Distributing quantum entanglement between remote nodes is one of the fundamental primitives for quantum information processing, such as quantum communication [1–4], distributed quantum computing [5–7], and quantum teleportation [8–10]. Direct transmission of qubits seems to be a straightforward strategy. However, due to the increasing photon loss and noise in the channel [11,12], it is attainable just within a moderate distance. A promising solution is the quantum repeater scheme, where entanglements are preliminarily generated between intermediate nodes within the attenuation length and then extended via linking the adjacent segments . This hierarchical architecture shifts the experimental focus from reducing transmission loss into overcoming the probabilistic generation of the entanglement for each segment. It necessitates the nodes functioning as quantum memories, and therefore the generated entanglement can be kept for waiting for the other to be accomplished [14–16].
Besides, connecting entangled segments is usually mediated by photons retrieved from neighboring nodes [17–19]. While two photons are respectively correlated with the internal state of the remaining nodes, their interference validates operations like Bell state measurement to project the matter systems into an entangled state. An essential requirement in this optical scheme is the indistinguishability of photons from different repeater nodes, which can be demonstrated by the Hong–Ou–Mandel (HOM) interference [20,21].
So far, HOM interference between photons retrieved from two single-photon sources has been realized in various systems, such as cold atomic ensembles [22,23], single atoms , nitrogen vacancy centers [25,26], and trapped ions . To avoid noise and decoherence from atomic thermal motion, these systems are mostly operated at cryogenic temperatures and in well-isolated environments [28,29]. Recent progress has shown interest in room-temperature systems [30,31], which offer better scalability as they are free from the complex cooling apparatus. Quantum interference between two single photons from the spontaneous four-wave mixing (SFWM) process in room-temperature atomic ensembles has been reported . It obtains high interference visibility but does not operate on demand. Recently, the far off-resonance Duan–Lukin–Cirac–Zoller (DLCZ) protocol demonstrates the feasibility of combining single-photon generation with memory capability in a room-temperature system [32–34]. This DLCZ-type source prototypes repeater nodes in the pioneering proposal  for quantum networks, and the far-off-resonance configuration endows extra broadband feature for high operation rate. But for further application, proving the ability of generating indistinguishable photons from independent sources remains to be proved.
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In this work, we prepare two individual single-photon sources based on quantum memories, operating in a heralded, low-noise, and broadband fashion. The memory-built-in feature of our ensemble-based source enables a repeat-until-success strategy in the single-photon generation, thereby speeding up the process of HOM interference, representing a promising way towards realizing large-scale quantum networks at ambient conditions.
2. EXPERIMENTAL SETUP
We perform the experiment on two vapor cells containing cesium atoms, each acting as a memory-built-in single-photon source. Figure 1(a) shows the -type atomic configuration employed for the single-photon generation, consisting of a ground state for initialization, another ground state for storing excitation, and an excited state labeled . For each trial, all atoms are initially prepared in the ground state via a pump light resonant with transition. Afterward, a collective excitation is created via spontaneous Raman scattering, which is heralded by the accompanying Stokes photon. After a programmable delay, the stored collective excitation can be mapped into a single photon by applying a read pulse [35,36]. Notably, a large detuning is applied (13.2 GHz in the write process and 4 GHz in the read process, respectively) to avoid the fluorescence noise in room-temperature ensembles. Making use of the orthogonal polarization, the signal photons are separated from the strong control light via a high-extinction-ratio Wollaston prism. They are further purified by a cascaded Fabry–Perot cavity, which also serves as a splitter to transmit Stokes photons and anti-Stokes photons into different paths. Finally, the heralded anti-Stokes photons from two independent sources are respectively collected by single-mode fibers and directed into a fiber beam splitter for HOM interference. More experimental details can be found in Appendix A.
Figure 1.Schematic view of the experiment. (a) The atomic energy level of
In an ideal case, the indistinguishability between two incident photons governs this completely destructive two-photon interference ; while in practice, the multi-photon component of the photon sources also contributes to the coincidental events at outputs of the fiber beam splitter and therefore leads to a reduction of interference visibility. For the purpose of suppressing the multi-photon component, the ensemble-based source applies a weak pulse in the write process to reduce the creation of high-order excitation . However, this causes a limited single-photon generation rate for the interference experiment.
