A promising approach to realize a quantum internet [1] is to use a hybrid quantum network - a network composed of many different quantum devices, such as quantum emitters, quantum repeaters, or quantum gates, interconnected via photonic links. However, such a wide variety of quantum devices tends to be spectrally incompatible. Especially, the challenge arises to interface different single-photon spectral bandwidths with high efficiency. In particular, an important link is bridging the ultrafast optics with hundreds of GHz spectral bandwidths with nanosecond timescales of single-photon pulses, hence MHz-wide spectra. Such an interface corresponds, e.g., to coupling a single photon produced in a commonly used bulk spontaneous parametric down-conversion (SPDC) photon sources to atomic-based quantum memories. The already demonstrated spectral compression techniques, based mostly on optical nonlinearities, operate only in the above GHz regime and are not suitable for this task [2].
A promising approach to realize a quantum internet [1] is to use a hybrid quantum network - a network composed of many different quantum devices, such as quantum emitters, quantum repeaters, or quantum gates, interconnected via photonic links. However, such a wide variety of quantum devices tends to be spectrally incompatible. Especially, the challenge arises to interface different single-photon spectral bandwidths with high efficiency. In particular, an important link is bridging the ultrafast optics with hundreds of GHz spectral bandwidths with nanosecond timescales of single-photon pulses, hence MHz-wide spectra. Such an interface corresponds, e.g., to coupling a single photon produced in a commonly used bulk spontaneous parametric down-conversion (SPDC) photon sources to atomic-based quantum memories. The already demonstrated spectral compression techniques, based mostly on optical nonlinearities, operate only in the above GHz regime and are not suitable for this task [2].
A quantum network is believed to be the next generation of quantum technology [1]. In the past decades, individual quantum systems—for example, quantum dot (QD) [2–4], etc.—have been studied in depth and the technologies are mature; therefore, the consideration of combining different systems to construct a quantum network (especially a hybrid one) is timely. Moreover, a quantum network is absolutely necessary in the fulfilment of a general quantum task, which needs the cooperation of many different kinds of quantum units. On a larger scale, the local quantum networks can be further linked to construct a global quantum network, namely the quantum Internet [1]. With this technology at hand, distributed quantum computation can be realized, making scalable quantum information processing possible in multiple sites over long distances. The primary challenge of the construction of a quantum network is the state distribution among different nodes. An elementary quantum network based on two identical nodes each constituted by a single atom in the optical cavity has been realized in an experiment [5]. However, here we focus on the quantum network comprising heterogeneous nodes, which is more general and can combine advantages of different quantum systems to complete more complicated quantum tasks. The construction of a hybrid quantum network is more difficult, since heterogeneous quantum systems have different properties that are not naturally matched, such as the different emission (or absorption) wavelengths and different bandwidths [8], etc. To establish the hybrid interface, QD is a good candidate. QD can act as a deterministic single [2] or entangled [3] photon source and is also a promising physical carrier for solid-state spin qubit [4]. QD has been interfaced with hot atoms [6] and single ions [7] in recent years. Almost at the same time, Li's group experimentally demonstrated the first optical connection between QD and a solid-state quantum memory [8]. Distinguishing from the former works, the all-solid-state character of this work makes the whole architecture more stable and easier to be manipulated and integrated. During this work, the sample was grown by Niu's group [8]. A special sample design moves the emission band of QDs to approximately 879.7 nm—the memory band of the solid-state memory [9]. Since the fine-tuning range is only several 0.1 nm, hundreds of QDs on the sample were detected by Li et al. and finally one of them was selected, whose emission line is located at 879.5 nm. Using a local-heating technique, the researchers precisely tuned the emission wavelength of this QD to the solid-state memory's memory band, whose bandwidth is as narrow as hundreds of MHz [9]. The quantum memory in this experiment was based on the atomic frequency comb (AFC) protocol [10]. The memory efficiency is as high as 20% when the storage time is 40 ns, and the non-collinear configuration for the pump light and the signal photons can substantially reduce the noise from the pump light. To further reduce the detection noise, a superconducting single-photon detector (SSPD), whose dark count rate can be as low as 1.5 per second, is used instead of the silicon single-photon avalanche