HOW SCIENCE WORKS · ATOMIC PHYSICS
Matter-Wave Collapse and Revival — How Quantum Phases Reassemble
A condensate’s interference pattern can fade and later return even while the system remains isolated. In a deep optical lattice, interactions make different atom-number components acquire different phases; their later realignment rebuilds the observable matter-wave coherence.
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Understand the mechanism · Chapters 1–2
Work through the prediction · Chapters 3–4
Read the experiment and limits · Chapters 5–6
A condensate loaded into an optical lattice occupies many wells. If their phases are coherent, releasing the atoms produces a sharp interference pattern. A rapid increase in lattice depth suppresses tunnelling and lets interactions within each well dominate.
After a suitable hold time, the interference peaks can weaken. This loss of visible contrast need not mean the atoms have disappeared or that every quantum correlation has been destroyed. The relevant question is how the state evolved before the image was taken.
For an isolated lattice site with two-body interaction energy U, a simple Hamiltonian is H = U n(n−1)/2. A component containing n atoms acquires phase exp[−iUn(n−1)t/(2ℏ)].
An initial state with several occupied number components therefore develops a structured spread of relative phases. Their contributions to the mean matter-wave field stop adding constructively, and the interference contrast collapses.
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In the ideal two-body model, the phases reassemble after trev = h/U. Because n(n−1) is always even for integer n, every number component returns to the same relative phase at that time.
If U/h = 800 Hz, the predicted revival time is 1/800 second = 1.25 ms. A lattice-depth scan changes U and should change the revival period accordingly. This illustrative calculation is a stronger test than simply noting that a contrast maximum returned once.
| Experimental handle | Physical role | Evidence check |
|---|---|---|
| Interaction U | Sets ideal revival period | Test trev = h/U |
| Initial number distribution | Controls collapse envelope | Model preparation statistics |
| Lattice homogeneity | Controls revival contrast | Compare depth and trap gradients |
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Here the word collapse describes the decay of a field expectation value or interference visibility under interaction-driven evolution. It is not a claim that a projective measurement has irreversibly selected one atom-number state.
The global state can remain coherent while the chosen first-order observable becomes small. A revival shows that some phase information remained in the dynamics. It does not imply that all apparent decoherence in other systems must be reversible.
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Greiner and colleagues observed collapse and revival of a condensate’s matter-wave field in an optical lattice. Time-of-flight interference patterns revealed the disappearance and return of coherence after controlled hold times.
The primary result exposed the role of discrete atom number and interactions. A classical average-density treatment does not retain the same number-dependent phase structure, so the revival sequence probes a deeper description than a single smooth density profile.
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Different wells can have different interaction strengths and occupancies. Residual tunnelling, external potential gradients, atom loss and effective higher-body terms can shift or wash out the revival pattern.
Researchers vary lattice depth, compare several revival periods, calibrate trap gradients and model the initial number distribution. The scientific lesson is that a missing signal can reflect dephasing among structured contributions; its controlled return can reveal the energy spectrum that organised them.
Primary research: Greiner and colleagues, Collapse and revival of the matter wave field of a Bose–Einstein condensate (Nature, 2002).
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