---
title: "Cavity Quantum Excitation Exchange Interactive Lab | Sandbox Physics"
description: "Can a cavity give a photon back to the atom that emitted it? Yes, again and again."
canonical_url: "https://sandboxphysics.com/labs/cavity-quantum-exchange/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/cavity-quantum-exchange/"
last_modified: "2026-10-28"
---

Q031 · An atom and a cavity trade one excitation

# Cavity Quantum Excitation Exchange

**Can a cavity give a photon back to the atom that emitted it?** Yes, again and again. An excited atom coupled to a single cavity mode hands its excitation to the cavity as a photon, then absorbs it back. These are vacuum Rabi oscillations. Extra photons in the cavity speed up the exchange, and leakage out of the cavity damps it.

Start with one excited atom in a cavity. Watch its excitation pass into the cavity field and come back, then add photons or let them leak out.

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

The dynamics follow the single-mode Jaynes–Cummings model with the rotating-wave and Markov approximations. The field starts in a Fock state or in a phase-averaged Poisson mixture. The cavity and the atom lose population independently. The glow of the mode shows its mean occupation, not a classical electric field. State readings are simulated, and the output flux is computed separately as a model diagnostic.

02 / Follow the exchange

## Watch the excitation return.

Excited atom 0%

Empty cavity 0%

Blue line: excited atom. Amber: mean cavity photons, divided by initial total excitation. Dots and 95% Wilson bars: atomic state readings.

Drag across the plot or use the time slider. Playing only changes the preview; it does not take measurements.

Cavity photons · model

$\text{—}$

Leaked photons · integrated model flux

$\text{—}$

03 / Oscillator occupation

## How many photons are inside?

$\epsilon_{\rm tail}=0$

04 / Save the evidence

## Fresh preparations at every time

Acquire a comparison to fill the table. The table keeps the settings it was taken with, even if you change the controls.

| Probe | Read / total | Excited |
| --- | --- | --- |

Model and measurement boundaries

Ideal binary state discrimination when available; unread trials are retained. No fluorescence photon arrival stream is simulated. Every trial uses an independent preparation. Model number distributions are not reconstructed from these binary counts.

An initially excited atom couples to a single mode. Poisson mixtures retain photon-number statistics but no optical phase. They reproduce the atomic population collapse and revival of a coherent preparation in this model; they do not reproduce its full state. No driven transmission spectrum or entanglement certification is claimed.

The sideband and cavity protocols use an arbitrary reference time unit. The separate RF protocol below uses physical SI units. Geometry is schematic, with enlarged atoms and mode envelopes.

Primary sources: [Bina · Jaynes–Cummings dynamics](https://arxiv.org/abs/1111.1143)

## From this model to the evidence

Can an empty mode exchange an excitation?

- **Try**: Switch off both loss channels. Start from the vacuum and run a time scan, then repeat with four photons, keeping the coupling and detuning the same.
- **Read**: Compare how often the atom is found excited in the two scans. Without loss, the reference exchange frequency for a number state rises with photon number. Cavity occupation and leakage are model predictions, listed separately.
- **Scope**: This is resonant exchange; the article’s QND probe is dispersive, which is a different protocol. Atomic populations alone cannot reconstruct the joint state. The Poisson preparation averages over phase, so it is not a coherent field with a resolved phase.

$$
\Omega_n=\sqrt{\Delta^2+4g^2(n+1)}
$$

Model reference: [Bina · Jaynes–Cummings model, §§ 4–9](https://arxiv.org/abs/1111.1143)

[How to measure one quantum system and keep it available](https://sandboxphysics.com/stories/quantum-evidence/single-quantum-measurement-backaction/)

Physics tutorial

## Follow a quantum of excitation

**Background** A two-level system can exchange energy with a quantized oscillator.

**Why it matters** Change how the system is prepared, then test the model against many independent state readings.

Start with the essentials

- **Focus question**: What changes when the oscillator contains no quanta?
- **One-sentence intuition**: A model curve and a finite set of measurements are different kinds of evidence.

### Core mathematical model

#### One mode and one atom

$$
\frac{H}{\hbar}=\Delta\sigma_+\sigma_-+g(a\sigma_++a^\dagger\sigma_-)
$$

The atom starts excited, and the mode starts in a number state or a phase-averaged Poisson mixture. Time and rates are in reference units.

#### Excitation exchange

$$
|e,n\rangle\leftrightarrow|g,n+1\rangle,\quad\Omega_n=\sqrt{\Delta^2+4g^2(n+1)}
$$

More photons make the exchange faster. Components with different photon numbers drift out of step and can come back into step, so the population collapses and later revives.

#### Independent losses

$$
\dot\rho=-i[H/\hbar,\rho]+\kappa\mathcal D[a]\rho+\gamma\mathcal D[\sigma_-]\rho
$$

Both rates are population decay rates. When a photon leaks out, the block solver feeds coherence from one excitation sector into the next, rather than simply damping a sine wave.

#### Where the excitation goes

$$
\langle n\rangle+P_e+\int_0^t(\kappa\langle n\rangle+\gamma P_e)\,dt=1+\langle n(0)\rangle
$$

Without losses, the total excitation stays constant. The integrated output is a model expectation value, kept apart from the sampled atomic-state readings.

#### What is measured

$$
\hat P_e=\frac{N_e}{N_{\rm read}}
$$

Only the atomic state is sampled. The photon-number distribution and the leakage are model diagnostics. Counts of two possible outcomes cannot reconstruct the joint density matrix or prove entanglement.

### Common difficulties

#### The glow is not a path

**Typical misconception** The glowing object traces the path of a single particle.

**Better mental model** The fixed marker only shows where the particle sits. Brightness shows a probability or a mean occupation. Only the recorded tiles are actual samples.

#### Limits of the model

**Typical misconception** This is a calibrated real apparatus.

**Better mental model** The cavity has a single mode, rotating-wave coupling and Markov loss at zero temperature. The model does not compute the transmission of a driven cavity, and it does not keep the optical phase of a coherent state.

### Run the experiment

1. 01

   #### Prepare

   Begin with the vacuum, then add four photons.

   **What to observe:** The whole response curve changes between the two cases.

2. 02

   #### Probe

   Drag the time cursor and read out 200 fresh preparations.

   **What to observe:** The preview never produces data by itself.

3. 03

   #### Compare

   Acquire a time scan, then compare the lossless case with the leaky one.

   **What to observe:** You can export the raw CSV and recompute the state frequencies yourself. Saved comparisons keep the settings they were taken with.

Physical conclusion

Before you interpret a ratio of counts, check what was assumed about the preparation and the measurement.

## Related experiments and articles

Cavity and waveguide quantum light · Reading path

### From one excitation to photon pairs and collected modes

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

1. [Article **How an excitation moves from an atom into light**](https://sandboxphysics.com/stories/waveguide-qed/atom-cavity-exchange/)

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 to measure one quantum system and keep it available**](https://sandboxphysics.com/stories/quantum-evidence/single-quantum-measurement-backaction/)
2. [Lab **Fluorescence & Quantum Jumps** See quantum jumps in one atom’s fluorescence](https://sandboxphysics.com/labs/fluorescence-quantum-jumps/)
3. [Lab **Trapped-Ion Sideband Spectroscopy** Probe a trapped ion’s motion through its sidebands](https://sandboxphysics.com/labs/trapped-ion-sideband-spectroscopy/)
4. [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)