Deterministic Single-Atom Loading

• Deterministic single-atom loading is the precise preparation of one atom per designated site with near-unity probability across diverse platforms.
• The approach overcomes the exponential decline in full-array yield through engineered collisions, chemical reaction control, and feedback mechanisms.
• Various methods—from KMC modeling in semiconductor fabrication to collision-engineered optical tweezers—demonstrate practical pathways to achieve defect-free atom arrays.

Deterministic single-atom loading is the preparation of exactly one atom, ion, or single incorporated dopant at a designated site with probability near unity, rather than relying on stochastic occupancy. Across atomic-precision semiconductor fabrication, optical tweezer arrays, integrated photonic resonators, trapped-ion systems, and implantation-based solid-state devices, the central issue is the same: a per-site loading probability below unity produces an exponentially worsening probability that an entire target structure is defect free. In semiconductor acceptor loading this is written as $Y_{\mathrm{array}} = (P_{\mathrm{inc}})^N$, and in neutral-atom array assembly analogous products such as $p^n$ or reservoir-tail probabilities govern full-array yield (Campbell et al., 2021, Brown et al., 2018).

1. Deterministic loading as a probability problem

The defining criterion is platform dependent in implementation but not in logic. For single-acceptor incorporation on hydrogen-resist patterned Si(100)-2×1, deterministic means a probability “≈1” for single-acceptor incorporation at a patterned site, with practical analysis treating “near-unity” probabilities $(\ge 95$–$99\%)$ as deterministic (Campbell et al., 2021). In neutral-atom arrays, deterministic loading means that all target sites are filled with exactly one atom at the end of preparation; the same distinction appears in ion traps and implantation, where “one-and-only-one” ion or dopant is the relevant endpoint (Zhu et al., 22 Dec 2025, Pacheco et al., 2017).

The reason the problem is stringent is that array yield compounds multiplicatively. The single-acceptor analysis gives $Y_{\mathrm{array}} = (P_{\mathrm{inc}})^N$ and explicitly notes that even $P_{\mathrm{inc}} = 0.9$ yields $(0.9)^9 \approx 0.4$ for a $3 \times 3$ array (Campbell et al., 2021). In probabilistically loaded tweezer arrays the same exponential suppression appears as $p^K$ for $K$ predefined occupied sites, and in collisional-blockade loading the canonical single-site occupancy is about $p^n$0, making fully occupied large arrays intrinsically unlikely without additional control (Kim et al., 2016, IJspeert et al., 10 Jan 2025).

A common distinction is therefore between direct deterministic loading and deterministic assembly from imperfect initial loading. The ytterbium array study states this explicitly: direct deterministic loading requires $p^n$1, whereas deterministic arrays can also be assembled from a reservoir with imperfect initial $p^n$2 by rearrangement, buffer traps, or other feedback operations (Zhu et al., 22 Dec 2025). This suggests that “deterministic single-atom loading” is best understood as a systems-level objective rather than a single mechanism.

2. Atomic-precision semiconductor loading on Si(100)-2×1

In atomic-precision semiconductor fabrication, deterministic loading concerns single-acceptor incorporation on hydrogen-resist patterned Si(100)-2×1. The surface is hydrogen terminated, a small window is depassivated by STM lithography, and precursors adsorb preferentially on bare Si inside the window. Patterned windows are typically two or three dimers wide along the dimer-row direction, because dissociation and ligand removal require lateral space. “Loading” refers to exactly one acceptor per patterned site; the model counts a single bridging acceptor fragment, BH, BCl, or AlCl, as an incorporation, and counts two such fragments in the same row(s) as an electrically inactive dimer, hence a non-incorporation (Campbell et al., 2021).

The kinetics were analyzed with a KMC framework using DFT-derived barriers, Arrhenius rates

$p^n$3

and an attempt frequency $p^n$4 (Campbell et al., 2021). The decisive issue is pathway topology. Diborane has an early branching between B–B splitting and H shedding with barriers $p^n$5 and $p^n$6, described as “essentially a coin toss,” and incorporation requires overcoming a barrier of at least $p^n$7 (Campbell et al., 2021). Boron trichloride has “only three possible steps” with a likely reaction barrier of $p^n$8, while AlCl$p^n$9 follows the same pathway with barriers lowered by $(\ge 95$0, enabling much faster dissociation (Campbell et al., 2021).

