Highly efficient storage of cavity SPDC single photons in room temperature gradient echo memory Open Access

Harnessing the full potential of quantum technologies will require linking quantum systems locally and globally^1–3 to share resources and enhance capabilities: similar to the multi-processor CPUs of local computers or the vast computing power that comes from connecting data centers to form the internet. Quantum interconnects will be an essential element in linking the nodes of a quantum network consisting of sensors,⁴ distributed quantum computers,^5,6 and quantum clock signals.⁷ To ensure information fidelity and practical transmission rates over long distances, the quantum network channels need to be optical,⁸ such as their classical counterparts. Synchronization between different systems will require the availability of quantum memories⁹ to store and relay the qubits and to build quantum repeaters¹⁰ that enable long distance communications.

A wide variety of quantum memory protocols have been demonstrated each with their own set of advantages and disadvantages in terms of performance metrics in efficiency, storage time, frequency bandwidth, and other metrics. Solid-state systems excel in storage times of the order of one minute¹¹ and the potential for many hours¹² with good memory efficiencies of up to 76%.^13,14 Recall efficiencies around 90% were demonstrated using both warm¹⁵ and laser-cooled gaseous alkali atoms.^16,17 Memories using off-resonant Raman transitions have demonstrated THz bandwidths¹⁸ and time–bandwidth products around 100.¹⁹ 

Efficient storage of the photonic qubit in these atom-based memories requires matching memory and photon source features. Due to the complexity of engineering a quantum light source to optimally integrate with the quantum memory’s temporal, spectral, and spatial acceptance bandwidth, most demonstrations have relied on attenuated classical light sources rather than true quantum light. However, weak coherent states cannot replace single photons for applications such as photonic quantum computation,²⁰ and physics at the quantum limit may exhibit fundamentally different interactions.^21,22 Even though weak coherent states can be useful for characterizing the performance of quantum memories in the quantum regime, they fail to elucidate the technical complexities encountered when interfacing a quantum light source with a quantum memory.^23–25 

To date, the most efficient realizations employed electromagnetically induced transparency in a rubidium magneto-optical trap (MOT) for the memory and four-wave mixing or spontaneous Raman scattering in a separate cold atomic ensemble as the single photon source.^26,27 These produced an outstanding recall efficiency of 85%, but the duty-cycle—the fractional time period where the memory is ready for read/write operations—was limited to 3% by the loading and cooling steps of the MOTs.²⁶ Utilisation of memories based on hot or room-temperature atomic vapors can alleviate the loading and cooling steps, but typically suffer from added noise,^9,28 low storage times, or both.²⁹ 

Gradient echo memory (GEM) is a high efficiency memory protocol that coherently stores photons using a frequency gradient and recalls by reversing the gradient. It is suitable for integration with hot or cold atomic ensembles. Its performance is well characterized, and efficiencies up to 87% have been demonstrated on both platforms.^15,17,30,31 All previous experiments, however, have only been performed with weak coherent states: the storage of true quantum states remained elusive due to the stringent spectral requirements on the single photons to be stored.

To the best of our knowledge, we report the first integration of a hot vapor rubidium GEM with a tailored single photon source. The single photon source is based on cavity-enhanced spontaneous parametric down-conversion (SPDC)³² and generates single photon states with a measured heralded second-order auto-correlation function $gs,s|i(2)(0)=0.032±0.003$⁠. Microsecond storage was achieved with recall efficiencies up to 84% ± 3%, demonstrating that GEM has the potential for similar performance with single photon states as already reported with weak coherent states.

