Optical Tweezer — Single-Atom Release & Recapture

Tweezer Beam

Trap depth U₀ 1.0 mK

Beam waist w₀ 1.00 µm

Atom temperature T 30 µK

Release time t_rel 20 µs

Trap State

Atom status

TRAPPED

Trials / Recaptured

0 / 0

Recapture rate

—

Live Physics

Radial ω_r/2π

— kHz

Axial ω_z/2π

— kHz

Rayleigh range z_R

— µm

Mech. energy E

— µK

Atom motion is replayed ~100,000× slower than real time so the oscillation is visible — the frequencies above are the true physical values for a rubidium-87 atom (m = 1.443×10⁻²⁵ kg) in an 850 nm trap.

How it works

A tightly focused, red-detuned Gaussian laser beam attracts a neutral atom toward its intensity maximum via the AC Stark shift. The resulting dipole potential is

U(r,z) = -U₀ · (w₀/w(z))² · exp(-2r²/w(z)²)
w(z) = w₀ √(1 + (z/z_R)²),  z_R = π w₀² / λ

where r is the distance from the optical axis and z is distance along it. Near the focus this well is harmonic, giving exact radial and axial trap frequencies

ω_r = √(4U₀ / m w₀²)      (radial, ⊥ to beam)
ω_z = √(2U₀ / m z_R²)     (axial, along beam)

The simulator integrates the atom's real equation of motion m dv/dt = -∇U(r,z) in this exact (non-harmonic) potential — not the harmonic approximation — using the analytic gradient, and samples the initial thermal velocity from a Maxwell-Boltzmann distribution at temperature T (⟨v²⟩ per axis = k_BT/m).

Trap depth / waist sliders — set U₀ and w₀, which together fix ω_r, ω_z and z_R exactly as in a real tweezer experiment.
Temperature slider — controls how energetically the atom jiggles inside the well before release.
Release & Recapture — switches the trap off for t_rel (pure ballistic flight), then back on. This is the real "release-recapture" thermometry technique (Tuchendler et al. 2008): an atom is recaptured only if its total mechanical energy E = ½mv² + U(r,z) is still negative (bound) when the trap turns back on — hotter atoms or longer release times drift too far and are lost.

Real-world relevance: this exact mechanism traps single neutral atoms in arrays used for quantum computing and simulation (e.g. Rydberg-atom tweezer arrays), and release-recapture remains a standard way to measure a trapped atom's temperature without a cycling transition.

Beam envelope w(z) Atom trajectory

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