---
title: "Single-Atom Photon Blockade Interactive Lab | Sandbox Physics"
description: "The first photon changes the rules for the second. Tune a laser onto a dressed atom–cavity resonance. Compare single-photon blockade, two-photon resonance and an empty cavity. Inspect the level ladder and collect repeated photon-number snapshots."
canonical_url: "https://sandboxphysics.com/labs/single-atom-photon-blockade/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/single-atom-photon-blockade/"
last_modified: "2026-10-19"
---

DRIVE / DRESS / COUNT

# Single-Atom Photon Blockade

Tune a laser onto a dressed atom–cavity resonance. Compare single-photon blockade, two-photon resonance and an empty cavity. Inspect the level ladder and collect repeated photon-number snapshots.

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

A resonant two-level atom in one driven cavity mode, solved with a zero-temperature Lindblad equation. Cavity population decay sets the units. Ideal independent intracavity number readouts are not transmitted-photon timestamps; the conditional output correlation is a separate model prediction. No atomic motion, multilevel structure or calibrated apparatus.

ONE DRIVEN CAVITY. ONE QUANTUM EMITTER.

ZERO-DELAY PAIR CORRELATION

$0$

MEAN CAVITY OCCUPATION

$0$

**01** COHERENT DRIVE

**02** ATOM / CAVITY

**03** IDEAL NUMBER READOUT

Schematic geometry. Standing-wave envelope scales with square root of mean occupation; atom glow with excitation. Number snapshots are ideal independent state readouts, not flying photon trajectories.

01 / THE DRESSED LADDER

### One step fits. The next does not.

Dressed energies in the laser rotating frame. Gold is zero energy. A one- or two-excitation level at zero marks the corresponding resonance; line thickness is visual only and does not represent a spectral linewidth.

$E_{n,\pm}/(\hbar\kappa)=-n\Delta/\kappa\pm(g/\kappa)\sqrt n$

02 / AFTER ONE PHOTON LEAVES

### How quickly can another one follow?

Model output correlation from quantum regression after a cavity-emission jump. The dashed Poisson reference is one. This is not a curve reconstructed from the independent number snapshots below.

$\kappa\tau\ \longrightarrow\quad g^{(2)}(\tau)$

PREPARE AGAIN. COLLECT AGAIN.

## Count the rare pairs.

0 / 20000

Every trial prepares the driven steady state again, then reads the intracavity photon number ideally. No sequential stream, time-tag detector, or destructive real-time counter is claimed. Rare pairs require many preparations; zero observed pairs is not proof of zero probability.

Recorded multiphoton fraction

$\text{—}$

95% Wilson interval

$\text{—}$

Model multiphoton probability

$\text{—}$

Stationary-equation residual

$\text{—}$

### One photon is welcome. Two are rarer.

Gold: recorded number frequencies. Cyan: the solved photon-number distribution. Gray: an independent Poisson reference at the same mean. Vacuum is retained in all counts. The vertical axis uses a square-root scale to reveal rare outcomes; ticks show probabilities.

Top photon sector $0$

Trace error $0$

Latest 20 records · export all

| Trial | Setting | Photons |
| --- | --- | --- |

Model, conventions and sources

The atom and bare cavity share a resonance. Detuning is laser minus resonance frequency. Cavity population decay is one, atomic population decay is 0.4. The solver retains photon numbers zero through eleven, evolves from vacuum for 48 cavity decay times, and computes output regression for another 12. No clipping or renormalization is used.

$$
H/\hbar=-\Delta(a^\dagger a+\sigma_+\sigma_-)+g(a^\dagger\sigma_-+a\sigma_+)+\epsilon(a+a^\dagger)
$$

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

$$
\mathcal D[L]\rho=L\rho L^\dagger-\tfrac12\{L^\dagger L,\rho\}
$$

$$
g^{(2)}(\tau)=\frac{\operatorname{Tr}[a^\dagger a\,e^{\mathcal L\tau}(a\rho_{\mathrm{ss}}a^\dagger)]}{\langle n\rangle_{\mathrm{ss}}^2}
$$

Single two-level atom, rotating-wave approximation, classical coherent drive, Markov vacuum reservoirs. The 2005 experiment contains additional atomic levels and two polarizations; this page illustrates the ideal Jaynes–Cummings mechanism rather than fitting that apparatus. Equal-time intracavity statistics agree with the normally ordered output of an otherwise vacuum loss port, but independent snapshots do not measure a time correlation.

- [Birnbaum et al. — Theory of photon blockade, sections I–III (2005)](https://arxiv.org/html/quant-ph/0507065v1)
- [Birnbaum et al. — Photon blockade with one trapped atom (2005)](https://www.nature.com/articles/nature03804)
- [QuTiP — Two-time correlation functions and quantum regression](https://qutip.org/docs/4.7/guide/guide-correlation.html)

Physics tutorial

## Single-Atom Photon Blockade

**Background** Tune a laser onto a dressed atom–cavity resonance. Compare single-photon blockade, two-photon resonance and an empty cavity. Inspect the level ladder and collect repeated photon-number snapshots.

**Why it matters** Use statistics to distinguish quantum light from a bright classical signal.

Start with the essentials

- **Focus question**: The first photon changes the rules for the second.
- **One-sentence intuition**: An anharmonic excitation ladder makes the second photon miss the first resonance.

### Core mathematical model

#### A quantitative signature

$$
g^{(2)}(0)=\frac{\langle n(n-1)\rangle}{\langle n\rangle^2}
$$

The numerator counts ordered pairs, not the square of a single-shot count.

### Common difficulties

#### Respect the energy source

**Typical misconception** The atom is a classical gate that counts passing balls.

**Better mental model** Coherent coupling changes the spectrum; excitation and loss are solved together.

#### Read the measurement contract

**Typical misconception** A displayed theoretical curve is already acquired evidence.

**Better mental model** A resonant two-level atom in one driven cavity mode, solved with a zero-temperature Lindblad equation. Cavity population decay sets the units. Ideal independent intracavity number readouts are not transmitted-photon timestamps; the conditional output correlation is a separate model prediction. No atomic motion, multilevel structure or calibrated apparatus.

### Run the experiment

1. 01

   #### Predict the contrast

   Compare the coupled atom with the empty cavity at resonance.

   **What to observe:** The empty cavity returns Poisson statistics; the atom changes pair probability.

2. 02

   #### Break the effect

   Tune between the one-photon and two-photon resonances.

   **What to observe:** A weak mean output can still have a large normalized pair correlation.

3. 03

   #### Collect and inspect

   Collect trials, pin a run, alter one control and restore it. Export every record as CSV.

   **What to observe:** The gold data come only from saved simulated records; cyan curves are model references.

Physical conclusion

A resonant two-level atom in one driven cavity mode, solved with a zero-temperature Lindblad equation. Cavity population decay sets the units. Ideal independent intracavity number readouts are not transmitted-photon timestamps; the conditional output correlation is a separate model prediction. No atomic motion, multilevel structure or calibrated apparatus.

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. [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)