Optical Lattice Superfluid–Mott Insulator Simulator

Optical Lattice

Superfluid

Lattice depth V₀ 6.0 Eᵣ

Tunneling J/Eᵣ

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On-site U/Eᵣ

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U/J ratio

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Coherence

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Time-of-flight image — press "Release & image" to snap it

How it works

Two counter-propagating laser beams along x and z interfere into a standing wave; the light shifts each atom's energy in proportion to local intensity, so the bright/dark fringe grid becomes a periodic "egg-carton" potential that traps one atom per site once the gas is loaded at unit filling. Raising the beam power deepens every well.

V(x,z) = V₀ [ sin²(πx/a) + sin²(πz/a) ]
J/Eᵣ ≈ (4/√π) V₀^0.75 e^(−2√V₀)   (tunneling)
U/Eᵣ ≈ 0.4 √V₀                    (on-site repulsion, qualitative)

Shallow lattice (low V₀) — wells are barely dented; atoms tunnel freely between sites and their matter waves stay phase-coherent across the whole lattice — the superfluid phase.
Deep lattice (high V₀) — tunneling J collapses exponentially while on-site repulsion U barely changes, so U/J crosses a critical value and it becomes energetically forbidden for two atoms to share a site: exactly one atom freezes per well, phase-locked to nothing — the Mott insulator.
Release & image — switches the trap off and lets the cloud expand ballistically, mimicking real time-of-flight absorption imaging: a coherent superfluid interferes with itself into sharp momentum peaks, while an incoherent Mott insulator expands into a single smooth, peak-free blob.

This is the Bose-Hubbard model for neutral atoms in light — a different physical system from electrons hopping through a real crystal, but the same competition between kinetic (tunneling) and interaction energy drives both toward a Mott-insulating state.

Trapped atom (1 per site) Laser standing-wave potential Tunneling / coherence link

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