To speed up the process of obtaining the HOM dip, a repeat-until-success protocol is introduced to enhance the generation rate of heralded single photons. For each source, write pulses with an equal interval are applied to the ensembles, repeating the write process until a Stokes photon is detected [23,37]. As two sources are mutually independently manipulated, one can continue to repeat the write process while the other one successfully stores the generated collective excitation. When the collective excitations are prepared in both atomic ensembles, read pulses at a pre-determined moment are applied to both ensembles to obtain the anti-Stokes photons simultaneously. Otherwise, the repeat-until-success write process also stops when the maximum number of write pulses has been reached.
Obviously, the ability to preserve the generated collective excitation is a key factor for this protocol. It is quantified by measuring the cross-correlation function between the Stokes photons and the anti-Stokes photons (see Fig. 2), which implies that the generated collective excitation can be preserved for an on-demand memory time [37,38]. To realize the repeat-until-success protocol, four write pulses are pre-programmed in each period and the output of the detector of the Stokes photon is transmitted into the pulse generation system. Upon detecting a Stokes photon, the signal from this detector triggers the pulse generation system to stop generating the subsequent write pulses. Otherwise, it works as pre-determined. Here, the time interval between adjacent write pulses is 125 ns, a litter bit longer than a single period of detection and feedback. In this case, the repeat-until-success protocol enables a 3.8 times enhancement of generation rate for each photon source and then about 15 times increase in the probability of simultaneously obtaining heralded single photons from two independent quantum memories.
Figure 2.Heralded single photon with a different time delay in quantum memory. The solid curves in the main part refer to the temporal shape of the generated single photon with a different time delay for retrieval, without reduction of any background noise. The red dots on the right side denote the corresponding cross-correlation function between the Stokes and anti-Stokes photons.
In addition, it is also accessible to manipulate the rate of four-fold coincidence by changing the power of the control light. As shown in Fig. 1, to adjust the power of the control pulse, a combination of a half-wave plate and a quarter-wave plate is placed in front of the polarization beam splitter, controlling the ratio of light incident into the ensemble. Figure 3(a) shows the counts of the heralded single photon increasing with the energy of the write pulse. It indicates that a strong control pulse is required for a high rate of four-fold events. But, on the other hand, when applying a stronger control pulse, both high-order excitation in the write process and the four-wave mixing process in the read process are strengthened [17,33]. Along with the energy-dependent leaking from the control pulses, the increased noise degrades the fidelity of the generated single photon and thereby results in a lower interference visibility. We analyze the photon statistic property via a Hanbury Brown–Twiss interferometer, and the single-photon character is quantified by an anti-correlation parameter [39,40]. For the chosen energy of 330 pJ per write pulse, the measured four-fold coincidence rate is about 20 events/h, and the anti-correlation parameter of the single-photon source is , therefore leading to a good trade-off between the rate of four-fold coincidence and the interference visibility.
Figure 3.Characterization of the two single-photon sources from independent room-temperature quantum memories. (a) The counts of the heralded anti-Stokes photons as a function of the write pulse power with 566,037,735 trials performed. The red pentagon refers to the chosen pulse energy in this experiment. (b) The temporal shape of the heralded anti-Stokes photons generated by two photon sources. The blue squares (purple rhombuses) mark the heralded anti-Stokes photons from one photon source detected by APD3 (APD4), while the red dots (orange triangles) represent the heralded anti-Stokes photons that are generated by another photon source and detected by APD3 (APD4). These data are obtained with a pulse energy of 330 pJ and 566,037,735 repeated trials.
To observe high-visibility HOM interference, the properties of the relative photons here are carefully engineered to be indistinguishable [24,25]. After coupling into single-mode fibers, the anti-Stokes photons from two independent sources are both in the transverse Gaussian mode. Different from the condition with the bulk beam splitter, a good spatial overlap is easily achieved when two incident photons are mixed in a fiber beam splitter. For the polarization degree of freedom, the anti-Stokes photons are both vertically polarized after being separated from the strong read pulse via a high-extinction-ratio Wollaston prism. But their polarization is dissimilarly rotated by fibers and other optical devices during the propagation. We then adjust the half-wave plates and quarter-wave plates, which are positioned at the input ports of the single-mode fibers, to compensate for this polarization difference before they superpose on the fiber beam splitter. In addition, the energy, the spatial profile, and the duration of the control pulse are finely tuned to match the temporal mode of the photons . Figure 3(b) shows the measured temporal shapes of the anti-Stokes photons from two sources, indicating high similarity between them.
