Design one trap, then scale it into an array
The page now follows the actual design order: choose atom and trap wavelength, check single-site physics, then ask whether the array spacing and total power are sane.
Start with species, resonance, trap wavelength, NA, and per-site power.
02Check one tweezerRead depth, waist, radial/axial frequencies, scattering, and Lamb-Dicke η.
03Scale to an arraySet Nx, Ny, and spacing to estimate total optical power and crosstalk.
04Reality checkUse the reference table and notes before trusting two-level estimates near magic wavelengths.
01 Single-Tweezer Physics
A tightly focused, far-red-detuned laser beam creates a conservative dipole potential. In the far-off-resonance limit (|Δ| ≫ Γ), the trap depth and photon scattering rate from the trap light follow directly from the two-level interaction:
where $I_0 = 2P/(\pi w_0^2)$ is the peak intensity, $\Delta = \omega_{\rm trap} - \omega_0$ (negative for red-detuned), and $w_0 \approx 0.52\lambda/\text{NA}$ is the diffraction-limited beam waist. The key trade-off: $|U_0| \propto 1/|\Delta|$ while $\Gamma_{\rm sc} \propto 1/\Delta^2$ — deeper detuning buys a lower scattering rate at the cost of needing more power. The harmonic frequencies near the potential minimum and the Lamb-Dicke parameter are:
where $z_R = \pi w_0^2/\lambda$ is the Rayleigh range. The Lamb-Dicke condition $\eta \ll 1$ and resolved sidebands $\omega_r \gg \Gamma_{\rm sc}$ are both required for ground-state sideband cooling.
02 Trap Parameter Calculator
Two-level approximation using the dominant optical transition (D2 for alkali, ¹P₁ for Yb/Sr). Accurate to ~10–20% for tweezers detuned more than 50 nm from resonance. For Yb/Sr near magic wavelengths, consult full polarizability calculations.
03 Array Geometry
Tweezer arrays are produced by a spatial light modulator (SLM) imposing a holographic phase on the trapping beam, or by acousto-optic deflectors (AODs) for dynamic reconfiguration. Cross-talk requires site spacing $d \gtrsim 3w_0$.
04 Species & Wavelength Reference
Typical tweezer parameters at NA 0.55 and 30 mW. Magic wavelengths eliminate differential AC Stark shifts on clock transitions — essential for AEL qubit coherence.
| Species | Resonance | Typical λ_trap | Depth (mK) | ωᵣ/2π (kHz) | η | Notes |
|---|---|---|---|---|---|---|
| Rb-87 | 780 nm D2 | 850 nm | ~0.8 | ~80 | ~0.22 | Most common; Ti:Sapph or diode |
| Cs-133 | 852 nm D2 | 938 nm / 1064 nm | ~1.0 | ~50 | ~0.18 | Heavy mass helps; Lukin / Thompson groups |
| Li-6 | 671 nm D2 | 1064 nm | ~0.5 | ~150 | ~0.30 | Light mass → high ωᵣ; fermion |
| Li-7 | 671 nm D2 | 1064 nm | ~0.5 | ~140 | ~0.29 | Boson partner to Li-6 |
| Na-23 | 589 nm D2 | 1064 nm | ~0.7 | ~100 | ~0.25 | Needs fiber amplifier; Greiner / Zwierlein |
| K-39 | 767 nm D2 | 1064 nm | ~0.6 | ~85 | ~0.22 | Feshbach resonances; Hulet / Salomon |
| Yb-171 | 399 nm ¹P₁ | 532 nm / 759 nm★ | ~1.2 | ~45 | ~0.16 | ★759 nm magic for clock; AEL qubit |
| Sr-88/87 | 461 nm ¹P₁ | 813 nm★ | ~0.9 | ~55 | ~0.18 | ★813 nm magic for ¹S₀→³P₀; Ye / Kaufman |
For alkaline-earth-like atoms used as optical clock qubits (¹⁷¹Yb, ⁸⁷Sr), the trap wavelength must be a magic wavelength where the ground state ¹S₀ and the clock state ³P₀ experience the same AC Stark shift, eliminating differential light shifts that otherwise dephase the qubit.
Yb-171: magic wavelengths near 759 nm and ~1030 nm. Sr-87/88: magic near 813 nm and 917 nm. Outside these wavelengths a fractional intensity noise δI/I translates directly to qubit frequency noise δν = (α₁−α₀)·δI/(2ħε₀c) — untenable for quantum computing coherence times.
Alkali atoms (Rb, Cs, Li) have no accessible clock transition — use whatever wavelength gives the best depth/scatter trade-off. For Rb, 850 nm is a common sweet spot: far enough from 780 nm D2 for low scatter, close enough to maintain reasonable trap depth per mW.
