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Sandbox Physics

Q027 · Listen / infer / intervene

Fluorescence & Quantum Jumps

Collect one atom’s fluorescence clicks. Infer its shelving probability from the record, reveal the simulated trajectory, and try a delayed repump.

Interactive modelFluorescence & Quantum Jumps
Recorded clicksN=0N=0
Inferred dark probability—\text{—}

02 / FOLLOW THE EVIDENCE

Watch the clicks stop. Follow the inference.

READ A QUIET INTERVAL

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Click or drag on the record to inspect a moment.

Top: recorded clicks. Below: inferred dark probability. Gray dashed: an ensemble reference without feedback. Orange: known repump pulses, or the hidden trajectory when Reveal is enabled.

Numerical results & model checks

Conditional dark probability at cursor

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Longest recorded silence / clicks

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Open-loop steady populations

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Ensemble comparison

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Raw records & scientific boundary

Each run starts in ground. The filter uses no hidden transition or missed-photon labels. A click can be background, and no click can be loss. Feedback acts on the recorded silence, schedules one ideal pulse, and waits for a later click before rearming. The pulse can arrive after the atom has already recovered. No claim is made about a unique interpretation of quantum trajectories.

Independent records — the latest is replayed above
Latest 12 clicks; CSV includes every click and each exposure

Primary references: Wineland · Nobel lecture · Kimble et al. · 1977 · quED · HBT

Physics tutorial

Read a quantum jump record

BackgroundFluorescence is a noisy window into an atom.

Why it mattersConnect detector events to an explicit inference.

Start with the essentials

Focus question
Does silence imply a dark atom?
One-sentence intuition
Use the record first; reveal the model separately.

Core mathematical model

Units

τ=t/t∗,r,γ,s,k,b,Φ in t∗−1\tau=t/t_*,\qquad r,\gamma,s,k,b,\Phi\ \text{in}\ t_*^{-1}

The reference time is arbitrary; no atomic species or physical lifetime is calibrated. All times, rates and CSV values use this reference.

Diagonal Lindblad dynamics

ρ˙=∑aD[La]ρ,D[L]ρ=LρL†−12{L†L,ρ}\dot{\rho}=\sum_{a}\mathcal D[L_a]\rho,\quad\mathcal D[L]\rho=L\rho L^\dagger-\tfrac12\{L^\dagger L,\rho\}

The jump operators below preserve diagonal states. Exact exponential waiting times sample their population dynamics; this model has no coherent Hamiltonian drive.

Four physical transitions

Lr=r ∣e⟩⟨g∣,Lγ=γ ∣g⟩⟨e∣,Ls=s ∣d⟩⟨e∣,Lk=k ∣g⟩⟨d∣L_r=\sqrt r\,|e\rangle\langle g|,\quad L_\gamma=\sqrt\gamma\,|g\rangle\langle e|,\quad L_s=\sqrt s\,|d\rangle\langle e|,\quad L_k=\sqrt k\,|g\rangle\langle d|

Only the fluorescence channel is observed, with imperfect efficiency. The dark state interrupts the bright excitation–emission cycle.

Population master equation

p˙=Qp,Q=(−rγkr−γ−s00s−k)\dot{\mathbf p}=Q\mathbf p,\quad Q=\begin{pmatrix}-r&\gamma&k\\r&-\gamma-s&0\\0&s&-k\end{pmatrix}

Columns sum to zero. The independent ensemble curve starts in the ground state and applies only with feedback off. A 200-trajectory check is available below the record.

Inference from silence and clicks

p~˙=(Q−ηγ∣g⟩⟨e∣−bI)p~,p+=ηγpe∣g⟩+bpηγpe+b\dot{\widetilde{\mathbf p}}=(Q-\eta\gamma|g\rangle\langle e|-bI)\widetilde{\mathbf p},\quad\mathbf p_{+}=\frac{\eta\gamma p_e|g\rangle+b\mathbf p}{\eta\gamma p_e+b}

Normalize the no-click likelihood to condition on silence. A click can be background; it does not always reset the inferred atom to ground. The filter never reads the hidden trajectory.

A delayed intervention

p⟼(pg+pd, pe, 0)T\mathbf p\longmapsto(p_g+p_d,\ p_e,\ 0)^{\mathsf T}

After a recorded silence exceeds the trigger, schedule one ideal repump after the chosen latency. Scheduled pulses are not cancelled by intervening clicks. A pulse transfers the dark population to ground and has no effect on the excited state. Rearm after the first later click.

Common difficulties

Model and evidence

Typical misconceptionA missed click proves shelving.

Better mental modelLoss and background must enter the conditional likelihood.

Run the experiment

  1. 01

    Predict

    Is silence proof of shelving? Try the missed-photon case.

    What to observe: A quiet detector need not mean a dark atom.
  2. 02

    Record

    Collect a record; scrub the cursor and inspect inferred probability.

    What to observe: Reveal the simulated state only after making the inference.
  3. 03

    Intervene

    Enable feedback and vary its latency. Then turn it off for the ensemble check.

    What to observe: A causal controller acts on clicks, not on hidden jumps.