For an HOM interference experiment in the time domain, the time interval between two heralded anti-Stokes photons is changed from overlap to separation . We introduce this time delay by varying the time interval between two electric control signal sequences, which are respectively applied to drive two pulse generation systems. Figure 4 shows the registered four-fold coincidence counts as a function of the arrival time difference for two independent anti-Stokes photons, where the time step is 3.75 ns. The solid curve is the theoretical result based on the parameters in our experiment [42,43]. Without subtracting the accidental coincidence from the background noise and the detector dark counts, the result gives a visibility of ()%. The obtained visibility exceeds the classical limit of 50%, indicating the non-classical property of two anti-Stokes photons and the indistinguishability between them [22,30].
Figure 4.Four-fold coincidence as a function of the time delay between two photons from independent room-temperature quantum memories. The blue dots correspond to the experimental data with an effective measurement of 11,886,792,452 trials, and the solid line represents the theoretical curve. The error bars denote one standard deviation.
To further investigate the nonideal interference at zero delay, we analyze our result with the model from Ref. . In this model, the nonvanishing dip is attributed to the imperfect indistinguishability between two photons and multi-photon component of the photon sources [44,45]. In our experiment, the measured anti-correlation parameters of the single-photon sources are and , respectively. According to the model in Ref. , these multi-photon components reduce the achievable visibility to ()%. The estimated value is quite close to the measured one, leaving a small residual reduction of visibility caused by the distinguishability between photons. At present, this indicates that the single-photon purity of the sources is the dominant factor for visibility degradation. Therefore, efforts for improving the single-photon purity, like adding clear pump pulses between adjacent write pulses and suitably decreasing the energy of the control pulses, will significantly enhance the interference visibility.
4. CONCLUSIONS AND DISCUSSION
In summary, we have successfully demonstrated HOM interference between heralded single photons from two independent room-temperature quantum memories. The measured interference visibility shows the capability of such independent sources for constructing a quantum memory-enabled network. Its further analysis highlights the potential improvement by suppressing the multi-photon component, e.g., by elaborating the cavity engineering to reduce four-wave-mixing noise  or adding clear pump pulses between write pulses to reinitialize the state of the atomic ensemble . Along with the achieved near-millisecond lifetime , our result certifies the feasibility for engineering, manipulating, and transferring quantum resources with room-temperature quantum memories, and the realization of long-distance quantum communication and optical quantum computing at ambient conditions.
Acknowledgment. The authors thank Jian-Wei Pan for helpful discussions. X.-M. J. acknowledges additional support from a Shanghai talent program and support from the Zhiyuan Innovative Research Center of Shanghai Jiao Tong University.
APPENDIX A: EXPERIMENTAL DETAILS
As shown in the Fig.
Signal photons with vertical polarization and control pulses with horizontal polarization are separated by a Wollaston prism. Due to the non-negligible noise from the leakage of the control pulses, further purification is needed for a higher signal-to-noise ratio. Therefore, the Stokes photons and anti-Stokes photons are collected into a single-mode fiber and transmitted to frequency filters (cascaded cavities) to filter out the residual control pulses. The measured peak transmission of the single cavity reaches 90%, and a high extinction ratio of about is obtained after Stokes (anti-Stokes) photons pass three cascaded resonant cavities. After leaving the cavity, the purified Stokes photons and anti-Stokes photons are detected by single-photon detectors, providing information about the properties of the single-photon sources. For the chosen energy of write pulse, the measured probability of detecting a Stokes photon in a trial is about by utilizing the repeat-until-success protocol. Conditioned on the detection of a Stokes photon, the probability of detecting an anti-Stokes photon is about 1.53%. Notably, the above parameters are obtained by analyzing the recorded photon counts, where loss from coupling, filtering, and inefficient detection has been included. For the propagation from the atomic ensemble to the detector, the transmission efficiency of the fiber coupling and the filter together is about 17.3% in the Stokes channel and 16.5% in the anti-Stokes channel. The quantum efficiency of the detector is about 50%. For clarity, some important experimental parameters are shown in Table Characteristics of the Single-Photon Source and Measured Four-Fold Coincidence Rate
Parameter Value Counting rate of Stokes photon Counting rate of the heralded anti-Stokes photon Anti-correlation parameter Four-fold coincidence rate
Characteristics of the Single-Photon Source and Measured Four-Fold Coincidence Rate
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