Quantum interference between independent solid-state single-photon sources separated by 300 km fiber

In the quest to realize a scalable quantum network, semiconductor quantum dots (QDs) offer distinct advantages including high single-photon efficiency and indistinguishability, high repetition rate (tens of GHz with Purcell enhancement), interconnectivity with spin qubits, and a scalable on-chip platform. However, in the past two decades, the visibility of quantum interference between independent QDs rarely went beyond the classical limit of 50$\%$ and the distances were limited from a few meters to kilometers. Here, we report quantum interference between two single photons from independent QDs separated by 302 km optical fiber. The single photons are generated from resonantly driven single QDs deterministically coupled to microcavities. Quantum frequency conversions are used to eliminate the QD inhomogeneity and shift the emission wavelength to the telecommunication band. The observed interference visibility is 0.67$\pm$0.02 (0.93$\pm$0.04) without (with) temporal filtering. Feasible improvements can further extend the distance to 600 km. Our work represents a key step to long-distance solid-state quantum networks.


Introduction
Quantum communications exploit the fundamental properties of quantum mechanics, such as superposition and entanglement, to implement communication tasks that are infeasible with the classical means. Examples include quantum key distribution 1,2 and quantum teleportation 3 . Since the early days of table top experiments 4,5 , one of the most significant challenges of the field is to extend the distance of quantum communication to a practically useful scale. Exciting progress 6 has been made over the past decades that culminated at satellite-based quantum communication over thousand kilometers [7][8][9][10][11][12] . Taking advantage of the negligible photon loss in the empty outer space, the satelliteground link has proven as an ultra-low-loss photonic channel.
In addition to the quantum channel, another important ingredient of the long-distance quantum communications is the quantum light source 13 . An ideal candidate is a singlephoton source that emits one and only one photon each time [14][15][16] . To obtain a high count rate after transmission, the single-photon sources should have a high system efficiency (which includes the generation 17 , extraction 18,19 , and collection 20 efficiencies) and high repetition rate 21,22 (which is intrinsically limited by the emitter's radiative lifetime). For quantum network applications, such as quantum teleportation that requires interfering independent photons, the single photons should be transform limited 23 . Additional requirements include a scalable platform, tunable and narrowband linewidth (favorable for temporal synchronization) and interconnectivity with matter qubits. Quantum dots (QDs) have been considered a promising solid-state system for quantum networks 14,23,24 . However, previous attempts on quantum key distribution [25][26][27] with QDs were up to a few kilometers only, and QD-based two-photon interferences [28][29][30][31][32][33][34][35] were also limited to kilometer scale and mostly below 50% visibility. There are a number of challenges to achieve a long-distance quantum interference, including high performances on singlephoton source brightness, purity, indistinguishability, wavelength band and matching, high-fidelity transmission, and more crucially, integrating all these parameters together compatibly.
In this Article, we report high-visibility quantum interference between two independent QDs linked with ~300 km optical fibers by developing efficient and indistinguishable single-photon sources, ultra-low-noise and tunable single-photon frequency conversion, and low-dispersion long fiber transmission. As a first step, our experiment points to a promising route to long-distance solid-state quantum networks.

Single-photon sources
Our experimental configuration is shown in Fig. 1. Two QDs are housed inside two cryogenic-free cryostats with a temperature of 4 K and 1.7 K, respectively. To maximize the efficiency and indistinguishability of the single photons, the QDs are spectrally and spatially optimally coupled to microcavities. As in our previous work 20   These two single photons are consecutively emitted from the same QDs with a time separation of 12.5 ns. Figure 2b shows the histograms of normalized coincidences for the two photons set at parallel and orthogonal polarizations. After correction of the residual second-order correlation, we extract a photon indistinguishability of 91.9(1)% and 83.9(3)% for QD1 and QD2, respectively.
It is important to note the difference between the mutual indistinguishability at 12.5-ns separation and Fourier transform limit 23 . The former is immune to any environmentally induced spectral diffusion that occurs at a time scale much slower than 12.5 ns. What really matters for the quantum interference between independent QDs is the degree of transform limit, that is, the ratio of T2/2T1, where T1 and T2 are radiative lifetime and coherent time of the single photons, respectively. We measure T1 using time-resolved pulsed resonance fluorescence. By fitting the exponential decay, we extract the radiative lifetime T1 of 78.0(1) ps for QD1 and 69.9(1) ps for QD2, as illustrated in the insets of and 75.1(1)% for QD2, which are slightly lower than the 12.5-ns indistinguishability as we expected.

