Quantum memory / Constrained dynamics

Rydberg Many-Body Scars

Does an interacting chain of atoms always forget the pattern it started in? Not always. In a ring of twelve Rydberg atoms where neighbors cannot both be excited, an alternating start keeps coming back: near its first revival it reappears with about 84 percent probability, and later revivals are weaker. Started all in the ground state, the same ring returns with under 1 percent. Erasing one excitation from the alternating pattern cuts the return to about 20 percent.

Twelve atoms sit on a ring, and no two neighbors can be excited at the same time. Start from an alternating pattern and watch it nearly return. Then erase one excitation and compare the evolution under the same Hamiltonian, including the full bit-string records.

The model is a twelve-site PXP ring with ideal nearest-neighbor blockade and an optional detuning. Revivals in this finite system illustrate scar dynamics, but they support no claim about thermalization or a time crystal. Long-range interactions, leakage through the blockade, decay and experimental imaging are left out.

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 shows averages; a shot gives one outcome

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

Each row is one complete readout.

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

05 / THE MECHANISM

The sites are correlated.

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

Show the raw records

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 the hard blockade between nearest neighbors is kept. Long-range tails, finite blockade leakage, atomic motion, decay and imaging errors are left out. A revival on twelve sites does not prove scarring, localization or a time crystal in the thermodynamic or spectral sense. The correlation map is calculated from the state; it is 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: Does an interacting chain of atoms always forget the pattern it started in?
One-sentence intuition: The same constrained Hamiltonian treats different initial patterns very differently.

Core mathematical model

Evolution of the full state

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

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

The target probability

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

This is the probability of getting exactly the initial bit string back, not just a similar average brightness on each site.

Common difficulties

The scene is a model

Typical misconceptionThe glowing nodes show a single measurement.

Better mental modelThe scene shows the expected occupation of each site. A single shot is one complete row of bits in the record.

What the model leaves out

Typical misconceptionA revival proves a perfect memory device.

Better mental modelThe model is a twelve-site PXP ring with ideal nearest-neighbor blockade and an optional detuning. Revivals in this finite system illustrate scar dynamics, but they support no claim about thermalization or a time crystal. Long-range interactions, leakage through the blockade, decay and experimental imaging are left out.

Run the experiment

01
Compare
Choose the first two presets in turn, keeping the time the same.
What to observe: The alternating pattern comes back much more strongly than a start with every atom in the ground state.
02
Break the effect
Try the third preset and edit the initial sites.
What to observe: Removing one excitation changes the revival. The model does not allow two neighbors to be excited together.
03
Read every shot
Collect snapshots, pin the run and export the complete record.
What to observe: Each row comes from a separate preparation. The measured fraction of target outcomes fluctuates around the model probability.