These pathway differences produce sharply different deterministic regimes. For B$(\ge 95$1H$(\ge 95$2, a typical experimental-like dose of $(\ge 95$3 Torr for 10 min at $(\ge 95$4 followed by a $(\ge 95$5 anneal for 1 min yields $(\ge 95$6 in a three-dimer window; the best value reported over the explored grid is only $(\ge 95$7 at $(\ge 95$8 hot dosing (Campbell et al., 2021). The same study concludes that diborane is unlikely to achieve deterministic single-acceptor incorporation under practical dosing conditions. By contrast, BCl$(\ge 95$9 at room temperature already gives $99\%)$0 in a three-dimer window for $99\%)$1 Torr and 900 s, and “all doses $99\%)$2 L” achieve deterministic single-acceptor incorporation at $99\%)$3 (Campbell et al., 2021). AlCl$99\%)$4 is more favorable still: “any dose $99\%)$5 L” at room temperature yields deterministic single-acceptor incorporation in both two- and three-dimer windows (Campbell et al., 2021).

Al$99\%)$6Cl$99\%)$7 occupies an intermediate position. Its first step is dimer splitting with a $99\%)$8 barrier, favored over chlorine shedding at $99\%)$9, and room-temperature dosing followed by a $Y_{\mathrm{array}} = (P_{\mathrm{inc}})^N$0 anneal is “crucial” to achieve deterministic incorporation for all doses $Y_{\mathrm{array}} = (P_{\mathrm{inc}})^N$1 L (Campbell et al., 2021). Without anneal, $Y_{\mathrm{array}} = (P_{\mathrm{inc}})^N$2 can be sub-deterministic, for example $Y_{\mathrm{array}} = (P_{\mathrm{inc}})^N$3 at $Y_{\mathrm{array}} = (P_{\mathrm{inc}})^N$4 Torr and 900 s, and the predicted outcome is highly sensitive to whether nearby Al fragments later diffuse or instead form electrically inactive dimers (Campbell et al., 2021). In this domain, deterministic loading is therefore limited not only by adsorption probability but by detailed reaction branching, steric blocking within narrow windows, and the chemical definition of an electrically active endpoint.

3. Collision-engineered loading in optical tweezers

In optical tweezers, deterministic loading has largely proceeded by engineering light-assisted collisions so that multiply occupied traps preferentially lose atoms until only one remains. A central example is $Y_{\mathrm{array}} = (P_{\mathrm{inc}})^N$5-enhanced grey-molasses loading of $Y_{\mathrm{array}} = (P_{\mathrm{inc}})^N$6Rb on the D1 line, where blue-detuned cooling simultaneously cools and drives controlled repulsive-state collisions. This yielded $Y_{\mathrm{array}} = (P_{\mathrm{inc}})^N$7 in a single $Y_{\mathrm{array}} = (P_{\mathrm{inc}})^N$8 tweezer and $Y_{\mathrm{array}} = (P_{\mathrm{inc}})^N$9 per site in a $P_{\mathrm{inc}} = 0.9$0 array at $P_{\mathrm{inc}} = 0.9$1 (Brown et al., 2018). The relevant energy scale is the collision energy release

$P_{\mathrm{inc}} = 0.9$2

whose position relative to $P_{\mathrm{inc}} = 0.9$3 and $P_{\mathrm{inc}} = 0.9$4 determines whether a collision ejects zero, one, or two atoms (Brown et al., 2018).

The same logic has been extended to alkaline-earth-like atoms. In $P_{\mathrm{inc}} = 0.9$5Yb tweezer arrays, blue-detuned collision light near the $P_{\mathrm{inc}} = 0.9$6 intercombination line at $P_{\mathrm{inc}} = 0.9$7 and $P_{\mathrm{inc}} = 0.9$8 produced a loading efficiency of $P_{\mathrm{inc}} = 0.9$9 that remained largely unchanged from tens to $(0.9)^9 \approx 0.4$0 tweezers, with a single-shot demonstration of $(0.9)^9 \approx 0.4$1 atoms loaded into $(0.9)^9 \approx 0.4$2 sites (Zhu et al., 22 Dec 2025). The mechanism was modeled microscopically with dipole-dipole-coupled molecular channels and Landau–Zener tunneling, and strong enhancement was observed not only for globally repulsive potentials but also for partially repulsive ones (Zhu et al., 22 Dec 2025). The study emphasizes, however, that for direct deterministic filling of arrays with $(0.9)^9 \approx 0.4$3–$(0.9)^9 \approx 0.4$4 sites, $(0.9)^9 \approx 0.4$5 must be very close to unity because $(0.9)^9 \approx 0.4$6 becomes exponentially small once $(0.9)^9 \approx 0.4$7 is large (Zhu et al., 22 Dec 2025).