In the warm, rubidium-vapor based Gradient Echo Memory (GEM)¹⁵ scheme, an optical lambda transition in rubidium 87 links the F = 1 and F = 2 states of the 5S_1/2 ground state; see Fig. 1(e). The photon from the single-photon source addresses the probe transition (Rb87 D1 5S_1/2F = 1 → 5P_1/2F = 2), and the bright (50 mW) control beam (Rb87 D1 5P_1/2F = 2 → 5S_1/2F = 2) transfers the excitation into the long lived ground state of the memory. Both optical fields are blue detuned by 804 MHz from resonance with the excited 5P_1/2F = 2 state. The detailed laser setup to facilitate this can be found in the supplementary material, Sec. 1. To gain control of the read and write times³⁰ and avoid reabsorption of the recalled signal in the memory, we apply a linear magnetic field gradient to the memory cell with coils of varying pitch. This creates a spatially varying shift of the atomic resonance, causing the memory to store different frequency components of the optical field at different spatial regions of the memory. Reversal of the magnetic field gradient and the presence of the optical control beam initiate the recall of the stored signal. As the GEM protocol eliminates unwanted reabsorption, its theoretical efficiency can reach 100%, and experimental results confirm that no resonant noise is added to stored states making GEM highly suitable for single photon storage.³¹ To maximize our experimentally achievable memory efficiency, we use a Rb87 enriched cell with 0.5 Torr of Kr buffer gas heated to about 80 °C with the coils and the cell contained inside a Mu-metal tube to shield from stray magnetic fields.

We keep the memory in write mode—magnetic field gradient and control field on—at all times until an idler photon detection event heralds a single photon storage event in the memory. This triggers a set of relays to block the control field, end the write phase, and flip the magnetic field gradients. Once the gradient is fully reversed and the control field is turned back on, recall of the single photon commences. We switch the field gradient again after a predetermined time period related to the desired storage time to reset the memory back into write mode, ready to store for the next single photon from our source. This sequencing will again be emphasized in Sec. III.

To match the strict spectral requirements of GEM, a cavity-enhanced SPDC source was designed to produce sub-MHz bandwidth biphoton pairs suitable for integration with the memory protocol.³² A periodically poled potassium titanyl phosphate (ppKTP) crystal, cut for type-II quasi-phase matching, is used to produce orthogonally polarized photon pairs from a bow-tie cavity, as depicted in Fig. 1(a). When placed in a cavity, the otherwise broadband process of SPDC is modified so that emission into resonant modes is enhanced and, in the case where both downconverted modes are simultaneously resonant, further narrowed.^33,34 Our source produces roughly 1000 frequency modes with a bandwidth of 429 kHz separated by the cavity’s free spectral range (120.8 MHz) over the entire phase matching bandwidth of ≈100 GHz. GEM can only store one of these frequency modes at a time; thus, a concatenation of external filtering systems shown in Fig. 1 is required to isolate the single central frequency mode relevant for GEM. The first stage of this system is an air-spaced flat surface etalon [SLS Optics, free spectral range FSR = 75 GHz, Finesse $F=15$] placed immediately after the dichroic mirror and ultra-narrow bandpass filter at 795 nm (FWHM 1.0 nm) to remove any residual pump exiting the SPDC cavity. A polarizing beam splitter follows the etalon to separate the idler and signal modes of the SPDC, which are fiber-coupled and sent to the heralding and memory arms, respectively, as shown in Fig. 1.

The herald photon is further filtered by a mode-cleaning cavity (764 MHz FSR, 1 MHz linewidth), locked with a counter-propagating beam resonant to a Rb85 transition, and orthogonally polarized with respect to the herald photon (details in the supplementary material, Sec. 2). The filtered herald photons are then passed through a Rb85 cell, removing the backscattered locking signal, before being detected by a fiber-coupled single photon counting module (SPCM). Similarly, the stored signal photon is filtered after the memory with a different mode-cleaning cavity (877 MHz FSR, 1.6 MHz linewidth) locked in a similar fashion. The convoluted transmission spectrum of these two mode-cleaning cavities, etalon, and source cavity near perfectly isolates the central frequency mode of the SPDC [see the supplementary material, Sec. 2, Fig. S3(c)], ensuring that coincident events detected between the herald and the stored photons will be of photons resonant with the memory transition.