diode. With these conditions, Li's experiment clearly shows the stored and retrieved single photons that are originally generated from the QD. The signal-to-noise ratio (SNR) is 9:1. The second-order retrieved single photons are even seen in the data, which further validates the experimental result. Another advantage of Li's work is the demonstration of multi-temporal-mode quantum memory with up to 100 narrow deterministic-single-photon pulses [8]. This result is directly associated with the construction of a quantum repeater [11]—one of the essential components for a long-distance quantum network. The primary characteristics of this experiment, namely the deterministic single-photon memory (differing from the previous works) and the multimode memory, are both critically important in the improvement of a quantum repeater's efficiency [12]. Also, Li's further work finished the quantum memory of 51 spatial modes using the orbital angular momentum (OAM) modes of herald single photons [9]. By combining both the temporal and spatial multiplexing, and the deterministic single-photon source, more efficient quantum repeaters can be constructed. We hope that the recent studies [8,9] will pave the way for the construction of quantum repeaters, and furthermore quantum networks—both in the short term and the long term—based on all-solid-state devices. As a special application of a quantum network, quantum key distribution (QKD) can also benefit from Li's work both in security and transmission distance (key rate). QKD utilizes the principles of quantum mechanics to guarantee secure communication between two authorized parties (or quantum nodes, for instance) and the famous protocols including BB84 (proposed by Bennett and Brassard in 1984) [13]), etc. However, the commonly used weak-coherent-pulse photon source (typically attenuated laser) will decrease the security of QKD because of its multiphoton probability, which means that QKD suffers from several certain attacks, such as the photon number splitting (PNS) attack. Although a decoy state has been introduced to achieve potential solutions to this problem, a substantial shrinking of the sifted key will be required and the complexity of the protocol may contain loopholes [14,15]. Therefore, the unconditional security guaranteed by quantum mechanics still requires a single-photon source, such as QD (experimental work regarding QKD on the basis of a QD single-photon source can be referred to in [14,15]), etc. The deterministic-single-photon pulse train generated by QD in Li's experiment [8] can provide a single-photon-source node (in the network) and keep the security of QKD. Moreover, because of both the elimination of multiphoton probability and the multi-temporal-mode single-photon generation, the key rate of QKD will be improved, which is associated with a longer transmission distance. The quantum repeater that benefited from Li's work will also further improve the transmission distance of QKD.
Long-distance transmission of quantum information between various systems, such as single-photon sources, quantum memories or matter-based quantum information processing units is hampered by disparate spectral-temporal properties of photons that can be efficiently emitted or absorbed by such systems. Quantum frequency conversion, i.e. low noise nonlinear optical frequency conversion, is an established method to address photon central frequency distinguishability. However, it does not address the issue of single-photon spectral bandwidth and timescale variations, which can range from single picoseconds to hundreds of nanoseconds.
Photons as flying qubits are ideal carriers of quantum information. However, efficient quantum interfaces which transfer flying into stationary qubits and vice versa are needed to realize complex quantum networks. Stationary qubit systems (atoms, ions, or solid state implementations) couple to photons via characteristic optical transitions. In order to establish key quantum operations, such as coherent photon storage, entanglement swapping, etc., high-quality photons with a tailored spectral, spatial, and temporal mode are needed. One way to generate these photons is to use the stationary qubit systems themselves. Another approach which does not impose limitations in terms of the photon’s wavelength or bandwidth relies on all-optical single photon sources. An example is spontaneous parametric down conversion (SPDC) inside an optical cavity with well-defined linewidth. In SPDC, a pump photon incident on a nonlinear medium is split into two photons of lower energy that are often referred to as signal and idler. Resonating the fluorescent fields, the setup becomes an optical parametric oscillator (OPO) far below the threshold. The usually THz broad emission spectrum of SPDC then follows the Airy function of the resonator. The spectral bandwidth of the generated photons can easily reach values of several MHz, which is comparable to atom resonance linewidths. By introducing additional losses or simply changing the cavity mirror reflectivities the bandwidth is tunable up to several 100 MHz. This is comparable to the bandwidth of single photons generated by e.g. quantum dots.