A distinct route to exceed the collisional-blockade limit without rearrangement is depth control. The on-the-spot loading study with $(0.9)^9 \approx 0.4$8Rb uses a shallow loading trap and a deeper holding trap, with the time-averaged filling

$(0.9)^9 \approx 0.4$9

where $3 \times 3$0 is the mean dark time to load an atom and $3 \times 3$1 is the single-atom lifetime (IJspeert et al., 10 Jan 2025). A depth switch from $3 \times 3$2 $3 \times 3$3 to $3 \times 3$4 $3 \times 3$5 yielded a measured filling ratio of $3 \times 3$6 without rearrangement, while turning the MOT light off after capture nearly tripled the lifetime across a broad depth range (IJspeert et al., 10 Jan 2025). This separates fast capture from long hold, rather than relying solely on optimized two-body loss.

4. Rearrangement, reservoirs, and feedback as routes to deterministic arrays

Because direct per-site loading usually remains below unity, array-level determinism is often produced by combining stochastic loading with transport, matching, or local feedback. Dynamic holographic tweezer work made this explicit: with single-site loading probability $3 \times 3$7 in nine reservoir sites and per-atom transport survival $3 \times 3$8, the success probability for preparing four designated atoms rises to

$3 \times 3$9

compared with the naive $p^K$0 (Kim et al., 2016). The same work proposed scaling via larger reservoirs, noting that with a passive $p^K$1 DOE $p^K$2 and $p^K$3, the probability to have at least nine atoms initially captured exceeds $p^K$4 (Kim et al., 2016).

Once transport is used, assignment and path planning become part of the loading problem. In defect-free array formation with holographic optical-dipole traps, the atom-to-target matching was formulated as a bipartite assignment with cost

$p^K$5

solved by the Hungarian algorithm in $p^K$6 time (Lee et al., 2017). Using $p^K$7 suppresses trespassing trajectories, and for the $p^K$8 task the Hungarian solution gave over $p^K$9 higher success probability than the heuristic shortest-move method (Lee et al., 2017). The physical survival model factored motion time, flicker loss, and close-pass loss as

$K$0

making clear that deterministic loading at the array level depends on motion planning as much as on initial occupancy (Lee et al., 2017).

Reservoir architectures move this logic into continuous supply. A microlens-based $K$1Rb platform with a large-focus reservoir, buffer traps, and a transport tweezer achieved deterministic loading of a six-site hexagonal target using atoms solely originating from the reservoir; the cumulative success probability reached $K$2 after eight cycles and $K$3 after fifteen cycles, with a cycle time of $K$4 (Pause et al., 2023). In dual-wavelength $K$5Sr arrays, iterative reloading from multiple reservoir tweezers raised the filling fraction from $K$6 initially to $K$7 after three reloads and $K$8 after four shared-reservoir cycles (yan et al., 2024). The recurrence

$K$9

captures the interplay between refill probability $p^n$00 and survival $p^n$01 across cycles (yan et al., 2024).

Feedback can also be localized to individual traps. In a conveyor-belt transfer of $p^n$02Rb into a tightly confined static tweezer, real-time fluorescence thresholding with an FPGA increased the single-atom loading probability from $p^n$03 without feedback to $p^n$04 with feedback (Xu et al., 29 Jul 2025). In the $p^n$05Rb grey-molasses array, enhanced loading to $p^n$06 was already sufficient to locate a filled disjoint $p^n$07 subarray within a $p^n$08 load and assemble a contiguous $p^n$09 array by a single parallel move of rows and columns (Brown et al., 2018). A plausible implication is that deterministic single-atom loading in large arrays is frequently an emergent property of high initial $p^n$10, low-loss transport, and algorithmic defect correction rather than of any single loading event.

5. Integrated photonics, cavities, and near-field loading

Integrated photonic devices place deterministic loading under unusually tight spatial constraints, because the desired atom position can be only $p^n$11–$p^n$12 from a chip surface. One approach is direct capture by an evanescent-field mechanism. In an integrated Si$p^n$13N$p^n$14 microring resonator, ultracold $p^n$15Rb atoms were launched toward a repulsive blue-detuned evanescent field; a single spontaneous Raman event transferred an atom from $p^n$16 to $p^n$17, reduced the barrier, and placed it in a near-surface standing-wave trap (Margalit et al., 10 May 2026). The measured single-atom loading probability peaked at $p^n$18 per $p^n$19 SSL pulse near $p^n$20 and $p^n$21 input power, while antibunching with $p^n$22 confirmed single-emitter occupancy (Margalit et al., 10 May 2026). At the smallest atom-surface distance, the extracted cooperativity was $p^n$23 with $p^n$24 (Margalit et al., 10 May 2026).

