QUANTUM MEMORY / CONSTRAINED DYNAMICS

Rydberg Many-Body Scars

Twelve atoms. No neighboring excitations. Start with an alternating pattern and watch it almost return. Erase one excitation, then compare the same Hamiltonian and the full bit-string records.

12 ATOMS · ONE MANY-BODY STATE

EXACTLY THE INITIAL PATTERN

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MODEL PROBABILITY

Height and glow: square root of excitation expectation. Gold and cyan distinguish the two sublattices. A smooth ring of expectations is not a single measured configuration.

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EDIT THE INITIAL STATE

Toggle excitations. Neighboring excited sites are blocked, including across the ring seam.

THE PICTURE IS AN EXPECTATION. NOW TAKE A SHOT.

Read the whole pattern.

Each shot starts fresh, evolves to the selected time and reads every site once. Ideal projective readout; all bit strings are kept. The fixed simulation seed makes repeated runs reproducible.

Recorded target fraction

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95% Wilson interval

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Model excitation count

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Model odd–even contrast

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01 / TIMING

How much of the pattern returns?

$\Omega t$

02 / COUNTS

How many sites changed?

Gold: measured frequency. Cyan: model probability. Linear vertical scale; no rejected shots.

Hamming distance from the initial pattern

03 / THE FULL EVOLUTION

Order leaves a rhythm.

Model site excitation over time. Horizontal: site; vertical: time. Fixed square-root color scale, from zero to one. Gold line: selected time.

04 / RAW SHOTS

One row. One complete readout.

Latest 20 independent preparations. Filled: excited. Empty: ground. Rows are not a time sequence. CSV contains every shot.

05 / LOOK UNDER THE HOOD

The sites are correlated.

Connected occupation covariance from the many-body model. Gold: positive; blue: negative; white: zero. The diagonal is a variance.

Read the raw ledger

Trial	Sites, first to last	Target

Model, units & sources

\frac{H}{\hbar\Omega}=\frac12\sum_{j=1}^{12}P_{j-1}X_jP_{j+1}-\frac{\Delta}{\Omega}\sum_{j=1}^{12}n_j

P_j=1-n_j,\qquad\tau=\Omega t,\qquad C_{ij}=\langle n_i n_j\rangle-\langle n_i\rangle\langle n_j\rangle

Periodic boundary conditions: sites twelve and one are neighbors. The full allowed space has 322 binary configurations. We evolve every allowed amplitude, not independent atom oscillators. The reference starts all atoms in the ground state under the same Hamiltonian; for an all-ground selection, it instead uses the alternating preparation.

Only nearest-neighbor hard blockade is retained. Long-range tails, finite blockade leakage, atomic motion, decay and imaging errors are omitted. A twelve-site revival is not a thermodynamic or spectral proof of scarring, localization, or a time crystal. The correlation map is calculated from the state, not reconstructed from the displayed shots.

Turner et al. — Quantum many-body scars (2018), Eq. 1
Bernien et al. — Probing many-body dynamics on a 51-atom quantum simulator (2017)

I=\frac{2}{N}\sum_{j=1}^N(-1)^{j-1}\langle n_j\rangle

The odd–even contrast uses site one with positive sign. Model time is dimensionless. Evolution uses exponential action without renormalization; drift is reported below. Sampling intervals quantify only ideal finite-shot uncertainty.

E_0=\hbar\Omega

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Start with the essentials

Focus question: The pattern that keeps coming back.
One-sentence intuition: The same constrained Hamiltonian treats different initial patterns very differently.

Core mathematical model

Evolve the full state

|\psi(t)\rangle=e^{-iHt/\hbar}|\psi(0)\rangle

Probabilities, correlations and sampled records all come from this same state.

A measurable target

P_{\mathrm{return}}=|\langle\psi(0)|\psi(t)\rangle|^2

Exactly the initial bit string, not just similar average site brightness.

Common difficulties

A model picture

Typical misconceptionThe glowing nodes are a single shot.

Better mental modelThe scene shows site expectations. A shot is one full binary row in the ledger.

Limits

Typical misconceptionA revival proves a perfect memory device.

Better mental modelA twelve-site periodic PXP model with ideal nearest-neighbor blockade and optional detuning. Finite-size revivals illustrate scar dynamics; they do not prove thermalization or a time crystal. Long-range interactions, blockade leakage, decay and experimental imaging are omitted.

Run the experiment

01
Compare
Choose the first two presets, keeping the same time.
What to observe: The alternating pattern returns much more strongly than the all-ground preparation.
02
Break it
Try the third preset and edit the initial sites.
What to observe: One missing excitation changes the revival. Adjacent excitations are forbidden by the model.
03
Read every shot
Collect snapshots, pin the run and export the complete ledger.
What to observe: Every row is a separate preparation. The recorded target fraction fluctuates around its model probability.