Laser manufacturing of spatial resolution approaching quantum limit

Since early demonstrations of femtosecond laser as a three-dimensional (3D) processing tool, microdevices with exciting optical, electronic, mechanical, and magnetic functions have been manufactured, by which novel concepts from 3D quantum photonic integrated circuits to intelligent micro-robots are enabled. Much effort in the past decade in this field has been devoted to improving manufacture spatial resolution, and several tens of nanometre feature sizes have been reported based on multiphoton absorption, stimulation emission depletion, far-field-induced near-field enhancement, and photoexcitation-induced chemical bonding effects. Nevertheless, advanced applications, such as single-electron transistors, single-photon emitters (SPE), single-atom memory, or quantum-bit devices, require higher manufacturing spatial resolution (<10 nm, far beyond the optical diffraction limit), for example, the ability to address single-atom defect complex (SADC) for initiating atom-like optical transitions.

Along this line, the direct laser writing technique has been recently implemented to generate point defects called colour centres in wide-bandgap materials, such as centres in diamond, silicon carbide, aluminum nitride, and hexagonal boron nitride (hBN). Colour centres in hBN, in particular, have gained prominence among quantum platforms due to the van der Waals layered crystal structure, making them easy for photonic integration. However, current laser-written hBN colour centres suffer issues with stochastic yield and positional accuracy. In addition, there is a very high probability of forming multiple centres over individual sites, which is undesirable for many applications.

In this work, we propose and experimentally demonstrate close-to-atom scale manufacturing using a threshold tracking and lock-in (TTL) method, by which feature sizes are as small as a few nanometres, e.g., <5 nm, ~λ/100, approaching quantum uncertainty limit, are realised. It enables near unity yield fabrication of quantum emitter with high positional accuracy and minimal damage to the lattice, which persists the quality of optical properties of colour centres. We show the laser-induced colour centres exhibit high brightness, high emission purity, and high stability (no spectral diffusion and blinking). This close-to-atom scale laser manufacturing represents a significant step forward in scalable quantum photonic technologies.

The paper situates its contribution within prior advances in femtosecond laser 3D processing and nanoscale feature fabrication. Reported methods achieving several tens of nanometre features include multiphoton absorption, stimulated emission depletion (STED), far-field-induced near-field enhancement, and photoexcitation-induced chemical bonding effects. For colour centre creation, prior direct laser writing in wide-bandgap materials (diamond, SiC, AlN, hBN) has been demonstrated. However, existing laser-written hBN colour centres have suffered from stochastic yields, poor positional accuracy, and frequent formation of multiple centres at a single site, limiting deterministic single-emitter fabrication required for quantum technologies.

The authors introduce a threshold tracking and lock-in (TTL) method to achieve close-to-atom scale laser manufacturing in hexagonal boron nitride (hBN) flakes using femtosecond laser pulses. The key idea is to use additional laser pulses as a probe to precisely track the intrinsic material threshold (E_tho), which reflects the crystal’s chemical bond strength, independent of observation sensitivity. An initially imperceptible lattice modification created by the first pulse is amplified by subsequent pulses, enabling accurate determination of E_tho via shot-number dependence. Experimentally, the damaging area decreases markedly with fewer shots at fixed pulse energy (e.g., at E_p = 4.66 nJ, reducing shots from N=3 to N=1 shrinks the processed size from ~200 nm to ~6 nm). The dependence of required shot number on pulse energy (optically visible detection criterion) yields a single-shot energy of ~4.83 nJ and 2–5 shots needed for E_p = 4.70–4.66 nJ; extrapolation to infinite shots gives an intrinsic threshold E_tho = 4.65 ± 0.01 nJ. Below E_tho, excitation is reversible with no permanent defects. Using near-threshold single-shot irradiation identified by TTL, the team fabricates single-atom defect complexes (SADCs) with sub-5 nm dimensions confirmed by high-resolution TEM.

The physical limit is analyzed via statistical thermodynamics: near threshold, geometric confinement by the Gaussian intensity profile no longer dictates the initiation site; instead, stochastic electron kinetic energy fluctuations (∝ k_B T_e) dominate, leading to a random ablation location within a nanoscale range. A Maxwell–Boltzmann-based probability model is presented, and an uncertainty-limited ablation radius r_m ≈ 3 nm is estimated for hBN, consistent with observed <5 nm features.