To achieve a memory system ready to operate at 100% duty-cycle, the photon source also must always be operational, without down-time due to atomic state preparation or re-locking sequences. The source cavity is locked to the pump beam using the Pound–Drever–Hall method,^35,36 ensuring the SPDC process to be pumped at all times. Birefringence between the signal and idler modes is compensated with the half-waveplate “flip-trick,”³² which reduces double resonance of both modes to one resonance condition. Fine temperature control of the SPDC crystal then achieves triple resonance by overlapping the resonance of the two down-converted modes at 795 nm (red) with that of the pump at 397.5 nm (blue). Slight temperature drifts allowed the resonances between the pump and down-converted photons to drift apart with time. To compensate, we established a feedback-lock based on the discarded single photon counts of the herald’s filter cavity; see Fig. 1(b). This signal comprises the majority of frequency modes and thus total number of produced single photons, enabling automated tracking of the triple resonance condition and continuous user-intervention free data collection for 8+ h at a time. More details can be found in the supplementary material, Sec. 3.

Efficient storage and recall require a strong control beam (50 mW) to co-propagate with the single photons through the memory cell. Isolating the single photon signal after storage necessitates filtering of the control field, as shown in Fig. 1(d). First, an iris removed the part of the control beam that was larger than the signal beam. By tuning the control field to a Rb85 resonance (see the supplementary material, Sec. 1, Fig. S2), we gain 60 dB of isolation from a Rb85 filter cell. However, atomic filter cells emit broadband fluorescence when absorbing resonant light,³⁷ which we removed with the aforementioned signal beam filter cavity. A second Rb85 filter cell suppresses the leaking lock signal from this mode-cleaning cavity and adds further isolation against the control beam. Finally, an edge filter removes the remaining fluorescence noise. The combined filtering chain measured 133 dB suppression of the control beam, with an end-to-end transmission of 8% ± 2% for the signal where the error arises from drifts in system alignment over long periods of time.

Single photons are detected using avalanche photodiodes (Perkin Elmer SPCM-AQR-14-FC) and recorded using a time-tagging module (Roithner Lasertechnik, 100.1 ps time resolution). While both memory and source operated continuously, data taking was sequenced to compensate for long term drifts. The 2 s long sequence is broken into three different stages as shown in Fig. 2. In the first stage, labeled “no memory,” we measure the injected photon rate, while the control field is blocked; in the second stage, labeled “memory,” we implement the protocol to store and then recall single photons; and in the third stage, labeled “no input,” we measure background counts, including the control field, by blocking the single photon input. This allowed for extraction of the single photon recall efficiency of the memory independent of long term drifts or variations in the experiment.

In the memory stage, the recalled single photon signal is overlaid by leaked photons from the coherent control field contributing $∼5−10$k counts/s. Without detection in the coincidence basis between the signal and idler photon from the SPDC source, recovery of the stored single photon signal would have been prohibited by such noise. Depending on the pump power, we see between 1000 and 2400 counts/s on the heralding detector, with a heralding efficiency between 2% and 4%, impeded by our optical path efficiencies (⁠$∼8%$ for the memory arm and $∼40%$ for the heralding arm). Through our measurement sequencing, we can subtract the noise using the scaled background data from the “no input” sequence, an example of which is shown in Fig. 3. Such a process is used to evaluate all presented results, with more details on the subtraction procedure in the supplementary material, Sec. 4. Characterizing the memory operation in this way enables the extraction of the single photon recall efficiency of the memory—specifically the number of photons retrieved from the memory compared to that sent into it—independent of long term drifts, variations in the experiment, and optical path efficiencies of the system.

Previous homodyne measurements of GEM in warm vapor cells have shown that GEM does not add resonant noise-photons to the recall,³¹ confirming GEM as a noise-free memory protocol. The observed noise is highly likely non-resonant and stems from control light leaking through the filters directly and through other scattering processes or fluorescence from the filter cells. Due to the hot and physical large nature of our memory cell, we are unable to utilize the angular filtering techniques demonstrated in cryogenic atomic memories.^26,27 However, a recent demonstration from the University of Basel has demonstrated efficient filtering even for a hot vapor gas system,³⁸ giving us confidence that improved filtering will alleviate our noise problem in the future.

We use the temporal correlation between the photon pairs emitted from the SPDC source to provide single photon signal through the detection in the coincidence basis.^39,40 This technique enables us to conclusively identify the single photon signal in front of a background of leaked control field photons. Typical storage and recall of single photons for a 4 µs duration are presented in Fig. 4. Orange/red shaded regions indicate the times when the memory is in the read/write modes, respectively, as indicated by the magnetic field gradient state and presence of the control field shown in Figs. 4(a) and 4(b), respectively. The red histogram of Fig. 4(c) indicates single photons arriving at the memory with the memory turned off: they are detected as coincidences with a herald detection on the idler photon produced by the down-conversion source (see Sec. II for details). The blue histogram in Fig. 4(d) indicates photon coincidences with the memory active and set to delay the signal by 4 µs.

