Skip to main content
Sandbox Physics

Q032 · Separate / excite / compare

Rydberg Atom Blockade

Bring two trapped atoms together. Record both states after the same pulse and watch double excitation become rare.

Interactive modelRydberg Atom Blockade
Model at the cursor—\text{—}
Recorded at this time—\text{—}

02 / CHANGE ONE THING

Pull the atoms apart

R/R∗=1R/R_*=1

The distance changes the interaction, not the size of either atom. The slider offers the same keyboard control.

03 / EVOLUTION & MEASUREMENT

Count each joint outcome

Model populations at the cursor

Both ground0%
Only B excited0%
Only A excited0%
Both excited0%
Both groundOne excitationBoth excitedLines: model · circles: records · bars: 95% Wilson intervals

Click the plot to move the cursor. Each point combines only shots recorded at that time and those settings.

Model pair-level shift

—\text{—}

Recorded double-excitation fraction

—\text{—}

04 / TEST YOUR PREDICTION

When does double excitation return?

Run a scan to collect 200 new preparations at each of 13 settings.

SettingRead / totalDouble excitations
What is simulated?

Every record is simulated. State readout is ideal when available, with state-independent missing records. Changing preparation settings clears the active data; an already acquired scan retains its own settings until you replace or reset it. Model diagnostics are separate from measured frequencies.

The interaction remains active during all pulses, including the prepare–wait–analyze protocol. This demonstrates an interaction phase; it is not a certified controlled-phase gate. Traps define fixed sites; motion and recapture loss are omitted.

Time is in reference units; angular frequencies are in inverse reference time. No species or laboratory clock is calibrated.

Scientific sources: Gaëtan et al. · Blockade · Saffman et al. · Rydberg interactions

Physics tutorial

Measure a Rydberg blockade

BackgroundA coherent control sequence changes the state before a final measurement.

Why it mattersChange one operation, then test it with fresh preparations.

Start with the essentials

Focus question
Why does approaching suppress double excitation?
One-sentence intuition
The population curves are model predictions; the dots come only from recorded outcomes.

Core mathematical model

Reference units

τ=t/t∗,Ω,Δ,δ,γ,V in t∗−1\tau=t/t_*,\quad \Omega,\Delta,\delta,\gamma,V\ \text{in}\ t_*^{-1}

All rates are angular-frequency or population-decay rates. No physical species is calibrated.

Open-system dynamics

ρ˙=−i[H/ℏ,ρ]+∑j(LjρLj†−12{Lj†Lj,ρ})\dot\rho=-i[H/\hbar,\rho]+\sum_j\left(L_j\rho L_j^\dagger-\tfrac12\{L_j^\dagger L_j,\rho\}\right)

The full density matrix retains coherence. Fourth-order Runge–Kutta steps resolve the largest Hamiltonian scale, with pulse boundaries split explicitly.

A shifted pair state

Hℏ=∑j=A,B[Ω2σx(j)−Δnj]+VnAnB,V=V∗(R∗R)6\frac H\hbar=\sum_{j=A,B}\left[\frac\Omega2\sigma_x^{(j)}-\Delta n_j\right]+Vn_An_B,\quad V=V_*\left(\frac{R_*}{R}\right)^6

Basis: ground–ground, ground–excited, excited–ground, excited–excited. The repulsive coefficient is a chosen effective parameter, not a fit to a particular rubidium state. Independent local collapse operators return each atom to ground, retaining the other atom’s coherence.

Independent-atom reference

Prr=sin⁡4(Ωt/2)(V=Δ=γ=0)P_{rr}=\sin^4(\Omega t/2)\quad(V=\Delta=\gamma=0)

Without interactions the state factorizes. Double excitation can reach unity after a single-atom inversion pulse.

Collective oscillation

Pgr+Prg⟶sin⁡2(2 Ωt/2)(V/Ω→∞)P_{gr}+P_{rg}\longrightarrow\sin^2(\sqrt2\,\Omega t/2)\quad(V/\Omega\to\infty)

On resonance, a large pair shift suppresses double excitation. The symmetric single-excitation state oscillates faster. Finite interactions give a correction; occupation counts alone cannot certify this state’s entanglement.

Hold an interaction phase

∣rr⟩⟼e−iVT∣rr⟩|rr\rangle\longmapsto e^{-iVT}|rr\rangle

With drive off, the interaction contributes this conditional phase. The prepare–wait–analyze sequence uses two nominal quarter-turn pulses. Interactions and decay remain active during preparation and analysis, so this is not an ideal gate implementation.

Readout and uncertainty

p^=kNread,Nunread=N−Nread\hat p=\frac{k}{N_{\rm read}},\quad N_{\rm unread}=N-N_{\rm read}

The displayed interval is a 95% Wilson binomial interval for successful target-state or double-excitation outcomes, conditional on available state-independent readout. It is pointwise, not a simultaneous band or numerical-model error. Each shot starts from a fresh ground-state preparation.

Common difficulties

A probability is not a trajectory

Typical misconceptionThe glowing atom reveals a hidden path.

Better mental modelThe atom marker locates a fixed site. Light-beam brightness indicates drive amplitude. Only the result tiles represent sampled observations.

Reference and boundary

Typical misconceptionThis reproduces a calibrated apparatus.

Better mental modelSTIRAP follows Vitanov et al., Reviews of Modern Physics 89, 015006 (2017), section II. Blockade follows Gaëtan et al., Nature Physics 5, 115–118 (2009); the assumed off-resonant interaction follows Saffman et al., Reviews of Modern Physics 82, 2313 (2010), section II.C, rather than that experiment’s resonant pair potentials. These motivate the Hamiltonians; our dimensionless rates and schematic geometry are not fitted experimental values.

Run the experiment

  1. 01

    Predict

    Choose a contrasting case before collecting.

    What to observe: Keep the physical drive and measurement time in mind.
  2. 02

    Operate

    Drag pulse peaks or the separation handle, and scrub the time cursor.

    What to observe: Playing only replays the deterministic evolution; it does not manufacture observations.
  3. 03

    Acquire and compare

    Measure at the cursor, then collect a parameter scan. Export its raw outcomes.

    What to observe: The scan measures at the captured cursor time and preserves its own preparation settings.