define this parameter as the difference between the control and signal detunings on their respective single-photon transitions, ∆ tp = ∆ c − ∆ s . In the regime of our experiment where Ω ≈ ∆ < ∆ hfs , the presence of the control pulse induces a significant, time-dependent level-shift, which by this definition appears as a shift of the optimal detuning from ∆ tp = 0. Furthermore, different control beam waists are considered. The simulation confirms that by choosing a larger control beam waist the total efficiency can be improved. Fig. 5 (b) shows the performance for different control waist for optimal two-photon detuning. With a control beam significantly larger than the signal, more atoms experience the optimal control Rabi frequency, leading to a more efficient process.
For the parameters of the experiment shown in Figs. 3 (a) and 4 the measured value of the internal efficiency falls short of that predicted by our model. This leads us to identify effects not captured by the simulation. One is the unintentional read-out of the signal during the storage time by the leaking control light which is present due to a combination of ringing in the EOM as well as its finite extinction ratio (about 25 dB). A second issue is the quality of the temporal alignment of the control pulse to the signal, mainly limited by the > 350 ps jitter of the single photon detector measuring the idler photon. Based on tests with laser pulses where this jitter source can be eliminated, we expect this amount of variance in the temporal alignment to decrease the efficiency by a factor of < 0.90 (5). These issues, alongside the difficulty of stating an experimental value of ∆ tp with any certainty, makes modeling the exact experimental situation difficult. Experimentally, the signal frequency is set once, whereupon the control frequency is optimized on the storage efficiency at fixed Ω to compensate for drifts, without the possibility of a direct measurement of the two-photon de-tuning. Our simulations will guide future improvements by identifying the regimes were the best performance is expected, accounting for the interdependence of the many optimization parameters. This analysis highlights three main areas where technical improvements can still be implemented: lasers, optical switches, and detectors. A more powerful control laser would enable us to define a larger and more homogeneous interaction region. Optical switches without ringing and with a better on/off ratio would protect the spinwave during storage. Faster single photon detectors would improve the time alignment of the control pulse to the single signal photon. In particular, the currently remaining jitter on a control pulse, removing the jitter of the idler detection, is measured to be only 126(3) ps. The state-of-the-art in timing resolution of single photon detection is more than an order of magnitude smaller.
Upon addressing technical matters, a further improvement of the efficiency is possible by increasing the optical depth. Technically this is straightforward via the atomic temperature, but is bound to affect other figures of merit as well, in particular the readout noise. Due to their interdependence, parameters such as the detuning from the excited states and Rabi frequency would again require optimization, and accurate performance predictions concerning noise, fidelity, and lifetime predicate dedicated models not currently implemented. Additionally, some gains could be expected from shaping the temporal profile of the control pulses. This is fraught with ambitious demands on the time resolution of the pulse generation. A more straightforward change, still requiring some modifications to the electronic systems though, would be to optimize the amplitude of the read-in and read-out pulses independently. Although the optimal processes are well known to be linked by time-reversal symmetry both theoretically [49] and experimentally [50], the matter is less cut-and-dried in the experimentally implemented highbandwidth case with realizable Gaussian control pulses, where a full pulse shape optimization is technically prohibitive and a practical distinction between programmed and effective pulses is warranted.

VIII. SUMMARY AND OUTLOOK
In summary, we have for the first time demonstrated the interfacing of a heralded single photon source and a technologically simple atomic quantum memory with ground state storage successfully maintaining the single photon nature of the input upon retrieval. Through simulations we have laid a road map for future improvements that will simultaneously realize state-of-the-art efficiency. Moreover, the fidelity of the memory will be determined more directly with Hong-Ou-Mandel experiments [51]. Modern vapor cell fabrication techniques can produce cells with diameters < 1 mm [52]. Even with the currently available control power, which determines the mode size yielding the optimal control intensity, this would match the cell size to the optical mode. Under such conditions the atoms would remain in the interaction region despite their motion during storage. With corresponding improvements to the longevity of the Zeeman state preparation, which is known to be short but not currently limiting, a memory lifetime on the order of milliseconds is well within reach judging by similar systems [14]. Moreover, Zeeman-state preserving anti-relaxation coatings on cells have shown far longer relaxation times [53]. Possible applications of our source-memory system thus include photon synchronization and use in highbandwidth quantum networks for quantum information processing and simulation. The multi-photon rate enhancement provided by memories is given by the time-bandwidth product B, scaled by the memory efficiency [6]. Due to the high bandwidth operation of our memory we achieve B = 250 (20) despite the non-optimized storage time, which would be sufficient to demonstrate enhanced synchronized rates directly.