A promising approach towards implementation of large-scale quantum information and communication protocols is a multifunctional photonic quantum information processing system, where a variety of distributed components, such as quantum memories, trapped ions, or photonic quantum gates are coherently interconnected via photonic links. These components may exhibit a vast range of spectro-temporal properties. A key incompatibility is spectral bandwidth mismatch. For example the characteristic bandwidths of photonic communication channels and nonlinear-optical single-photon sources are in the 100 GHz range, whereas typical bandwidths associated with trapped ions or media exhibiting strong single photon nonlinearity, such as Rydberg atoms, are in the sub-GHz regime, reaching single MHz values. Single-photon-level bandwidth conversion has been experimentally demonstrated by techniques based on the temporal lensing principle, but only between multi-GHz bandwidth optical pulses [1, 2]. Here we present a numerical study of an electro-optic time-lens-based technique enabling bandwidth conversion from the 100 GHz bandwidth region towards single MHz bandwidths. We discuss progress towards experimental implementation and possible realizations using alternative temporal lensing platforms, such as three and four wave mixing.
The recent advent of optical metasurfaces, ultra-thin structures composed of nanoresonators facilitating strong light concentration [1–3], opens the path towards efficient \nfrequency conversion [4–7] in a material thousand times thinner than a human hair [8]. \nThere is a remarkable capacity to individually shape each nanoresonator of the metasurface to spatially and spectrally control the conversion process with unprecedented \nnanoscale resolution, facilitating an ultimate flexibility to selectively convert, focus, \nand image different colours with a single metasurface. The strong enhancement of the \nnonlinear processes in dielectric nanoresonators is largely due to the absence of material \nabsorption and the excitation of Mie-type bulk resonances [2]. The highest conversion \nefficiency to date has been achieved employing III-V semiconductor nanostructures, \nsuch as AlGaAs which is a non-centrosymmetric material with high quadratic nonlinear \nsusceptibility. In particular, second-harmonic generation efficiencies up to 10−4 have \nbeen recently demonstrated [8–12], six orders of magnitude higher than in plasmonics. \nSuch capabilities can make an immense fundamental and practical impact, including \nthe quantum state generation in nonlinear metasurfaces as we discuss in this chapter. \nThe quantum state of correlated photon-pairs is the essential building block for photon entanglement [13, 14], which underpins many quantum applications, including secure networks, enhanced measurement and lithography, and quantum information processing [15]. One of the most versatile techniques for the generation of correlated photons is the process of spontaneous parametric down-conversion (SPDC) [16, 17], see \nFig. 1. It allows for an arbitrary choice of energy and momentum correlations between \nthe generated photons, robust operation at room temperature, as well as for spatial and \ntemporal coherence between simultaneously pumped multiple SPDC sources. Alternative approaches based on atom-like single photon emitters, such as solid-state fluorescent atomic defects [18], quantum dots [19, 20], and 2D host materials [21, 22], have \nreached a high degree of frequency indistinguishability, purity and brightness [19, 20]. \nHowever, this comes with the expense of operation at cryogenic temperatures and lack \nof spatial coherence between multiple quantum emitters. These features might limit \npossible applications and reduce the potential for device scalability. Furthermore, the \nsmall size of the atomic sources often requires complex schemes aimed at coupling to \noptical nanoantennas and improving the photon extraction efficiency [21]. \nThe miniaturization of SPDC quantum-light sources to micro and nanoscale dimensions is a continuing quest, as it enables denser integration of functional quantum \ndevices. Traditionally, bulky cm-sized crystals were utilized for SPDC, entailing the \ndifficulty of aligning multiple optical elements after the SPDC crystal, while offering \nrelatively low photon-pair rates [17]. As a first step of miniaturization, SPDC was \nrealized in low-index-contrast waveguides, which allowed confining light down to several square micrometers transversely to the propagation direction, significantly enhancing the conversion efficiency [23]. However, this approach still requires centimetres \nof propagation length, which makes the on-chip integration with other elements challenging [24]. The introduction of high-index contrast waveguides and ring resonators \nallowed for shrinking the sizes necessary for SPDC to millimetres [25], and to tens \nof micrometers [26]. However, further miniaturisation down to the metasurfaces composed of nanoresonators requires conceptually different approaches.