Single-photon source (SPS) satisfies single-photon character, which means that the probability of detecting two or more photons simultaneously at any moment is zero. In quantum science and technology research, perfect single-photon character forms the basis for the security of quantum communications and also crucial for in optical quantum computing. Besides, to achieve efficient conversion of a quantum state between photons and atoms, the photon linewidth must be narrower than the atomic linewidth. Therefore, the SPS with subnatural linewidth is an ideal quantum information carrier for connecting remote atomic quantum nodes in quantum network. The simple fluorescence from single emitter, including atom and various atom-like systems (e.g., quantum dot, ion, molecule, and nitrogen-vacancy center), satisfies perfect single-photon character and thus fluorescent single photons is the most widely adopted SPS. Noteworthy, the single-photon character of fluorescence is a global property of all the spectral components of resonance fluorescence, including coherent and incoherent components, and the absence of a few spectral components can spoil the single-photon character. Studies based on two-level systems demonstrate that for resonance fluorescence, single-photon character and subnatural linewidth cannot be satisfied simultaneously, which means that the fluorescent single photons cannot have subnatural linewidth, and conversely, fluorescent components within subnatural linewidth cannot maintain single-photon character. Although there were many previous related studies, fluorescent single photons with subnatural linewidths were unsuccessfully realized. Consequently, it seems that the natural linewidth imposes a lower limit on the linewidth of fluorescent single photons.

Considering the importance of fluorescent photons from atomic and atom-like systems in quantum science and technology, the team has explored whether the limit imposed on the bandwidth of fluorescent single photons by natural linewidth can be broken. It is demonstrated that atomic and atom-like emitters are capable of emitting single photons with subnatural linewidth, breaking the above limit. Based on a simple level system as shown in Fig.1(a), subnatural linewidth fluorescent single photons are emitted directly and optimal single-photon character and subnatural linewidth can be simultaneously possessed and thus be observed in the fluorescence field. Moreover, by varying the intensities of external fields, the single-photon linewidth can be continuously and readily adjusted over a large range, therefore, the fluorescent single photons with an arbitrarily narrow linewidth can be emitted by an atom or atom-like system. The team also reveals the general constraint between the single-photon emission rate and linewidth, and deduce that the upper limit of the single-photon emission rate equals the single-photon linewidth. Moreover, the single-photon emission rate in the proposed scheme can reach this upper limit. By exploring detection response in time domain, the team reveals the general condition to generate fluorescent single photon with subnatural linewidth, i.e., the successive emission process of the target single photons is totally dominated by a transition loop with a metastable state. Relevant research results were recently published in Photonics Research, Volume 12, No. 4, 2024. [ He-Bin Zhang, Gao-Xiang Li, Yong-Chun Liu. Subnatural-linewidth fluorescent single photons[J]. Photonics Research, 2024, 12(4): 625 ]

Figure 1(a) Schematic diagram of the emitter and the detection setup in the subnatural-linewidth SPS scheme. On the left is a Λ-shape emitter. The transitions |g>→|e> and |g>↔|a> are driven by the external fields F1 and F2 in the weak excitation regime, respectively. Therefore, a transition loop composed of the transitions |g>→|e>→|a> and |a>→|g> is formed in the emitter. Fluorescent single photons with subnatural linewidth are emitted from the transition |e>→|a> and collected by a frequency-filtered HBT setup on the right. (b) Fluorescence spectrum for the transition |e>→|a>, with a spectral width much smaller than the natural linewidth. (c) Normalized two-photon correlations of the detector for the transition |e>→|a> as a function of filtering bandwidth κ and driving strength Ω. (d) Emission rates of the subnatural-linewidth single photons (red solid line) and two-level system (blue dashed line) as functions of driving strengths, respectively.

A -shape three-level system is used as an emitter to demonstrate the approach to generate sub-natural linewidth single photons. As shown in Fig.1(a), two coherent fields are applied to drive the transitions of the emitter. Of these, the laser field pumps the population from the ground state |g> to the excited state |e>, so that target fluorescent single photon can be emitted by the spontaneous decay |e>→|a>. The other coherent field pumps the population in the metastable state |a> into the transition channel directly driven by the laser field. We see that due to the common effect of the two coherent fields in the weak excitation regime and the spontaneous decay, a long-period transition loop shown in Fig.1(a) appears and totally dominates the successive emission process of the target photon. The transition |g>↔|a> driven by the coherent field ensures that the transition loop is closed, and the two coherent fields are in the weak excitation regime, which results in the long lifetime of the metastable state and thus the long period of the transition loop. In the above design, the time interval of two successive target photons can be much longer than the natural lifetime 1/γ of the emitter. Consequently, in terms of frequency, the single-photon linewidth is much smaller than the natural linewidth, which can be demonstrated by the single-photon response on a narrowband detector, as shown in Fig.1(c).

Benefiting from the revelation of general condition, this proposed approach can be generalized in various physical systems with Λ-shape and similar energy structures. Moreover, subnatural linewidth and narrowband single photons have many excellent properties and practical applications. For instance, single photons with subnatural linewidth can attain high coherence and achieve efficient conversion of quantum state between photons and matter, which are desirable for many crucial quantum technologies, including long-distance quantum communication and quantum networks. Besides, subnatural linewidth and narrowband single photons also facilitate the acquisition of highly indistinguishable and pure single photons by narrowband filtering while ensuring perfect single-photon character.

Prof. Yong-Chun Liu, one of the corresponding authors of the study, commented, "As a popular SPS, resonance fluorescence has been the focus of research in the fields of quantum optics and quantum technology. Subnatural linewidth single photons enable the efficient and stable conversion of the quantum state between flying photonic and stationary qubits, which is the key physical process for quantum information storage and processing and thus for long-distance quantum communications and quantum networks. Although the fluorescence radiated by atomic or atom-like systems has ideal single-photon character, the linewidth of fluorescent single photons seems to be difficult to break the limitation imposed by the natural linewidth according to previous studies. The proposal to generate subnatural-linewidth single photons proves that fluorescent single photons can break this limitation, thereby becoming the SPS with both perfect single-photon character and sub-natural linewidth. Further, a general condition for generating sub-natural linewidth single photons using the atom or atom-like system are revealed. Thereby, this work can significantly contribute to a deeper understanding on the quantum nature of single-photon and resonance fluorescence, and is valuable for research in the fields of quantum optics, photonics, and quantum technology."

In the next step, the team will explore methods for generating single photons and multi photons with subnatural linewidths on demand. The team will also study the quantum information processing and storage in systems accessible in practical quantum technologies based on the subnatural-linewidth single photons.