The plots shown in Fig. 4 were obtained after subtraction of background noise of ∼5–10k counts/s due to leaked control field photons. The raw coincidence counts of Fig. 4(d) are presented in Fig. 3, highlighting the signal, background, and corrected signal with a signal-to-noise ratio of 0.14 (see Sec. II and the supplementary material, Sec. 4, for details). In the raw counts of the recall, the leaked control field (which is coherent in nature) dominates the statistics to give a normalized cross-correlation measurement at the recalled time τ of $gs,i(2)(τ)=1.0±0.6$⁠. However, with the background subtraction, we recover $gs,i(2)(τ)=8±5$⁠, a value greater than the classical limit of 2 for a two-mode squeezed state, thus exemplifying the nonclassical nature of the correlation.⁴¹ This background noise made further characterization of the quantum nature of the recalled state, such as heralded second-order auto-correlation measurements,⁴² infeasible with our current setup. Raw and corrected normalized cross-correlation values for the input state at τ = 0 were $gs,i(2)(0)=7±4$ and $gs,i(2)(0)=548±370$⁠, respectively. More details of how these values are calculated can be found in the supplementary material, Sec. 5.

To ensure our memory was operating as expected, we compare the temporal shape of the recall when it was storing single photons with when it was storing coherent states. We temporally shape attenuated pump laser light using an acousto-optic modulator (AOM) so that it possesses the same temporal profile as the single photons. The input pulse without storage is shown as the black solid line in Fig. 4(c), which agrees well with the measured not-stored single photons. Recall of the coherent state from memory is shown in Fig. 4(e): it is strikingly similar to the recalled photon profile. The main difference being how sharply the single photon recall appears as the control field was turned back on. This phenomenon arises from different spectral bandwidths of the two states; single photons generated by cavity-enhanced SPDC (which is not Fourier-limited due to birefringence compensation) have a wider spectral bandwidth than the coherent state generated directly by the narrow linewidth laser. This is elucidated from a simulation for the same input temporal profile but with different relative bandwidths shown in Figs. 4(d) and 4(e), completed in XMDS2 and based on the simplified Maxwell-Bloch equations for a three-level system. All simulation parameters were set with measured experimental parameters from the same physical experiment, with no free parameters used. The simulated single photon output was obtained by increasing the input to memory bandwidth ratio by 25% from the simulated coherent output and caused the recall to appear earlier, and flattened, as observed in the single photon experimental results. This slight spectral mismatch delivers a substantial difference in the recall efficiency: the coherent state recall reaches a maximal value of 55% ± 1% compared to the 84% for the single photon. This demonstrated single photon recall efficiency is similar to that achieved in previous implementations of GEM with coherent state inputs¹⁵ where the memory operation was tailored to suit the coherent state spectral and temporal profile and highlights the importance of characterizing and optimizing a source-memory system as a whole as there may be nuanced differences that significantly vary performance.

Storage and recall experiments were completed at varying storage times shown in Fig. 5. We classified as recalled, any coincident photons detected after the control field was switched back on and before the magnetic field gradient was flipped back to the write mode. The data clearly show the center of the recalled signal shifting with the extended storage time for both the coherent state (solid lines) and the single photons (red and light blue histograms), which retain their scattered signal preceding the main recall associated with the larger bandwidth.