SLM (spatial light modulator): holographic phase pattern imprinted on a liquid-crystal SLM, then Fourier transformed by an objective. Can generate arbitrary 2D or 3D geometries — triangular, honeycomb, Kagome — but updating the pattern takes ~20 ms (one-sided liquid crystal). Efficiency (fraction of power in target sites) typically 40–70%; remaining light must be blocked or redirected.
AOD (acousto-optic deflector): two crossed AODs can deflect to any (x,y) position in ~μs by changing the RF frequency. Enables rapid rearrangement ("sorting") of atoms to fill defects — key for scaling. In time-averaged operation the effective power per site scales roughly as 1/N, while multi-tone static operation trades power uniformity against RF bandwidth and diffraction efficiency. Combining a static pattern with a dynamic steering beam is common when fast rearrangement is needed.
05 References & Further Reading
Key papers and reviews for optical tweezer physics, array assembly, and single-atom experiments.
- Grimm, Weidemüller & Ovchinnikov (2000) — "Optical dipole traps for neutral atoms." Adv. Atom. Mol. Opt. Phys. 42, 95–170. The canonical derivation of the dipole force, trap depth, and scattering rate starting from the two-level model. Every formula in this calculator follows directly from §2. DOI →
- Kaufman & Ni (2021) — "Quantum science with optical tweezer arrays of ultracold atoms and molecules." Annu. Rev. Condens. Matter Phys. 12, 137–164. The modern comprehensive review: tweezer physics, array assembly, Rydberg gates, AEL qubits, molecules. Start here if you want the full current picture. DOI →
- Saffman, Walker & Mølmer (2010) — "Quantum information with Rydberg atoms." Rev. Mod. Phys. 82, 2313. Reviews tweezer arrays as the hardware platform for Rydberg two-qubit gates; covers blockade radius, C₆ coefficients, and fidelity requirements. DOI →
- Metcalf & van der Straten, Laser Cooling and Trapping (1999) — Springer. Chapter 11 covers the dipole force and optical lattice/tweezer potentials from first principles. Good reference for the Rayleigh range geometry and adiabaticity conditions.
- Foot, Atomic Physics (2005) — Oxford University Press. Chapter 9 "Laser cooling and trapping" includes a clear derivation of dipole trap depth vs detuning and the photon scattering rate trade-off.
- Schlosser et al. (2001) — "Sub-Poissonian loading of single atoms in a microscopic dipole trap." Nature 411, 1024–1027. First demonstration of single-atom tweezer trapping via collisional blockade. Established the sub-Poissonian loading mechanism and measured trap frequencies from parametric excitation. DOI →
- Barredo et al. (2016) — "An atom-by-atom assembler of defect-free arbitrary two-dimensional cold atom arrays." Science 354, 1021–1023. SLM + moving tweezer assembly of defect-free 2D arrays. The method used in most neutral-atom QC experiments today. DOI →
- Endres et al. (2016) — "Atom-by-atom assembly of defect-free one-dimensional cold atom arrays." Science 354, 1024–1027. Greiner group (Harvard): complementary approach using a movable tweezer to sort atoms. DOI →
- Kaufman et al. (2012) — "Two-particle quantum interference in tunnel-coupled optical tweezers." Science 345, 306–309. Hong-Ou-Mandel interference of two Rb atoms in adjacent tweezers; demonstrates ground-state preparation and Lamb-Dicke regime operation. DOI →
- Norcia et al. (2019) — "Seconds-scale coherence on an optical clock transition in a tweezer array." Science 366, 93–97. First demonstration of alkaline-earth (Sr-87) single atoms in tweezers with clock-state coherence. Shows magic wavelength operation and nuclear spin qubits. DOI →
- Evered et al. (2023) — "High-fidelity parallel entangling gates on a neutral-atom quantum computer." Nature 622, 268–272. Lukin group (Harvard): 99.5% two-qubit gate fidelity in Rb tweezer array; current SOTA benchmark. DOI →
- Steck atomic data pages (steck.us/alkalidata) — precise spectroscopic constants, hyperfine structure, D1/D2 line parameters, oscillator strengths, and saturation intensities for Rb, Cs, Na, Li, K. The authoritative online reference for any AMO calculation.
- NIST Atomic Spectra Database (physics.nist.gov/asd) — transition wavelengths, A-coefficients, and energy levels for all elements including Yb and Sr.
- Lukin group resources (lukin.physics.harvard.edu) — open-access papers on tweezer arrays, Rydberg gates, and atom assembly protocols.