---
title: "Three Light–Matter Transitions Interactive Lab | Sandbox Physics"
description: "Does stimulated emission always mean amplification? No. The light that triggers stimulated emission is also absorbed by atoms in the lower level."
canonical_url: "https://sandboxphysics.com/labs/light-matter-transitions/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/light-matter-transitions/"
last_modified: "2026-10-28"
---

L02 · Laser foundations

# Three Light–Matter Transitions

**Does stimulated emission always mean amplification?** No. The light that triggers stimulated emission is also absorbed by atoms in the lower level. Net gain needs more atoms in the upper level than in the lower one. Even if you start with such an inversion, without a pump the emission soon uses it up, and the medium goes back to absorbing more than it emits.

Prepare 80 emitters, shine a light field on them, and count absorption, spontaneous emission and stimulated emission one event at a time. Compare one random run with the exact prediction for the ensemble.

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

The emitters are two-level systems with equal degeneracy and fast dephasing. The spontaneous lifetime is 1 ms. The external probe stays constant and is never depleted; the photon exchange count records what the emitters give to or take from that probe. The model does not solve for a cavity, coherent Rabi dynamics or the phase of the field. Each count is a physical event in the model; the animated pulses and emission directions are schematic. Changing a setting prepares a new ensemble with the selected seed.

Laser foundations · Light, gain and feedback

[L01 · Compare sources](https://sandboxphysics.com/labs/laser-source-comparison/) [L02 · Count transitions](https://sandboxphysics.com/labs/light-matter-transitions/) [L03 · Build inversion](https://sandboxphysics.com/labs/population-inversion/) [L04 · Amplify once](https://sandboxphysics.com/labs/single-pass-amplifier/) [L05 · Add feedback](https://sandboxphysics.com/labs/passive-optical-resonator/) [L06 · Start from noise](https://sandboxphysics.com/labs/laser-noise-startup/) [L07 · Build and debug](https://sandboxphysics.com/labs/build-debug-laser/) [L08 · Measure and diagnose](https://sandboxphysics.com/labs/laser-diagnostic-bench/) [L09 · Select axial modes](https://sandboxphysics.com/labs/gain-longitudinal-modes/) [L10 · Confine the beam](https://sandboxphysics.com/labs/stable-resonator-geometry/) [L11 · Select spatial modes](https://sandboxphysics.com/labs/transverse-laser-modes/) [L12 · Propagate and measure](https://sandboxphysics.com/labs/gaussian-beam-quality/) [L13 · Align and match](https://sandboxphysics.com/labs/alignment-mode-matching/) [L14 · Optimize extraction](https://sandboxphysics.com/labs/output-coupler-optimization/) [L15 · Drive the dynamics](https://sandboxphysics.com/labs/laser-dynamics-relaxation/) [L16 · Store and release](https://sandboxphysics.com/labs/q-switched-giant-pulse/) [L17 · Lock phases into pulses](https://sandboxphysics.com/labs/mode-locking-frequency-comb/) [L18 · Calibrate the comb](https://sandboxphysics.com/labs/optical-frequency-comb/) [L19 · Inject carriers](https://sandboxphysics.com/labs/semiconductor-laser-diode/) [L20 · Compare gain media](https://sandboxphysics.com/labs/laser-medium-zoo/) [L21 · Distributed gain](https://sandboxphysics.com/labs/fiber-fbg-laser/) [L22 · Choose feedback](https://sandboxphysics.com/labs/laser-feedback-architectures/) [L23 · Balance ultrafast pulses](https://sandboxphysics.com/labs/ti-sapphire-oscillator/) [L24 · Stretch and compress](https://sandboxphysics.com/labs/chirped-pulse-amplification/) [L25 · Trap and extract](https://sandboxphysics.com/labs/regenerative-multipass-amplifier/) [L26 · Convert frequencies](https://sandboxphysics.com/labs/nonlinear-frequency-conversion/) [L27 · Scatter and cascade](https://sandboxphysics.com/labs/raman-brillouin-lasers/) [L28 · Synchronize a slave](https://sandboxphysics.com/labs/injection-locking/) [L29 · Lock to a reference](https://sandboxphysics.com/labs/pdh-frequency-lock/) [L30 · Measure phase noise](https://sandboxphysics.com/labs/laser-linewidth-phase-noise/) [L31 · Scatter for feedback](https://sandboxphysics.com/labs/random-laser/) [L32 · Diagnose thermal scaling](https://sandboxphysics.com/labs/thermal-lensing/) [L33 · Combine coherent fields](https://sandboxphysics.com/labs/coherent-beam-combining/) [L34 · Sustain a Kerr pulse](https://sandboxphysics.com/labs/microresonator-kerr-comb/) [L35 · Return a delayed field](https://sandboxphysics.com/labs/external-feedback-chaos/) [L36 · Scan without mode hops](https://sandboxphysics.com/labs/tunable-laser-scan/)