Recall efficiency decreases with an increasing storage time, in part, due to addressed atoms moving out of the interaction region via atomic motion in the warm vapor and because of atom–atom collisions. The reduction in recall efficiency is clearly visible as the reduced area of the recalled signal in Fig. 5 and is plotted in Fig. 6. The efficiency drops from 84% ± 3% at 4 µs to 57% ± 3% at 13 µs before falling below the no-cloning limit⁴³ at 17 µs when we recall only 40% ± 3% of the stored signal. Even for our longest storage time, the normalized cross-correlation function is $gs,i(2)(τ)=4±2$⁠, indicating that the correlations remain nonclassical with background correction. Storage times shorter than 4 µs are inaccessible due to limitations of our setup. Error bars are derived from the propagated statistical noise in each measurement, directly related to the total number of coincidence counts measured. The decline of memory efficiency aligns with results for coherent state characterization of this memory.¹⁵ 

The relative scaling of the single photon and coherent state memory efficiency decay indicate that the single photon storage does not suffer from any additional degradation for extended storage times compared to the coherent state storage. A detailed discussion on how the memory efficiency was calculated can be found in the supplementary material, Sec. 6.

We, therefore, have demonstrated that GEM can operate with as higher performance in the single photon regime as it does for weak coherent states when appropriately optimized.¹⁵ Our demonstrated peak recall efficiency of 84% is within error equal to the best demonstration by Wang et al.,²⁶ but free of the complexity of vacuum systems and cold atom traps. In theory, this protocol is suitable for near continuous operation (only no storage during magnetic field switching times), although only a 60% duty cycle was demonstrated here due to the requirement of actively locking the filters and the need to characterize the noise. We note that during the switching phase of the field gradient indicated as the white background in Figs. 4 and 5, some additional signal is detected (not included in the recall efficiency). Possible explanations are noise from the change in currents in the coils or optical leakage of fields stored in the edges of the memory. See the supplementary material, Sec. 7, for more details.

To enable deployment in real world applications, improvement of the signal to noise of our memory output is still required. Ways to achieve this include the introduction of a non-poled crystal into the SPDC cavity to utilize the clustering effect for intracavity filtering^44–46 for enhanced brightness of the source in the relevant single frequency mode; improvements to the filtering systems to reduce the level of non-resonant noise due to the control field is also essential; additionally, performance of our system can be further improved through optimizing the memory geometry and magnetic field coil alignment, to improve coupling of the single photon wave function to the memory. This would bring GEM even closer to its theoretical limit of 100% recall efficiency.

We present the first storage and recall of single photon states using the gradient echo memory protocol. Our achieved 84% recall efficiency is comparable with the best demonstrated quantum memory efficiency and supports the potential of GEM as an efficient quantum memory compatible with real quantum states. This system is the first to surpass the no-cloning⁴³ threshold with single photons in a setup that is vacuum-system free, non-cryogenic, and capable of near continuous operation. Such a system might reduce operation overheads and increase operational efficiency for future network or communication applications.

The supplementary material is divided into seven sections and provides more detail to each aspect: laser setup and locking chains; single photon filtering spectrum; monitoring the SPDC cavity lock position; background subtraction methodology for memory data; cross-correlation measurements; quantifying memory efficiency; and leakage during magnetic field switching.

We thank Geoff T. Campbell and Daniel B. Higginbottom for valuable discussions during the initial stages of planning and prototyping the experiment. This research was supported by the Australian Research Council Centres of Excellence for Engineered Quantum Systems (EQUS, Grant No. CE170100009) and Quantum Computation and Communication Technology (Grant No. CE170100012).

The authors have no conflicts to disclose.

A.C.L. and W.Y.S.L. contributed equally to this work.

Anthony C. Leung: Conceptualization (equal); Data curation (lead); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). W. Y. Sarah Lau: Conceptualization (equal); Data curation (supporting); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (supporting); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Aaron D. Tranter: Conceptualization (equal); Data curation (supporting); Formal analysis (supporting); Investigation (equal); Methodology (supporting); Software (equal). Karun V. Paul: Investigation (supporting); Software (supporting); Validation (supporting). Markus Rambach: Conceptualization (equal); Methodology (supporting); Resources (supporting); Supervision (supporting). Ben C. Buchler: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (equal); Methodology (equal); Resources (equal); Supervision (equal); Writing – review & editing (supporting). Ping Koy Lam: Conceptualization (equal); Funding acquisition (equal); Methodology (supporting); Resources (equal); Supervision (equal). Andrew G. White: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (equal); Methodology (supporting); Resources (equal); Supervision (equal). Till J. Weinhold: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (supporting); Methodology (equal); Resources (equal); Supervision (equal); Validation (supporting); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.