Quantum frequency conversion
There are two major challenges in sending the QD single photons through long-distance optical fibers and observing quantum interference. First, the InAs QDs emission is at a wavelength of ~890 nm, which should be converted to telecommunication wavelength to exploit the low transmission loss in commercially available fibers. So far, the QDs directly emitting single photons in the telecommunications wavelength [39][40][41][42][43] have not yet reached a performance comparable to their near-infrared counterparts. Second, the selfassembled QDs emit single photons intrinsically at different wavelength, which would reveal which-way information to prevent the Hong-Ou-Mandel interference.
In this work, we use quantum frequency conversion [44][45][46] to overcome both problems. To this end, we fabricate Periodically Poled Lithium Niobate (PPLN) waveguide for difference frequency generation (see Fig. S3). The energy conservation demands 1/c=1/s−1/p, where s, p and c represent the wavelengths of the signal, pump, and converted photons, respectively. To precisely tune the two converted wavelengths into resonance, the pump lasers have both a coarse tuning range of ~1 nm and a fine tuning resolution of 3.6 MHz using the laser PZT actuator, which is ~40 times and ~0.1% of the QD emission linewidth, respectively (Fig. 3a). For the wavelengths of QD1 and QD2, the pump lasers are tuned at 2049.98 nm and 2043.46 nm, respectively, which convert both into 1582.75 nm (as labelled in Fig. 1).
By optimizing the nonlinear interaction, waveguide coupling, and transmission rate, the overall single-photon conversion efficiencies reach ~50% for both devices (Fig. 3b). To suppress the noise background from the residual pump laser, harmonic generation, and broadband Raman photons induced by the strong pump laser, we use a combination of dichromic mirrors and optical filters to obtain a signal-to-noise ratio of 28-30 dB (Fig,   3c). We note that an advantage of the frequency conversion process is that it does not interfere with the quantum emitter itself. To test whether the converted photons still preserve the coherence properties of the signal single photons, we measure the purity and coherence time of the single photons after conversion, which, as plotted in Fig. S4 and Fig. 2c, show near-perfect overlap with the data before conversion.

Fiber transmission of single photons
The dominant loss is from the long-distance fiber transmission of the single photons.
As the transmission rate of the fiber is 0.19 dB/km, the loss over 300 km is 57 dB. Efforts are taken to preserve the photon's properties during the fiber transmission. To reduce the drift of photon's arrival time, the temperature of the fibers is stabilized within ±0.1 degree. The measured typical time drift is within 10 ps per hour, which is much smaller than the photon's coherence time. A set of half-and quarter-wave-plates is used to control the polarization. As shown in Fig. S6, there is a slow wandering of polarization drift over hours, which is transformed into ~10% level efficiency loss by applying polarization filtering at the end of the optical fibers.
There is also an effect of frequency dispersion in optical fibers owing to a wavelengthdependent velocity, which could reduce the indistinguishability of the single photons.
The dispersions of QD1 and QD2 single photons over the 150-km fiber are 66.5 ps and 89.4 ps, respectively, which are comparable to the single photon's coherence time of 105-120 ps. However, if we arrange the identical single photons to go through the same fiber length, the photons will experience the same dispersion and thus remains identical.
Therefore, the symmetric transmission configuration set-up in our experiment makes the two-photon interference immune to fiber dispersion 47,48 .

Remote two-photon interference
After faithful transmission over the optical fibers, the two single photons in the outputs are synchronized and superposed on a beam splitter for quantum interference. We use superconducting nanowire single-photon detectors with an efficiency of 76% and a time resolution of ~70 ps to register the finally arrived photons. The two-photon coincidence counts when the two photons are controllably set at resonant (red) and far-tuned (black, Temporal filtering can also significantly increase the two-photon interference visibility.
The time resolution of the single-photon detectors is 70 ps, much smaller than photon's coherence time. We plot in Fig. 4f

The future
Figure 5a summarizes two-photon interference distance and visibilities of previously reported work between two QDs, to the best of our knowledge [28][29][30][31][32][33][34][35]53 . This experiment establishes a distance that is more than 2 orders of magnitude larger than the previous record, with simultaneously the highest visibility.  22 , the single photon system efficiency is feasible to reach 80%. In addition, ultra-low-loss optical fiber with transmission loss of 0.16 dB/km has become available. A numerical simulation curve is plotted in Fig. 5b. With these readily improvement, the transmission distance can be extended to ~600 km where the coincidence count rate will be 0.012 Hz with a signal-to-noise ratio of 10 dB. Such a distance scale is already comparable to the well-developed twin-field quantum key distribution experiments 54,55 .
In summary, our work represents an important step toward quantum telecommunication networks using semiconductor QDs and telecom fiber channels. The experiment creates a solid-state platform to implement quantum teleportation 5