For quantum emitter generation, hBN flakes are patterned by single femtosecond pulses with energies tuned around the threshold. Arrays and complex patterns (e.g., QR code, concentric circles, star, “hBN”, “tiger”) are written under 450 nm excitation for PL imaging. By gently varying E_p, the processed site size and resulting defect ensemble are controlled: higher E_p yields multiple emitters (polychromatic spectra), and lowering E_p towards E_tho yields single-colour single-photon emitters (SPEs). Optical characterization includes confocal PL, emission spectra (zero-phonon lines, ZPL), second-order autocorrelation g²(τ) using a Hanbury Brown–Twiss setup (fitted with a three-level model), saturation measurements (count rate vs excitation power), polarization analysis, and time-resolved stability tests (spectral time series, intensity time traces).

• TTL enables determination of an intrinsic hBN damage threshold E_tho = 4.65 ± 0.01 nJ, independent of observation sensitivity, via multi-shot amplification and extrapolation.
• Near-threshold single-shot writing produces single-atom defect complexes (SADCs) with feature sizes <5 nm (~λ/100), approaching a quantum/statistical uncertainty limit; uncertainty analysis predicts an ablation radius r_m ≈ 3 nm, matching experiments.
• At fixed E_p = 4.66 nJ, reducing shot number from N=3 to N=1 reduces processed size from ~200 nm to ~6 nm, illustrating the sensitivity of observed "thresholds" to criteria and the benefit of TTL.
• Deterministic creation of optically active colour centres at every addressed site: complex PL patterns (QR code, concentric circles, star, “hBN”, “tiger”) were written by single pulses at E_p ≈ (1 ± 5%) E_th ≈ 5.2 nJ, with bright emission observed at each site.
• By tuning pulse energy, the number of emitters per site is controlled: at E_p = 4.86 nJ, spectra show >10 peaks; at 4.78 nJ, 4 peaks; at 4.68 nJ, a single sharp ZPL (FWHM ≈ 3 nm), transitioning from polychromatic to monochromatic emission.
• Photon antibunching improves as E_p approaches threshold: g²(0) reduced from 0.48 (multi-emitter case) to 0.09 (single-emitter case) without background correction, confirming single-photon emission with high purity.
• Arrays of single-photon single-colour centres show high reproducibility: in a 4×4 array written at E_p ≈ (1 + 0.5%) E_tho, 15/16 (94%) sites behave as single-colour SPEs.
• High brightness and robustness: saturation count rate ~9.0 Mcounts s⁻¹ at a saturation power of ~764 µW; emitters exhibit strong polarization contrast, spectral stability (no spectral diffusion), and no blinking over extended measurements.

The study addresses the long-standing challenge of surpassing the optical diffraction limit for direct laser fabrication by leveraging a threshold tracking and lock-in (TTL) approach that isolates the intrinsic damage threshold of the material and operates near it. In this regime, feature formation is governed by statistical fluctuations in electron energy rather than beam intensity gradients, enabling sub-5 nm SADCs. This physics-driven insight allows deterministic, site-selective creation of quantum-emissive point defects in hBN.

These findings directly meet the requirements for quantum technologies that demand atomic- to few-nanometre-scale precision, such as deterministic single-photon emitters with high positional accuracy. By tuning pulse energy near E_tho, the method transitions emitter formation from stochastic to deterministic and from multi-emitter ensembles to single-colour, single-photon emitters. The high brightness, purity (low g²(0)), and stability (lack of blinking and spectral diffusion) underscore the practical relevance for scalable quantum photonic integration. Compared with other fabrication methods (e.g., nano-indentation, focused ion beam milling, nanopillar substrates) that often yield clustered or background-limited emitters, TTL-based near-threshold writing achieves cleaner, more controllable single-emitter generation with minimal lattice damage.

The work demonstrates close-to-atom scale femtosecond laser manufacturing in hBN by introducing a threshold tracking and lock-in (TTL) method that identifies and operates at the intrinsic material threshold. This enables reproducible formation of sub-5 nm single-atom defect complexes, approaching a quantum/statistical uncertainty limit, and deterministic fabrication of bright, stable, single-colour single-photon emitter arrays with high yield and positional accuracy. The approach bridges the gap between optical fabrication constraints and atomic-scale device requirements, providing a scalable path toward integrated quantum photonic technologies.

Future work could extend TTL-based near-threshold laser writing to other wide-bandgap materials and defect species, refine spatial placement and spectral control of emitters, integrate emitters with photonic structures for on-chip quantum circuits, and further quantify/optimize the trade-offs between yield, spectral purity, and positional precision.

While the emitters exhibit low g²(0), the antibunching measurements were conducted without background correction; the reported g²(0) can be limited by detector dark counts, stray light, and residual surface fluorescence. The precise emission site within the focus is subject to a small stochastic range (~3 nm) due to statistical electron-energy fluctuations. Morphologies of the sub-5 nm processed regions vary from spot to spot. Additionally, not all sites in arrays were single-colour SPEs (15/16 in one array), indicating residual variability near threshold.