---
title: "Fluorescence & Quantum Jumps Interactive Lab | Sandbox Physics"
description: "When the detector goes quiet, has the atom really gone dark? Probably, but not certainly."
canonical_url: "https://sandboxphysics.com/labs/fluorescence-quantum-jumps/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/fluorescence-quantum-jumps/"
last_modified: "2026-10-27"
---

Q027 · Reading an atom from its photon clicks

# Fluorescence & Quantum Jumps

**When the detector goes quiet, has the atom really gone dark?** Probably, but not certainly. The longer the silence lasts, the more likely the atom has jumped into a dark shelving state, a level that does not scatter the laser light. The detector misses some photons, though, so part of any silence is just missed light. All you can give is a probability, worked out from the pattern of clicks.

Record the fluorescence clicks from one atom and work out, from the clicks alone, how likely it is to be shelved. Then reveal the simulated trajectory and try a repump that fires after a delay.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

The atom is a three-level Lindblad model with incoherent pumping, and its state stays diagonal. The model includes emission, shelving, missed photons and independent background clicks. It leaves out coherent Rabi dynamics, atomic motion and the details of any particular ion species. The conditional probabilities hold for this monitoring model.

02 / Follow the evidence

## When the clicks stop, how does the inference change?

Read a quiet interval

—

Reveal the simulated state at this time

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

$\text{—}$

Longest recorded silence / clicks

$\text{—}$

Open-loop steady populations

$\text{—}$

Ensemble comparison

$\text{—}$

Raw records & scientific boundary

Each run starts in the ground state. The filter never sees the hidden transitions or which photons were missed. A click can come from background, and a silence can come from loss. Feedback responds to the recorded silence: it schedules one ideal pulse, then waits for a later click before it can fire again. The pulse can arrive after the atom has already recovered. This does not imply that quantum trajectories have a unique interpretation.

The detector dial and efficiency slider set the same model probability for registering an emitted photon. Turning it loads a fresh simulated record. Its angle is a user interface without manufacturer calibration; replay brightness still comes only from detected clicks.

Primary references: [Wineland · Nobel lecture](https://www.nist.gov/system/files/documents/2017/05/09/2677.pdf) · [Kimble et al. · 1977](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.39.691) · [quED · HBT](https://www.qutools.com/files/quED/quED-HBT/quED-HBT-manual.pdf)

Physics tutorial

## Read a quantum jump record

**Background** The light an atom scatters reveals its state, but the signal is noisy.

**Why it matters** You learn what the atom is doing by reasoning step by step from individual detector clicks.

Start with the essentials

- **Focus question**: When the detector goes quiet, has the atom gone dark?
- **One-sentence intuition**: Draw conclusions from the recorded clicks first, and only then look at the simulated state.

### Core mathematical model

#### Units of time and rate

$$
\tau=t/t_*,\qquad r,\gamma,s,k,b,\Phi\ \text{in}\ t_*^{-1}
$$

The reference time is arbitrary and is not tied to any atom or real lifetime. All times, rates and CSV values are given in this unit.

#### Diagonal Lindblad dynamics

$$
\dot{\rho}=\sum_{a}\mathcal D[L_a]\rho,\quad\mathcal D[L]\rho=L\rho L^\dagger-\tfrac12\{L^\dagger L,\rho\}
$$

The jump operators below keep a diagonal state diagonal. The simulation samples exact exponential waiting times between jumps, and the model has no coherent Hamiltonian drive.

#### Four physical transitions

$$
L_r=\sqrt r\,|e\rangle\langle g|,\quad L_\gamma=\sqrt\gamma\,|g\rangle\langle e|,\quad L_s=\sqrt s\,|d\rangle\langle e|,\quad L_k=\sqrt k\,|g\rangle\langle d|
$$

Only the fluorescence is observed, and the detector misses some of it. A jump to the dark state interrupts the bright cycle of excitation and emission.

#### Population master equation

$$
\dot{\mathbf p}=Q\mathbf p,\quad Q=\begin{pmatrix}-r&\gamma&k\\r&-\gamma-s&0\\0&s&-k\end{pmatrix}
$$

Each column sums to zero. The ensemble curve starts in the ground state and applies only when feedback is off. Below the record you can check it against an average of 200 trajectories.

#### Inference from silence and clicks

$$
\dot{\widetilde{\mathbf p}}=(Q-\eta\gamma|g\rangle\langle e|-bI)\widetilde{\mathbf p},\quad\mathbf p_{+}=\frac{\eta\gamma p_e|g\rangle+b\mathbf p}{\eta\gamma p_e+b}
$$

Normalizing the no-click likelihood gives the state probabilities, given that the detector stayed silent. A click might be background, so it does not always put the inferred atom back in the ground state. The filter never sees the hidden trajectory.

#### A delayed repump

$$
\mathbf p\longmapsto(p_g+p_d,\ p_e,\ 0)^{\mathsf T}
$$

When a recorded silence lasts longer than the trigger time, one ideal repump is scheduled after the chosen latency. A click in the meantime does not cancel it. The pulse moves the dark population to the ground state and leaves the excited state alone. The controller rearms after the next click.

### Common difficulties

#### A gap in the clicks does not prove shelving

**Typical misconception** A gap in the clicks proves the atom is shelved.

**Better mental model** The conditional likelihood has to account for missed photons and background clicks.

### Run the experiment

1. 01

   #### Predict

   Does a silence prove the atom is shelved? Predict, then try the missed-photon case.

   **What to observe:** A quiet detector does not have to mean a dark atom.

2. 02

   #### Record

   Collect a record, then drag the time cursor and watch the inferred probability.

   **What to observe:** Make your own inference first, and only then reveal the simulated state.

3. 03

   #### Add feedback

   Turn on feedback and vary its latency. Then turn it off to run the ensemble check.

   **What to observe:** The controller responds only to recorded clicks; it cannot see the hidden jumps.

Physical conclusion

Imperfect detection changes what you can conclude about the atom.

## Related experiments and articles

Quantum evidence · Reading path

### Clocks, traps and single-quantum control

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **How one trapped ion switches its fluorescence off and on**](https://sandboxphysics.com/stories/quantum-evidence/electron-shelving-single-ion-jumps/)
2. [Lab **Ramsey Frequency Measurement** Read out which level the atoms end in after a Ramsey sequence](https://sandboxphysics.com/labs/ramsey-frequency/)
3. [Article **Reading the sidebands in the first ion ground-state cooling experiment**](https://sandboxphysics.com/stories/quantum-evidence/sideband-asymmetry-ground-state-cooling/)
4. [Lab **Trapped-Ion Sideband Spectroscopy** Probe the sidebands of the ion’s oscillation](https://sandboxphysics.com/labs/trapped-ion-sideband-spectroscopy/)
5. [Article **How to measure one quantum system and keep it available**](https://sandboxphysics.com/stories/quantum-evidence/single-quantum-measurement-backaction/)
6. [Lab **Cavity Quantum Excitation Exchange** Watch an atom and a cavity trade one excitation](https://sandboxphysics.com/labs/cavity-quantum-exchange/)
7. [Lab **Decoherence Channels & Information Loss** Compare the ways a quantum state loses coherence](https://sandboxphysics.com/labs/decoherence-channels/)

Quantum & fields · Starter path

## Start from a single measurement

Predict an outcome, then count what the measurements actually give. The path starts with one qubit and moves on to wave packets, bound states and two-photon interference.

[Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare your prediction with the measured frequency over many 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. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/)

[View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)