A more explicit deterministic architecture uses external delivery plus on-chip feedback. On a photonic integrated circuit with a Cs microring resonator, a moving optical lattice in a top-focused tweezer delivered atoms to the chip with a measured position reproducibility of $p^n$25 (Zhou et al., 5 Jun 2026). Continuous monitoring of resonant probe transmission through the ring gave site-synchronous pulses from approaching atoms, with a thresholded FPGA trigger probability of $p^n$26 over 60 populated lattice sites (Zhou et al., 5 Jun 2026). Once triggered, the conveyor detuning was ramped down and the tweezer power ramped up to project atoms into a stationary near-field trap. The conditional transfer success was reported as $p^n$27, and among successful transfers the outcome was one atom with probability $p^n$28 and two atoms with probability $p^n$29 (Zhou et al., 5 Jun 2026). In the final stationary trap, the extracted single-atom coupling was $p^n$30 and the single-atom cooperativity was $p^n$31 (Zhou et al., 5 Jun 2026).

High-finesse cavity QED arrays represent a third variant: deterministic atom number by verified site occupancy. In a $p^n$32 array of single Cs atoms inside a $p^n$33 Fabry–Perot cavity, each occupied tweezer contained at most one atom by collisional blockade, and EMCCD imaging within $p^n$34 of the spectroscopy run identified the exact atom number $p^n$35 in each shot (Liu et al., 2022). This allowed vacuum Rabi splitting spectra to be measured for deterministic atom numbers from 1 to 8, with a measured single-atom coupling $p^n$36 and a collective coupling consistent with $p^n$37 (Liu et al., 2022). Here determinism lies in real-time number verification and controlled positioning of already singly occupied sites, not in direct one-shot unit-probability loading.

6. Alternative deterministic mechanisms and non-neutral-atom realizations

Not all deterministic single-atom loading relies on collisional filtering. In strongly blockaded Rydberg ensembles, adiabatic rapid passage with a chirped pulse produces a single collective Rydberg excitation that is insensitive to unknown site occupancy $p^n$38. In cubic volumes of $p^n$39 with $p^n$40–$p^n$41 atoms, exact simulations gave single-excitation probability $p^n$42 for representative pulse parameters, and the proposed loading protocol used this excitation, a push-out of residual ground-state atoms, and a reverse transfer back to the ground state to leave exactly one atom per site (Beterov et al., 2011). A related but experimentally distinct fast-preparation protocol uses intra-tweezer Rydberg blockade and autoionization in $p^n$43Yb. In the two-photon ground-state scheme, 18 cycles in $p^n$44 reduced the multi-atom probability to $p^n$45 while retaining single atoms in $p^n$46 of tweezers; in the metastable $p^n$47 single-photon scheme, the final single-atom filling fraction reached $p^n$48 at $p^n$49 (Li et al., 2 Jun 2026). Simulations in the same work indicate that with low single- and two-body loss, optimized detuning sequences could yield $p^n$50 at $p^n$51 (Li et al., 2 Jun 2026).

In trapped ions, deterministic loading can be achieved by high-probability single-particle capture per attempt. Surface-electrode loading of a single $p^n$52 using pulsed laser ablation plus two-step photoionization reached a single-ion loading probability of $p^n$53 per ablation pulse at a fluence of $p^n$54 (Osada et al., 2021). Because repeated attempts are fast and the fluorescence plateaus identify the ion number, a “load-until-single” protocol makes the preparation deterministic in practice (Osada et al., 2021). In solid-state implantation, deterministic single-dopant loading is achieved by counting rather than by cooling dynamics: a focused ion beam is pulsed at $p^n$55 ions per pulse, a solid-state detector resolves the number of implanted ions in real time, and implantation at a site stops when a one-ion event is detected (Pacheco et al., 2017). This produced spatial placement accuracy $p^n$56, intrinsic detection efficiency $p^n$57 for $p^n$58 Si, and $p^n$59 for $p^n$60 Sb through $p^n$61 SiO$p^n$62 (Pacheco et al., 2017).

A broader generalization appears in waveguide QED with superconducting artificial atoms. In a semi-infinite one-dimensional transmission line, an exponentially rising coherent-state waveform matched to the decoherence time of a transmon enabled loading efficiencies above $p^n$63, and the calculated loading efficiency for Fock-state microwave photons was $p^n$64 (Lin et al., 2020). Although this is a single artificial atom rather than a trapped particle, it makes the same conceptual point: determinism emerges when the temporal or spatial mode of the incoming object is impedance matched to the single-quantum absorber.

Across these implementations, two recurrent themes dominate. First, deterministic loading is rarely just a matter of increasing a raw loading rate; it is the suppression or controlled redirection of competing pathways such as double occupancy, non-incorporating chemistry, uncontrolled desorption, or excess-particle survival. Second, exact one-particle preparation is often achieved by combining a high-probability microscopic mechanism with real-time verification, feedback, or postselection. This suggests that deterministic single-atom loading is best viewed as a control problem over discrete occupation states, realized by very different physical means in semiconductors, neutral atoms, ions, and artificial quantum nodes.