--- title: "Rydberg Many-Body Scars Interactive Lab | Sandbox Physics" description: "The pattern that keeps coming back. 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." canonical_url: "https://sandboxphysics.com/labs/rydberg-many-body-scars/" language: "en" page_type: "lab" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/labs/rydberg-many-body-scars/" last_modified: "2026-10-18" --- 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. > Interactive simulation: open this page in a web browser to change the parameters and run the model. A 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. 12 ATOMS · ONE MANY-BODY STATE EXACTLY THE INITIAL PATTERN $0$ 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. $0$ 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. 0 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 $\text{—}$ 95% Wilson interval $\text{—}$ Model excitation count $\text{—}$ Model odd–even contrast $\text{—}$ 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](https://arxiv.org/html/1711.03528) [Bernien et al. — Probing many-body dynamics on a 51-atom quantum simulator (2017)](https://arxiv.org/html/1707.04344) $$ I=\frac{2}{N}\sum_{j=1}^N(-1)^{j-1}\langle n_j\rangle $$ 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. $E_0=\hbar\Omega$ $0$ $0$ Physics tutorial ## Rydberg Many-Body Scars **Background** 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. **Why it matters** A return needs an explanation. Change one cause and keep the observation time fixed. 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 misconception** The glowing nodes are a single shot. **Better mental model** The scene shows site expectations. A shot is one full binary row in the ledger. #### Limits **Typical misconception** A revival proves a perfect memory device. **Better mental model** A 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 1. 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. 2. 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. 3. 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. Physical conclusion A 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. Quantum & fields · Starter path ## Start from a single measurement Predict outcomes and collect counts, building from one qubit to wave packets, bound states and two-photon interference. [Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare it with the frequency of acquired shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/) 1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/) 2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/) 3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/) 4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/) 5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/) 6. 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