Physical basis: [MIT: coherence and spectrum](https://ocw.mit.edu/courses/res-6-006-video-demonstrations-in-lasers-and-optics-spring-2008/resources/coherence-length-and-source-spectrum/) · [Rate equations](https://ocw.mit.edu/courses/6-977-ultrafast-optics-spring-2005/resources/chapter2/) · [Pumping and gain media (§7.2)](https://ocw.mit.edu/courses/6-974-fundamentals-of-photonics-quantum-electronics-spring-2006/bf3bdeb971819ddc9c68719d28bb2745_classnotes.pdf) · [Laser dynamics](https://ocw.mit.edu/courses/6-977-ultrafast-optics-spring-2005/resources/chapter4/)

Physics tutorial

## Count both sides of the competition

**Background** The incident light mode can lose a photon to an emitter in the lower state, or gain one from an emitter in the upper state. An excited emitter can also decay on its own, with no driving field.

**Why it matters** Seeing stimulated emission does not show that the light has net gain. The emitters that absorb must be counted too.

Start with the essentials

- **Focus question**: Can stimulated emission happen while the incident light is losing photons overall?
- **One-sentence intuition**: Whether the light gains or loses depends on the difference between the upper and lower populations. Without a pump, spontaneous and stimulated emission use up any inversion you prepare.

### Core mathematical model

#### Three event rates

$$
R_a=WN_l,\quad R_s=WN_u,\quad R_{sp}=AN_u
$$

Each rate counts events in the whole ensemble per millisecond. The spontaneous coefficient is one per millisecond. The driving rate is per emitter and includes the Lorentzian detuning factor.

#### Detuning weakens the driven processes

$$
W=\frac{W_0}{1+(\delta/\gamma)^2}
$$

Detuning is measured in units of the frequency half-width at half maximum. At one half-width, the absorption and stimulated rates fall to half for the same populations. The intrinsic spontaneous lifetime does not change.

#### Exact mean for a fixed number of emitters

$$
\dot n_u=W(1-2n_u)-An_u
$$

There are always 80 emitters in total. The dashed curve is the exact ensemble mean; the solid curve is one direct Gillespie random run. With a finite sample, the solid curve can stray from the dashed one.

#### Event counts conserve the emitters

$$
N_u(t)-N_u(0)=C_a-C_s-C_{sp}
$$

Each event is counted once and moves one emitter. The net photon exchange with the driving mode is the stimulated count minus the absorption count; spontaneous photons are counted separately. The external probe is held fixed, so its strength does not respond to the photons it gains or loses.

### Common difficulties

#### Stimulated emission is not a collision

**Typical misconception** A photon hits the atom like a ball and knocks out a copy of itself.

**Better mental model** The animation only marks an event in a rate model. Stimulated emission adds a photon to the driving optical mode. Absolute optical phase and coherent atomic amplitudes are not part of this model.

#### An average is not a single run

**Typical misconception** A random trace is wrong whenever it strays from the exact curve.

**Better mental model** The mean describes the average over many runs. Every single run must conserve the emitters, but agreement with the mean can only be tested statistically, across many seeds.

### Run the experiment

1. 01

   #### Turn off the light field

   Choose Field off. Step or advance, and watch the upper population and the spontaneous-event count.

   **What to observe:** Excited emitters still decay with no incident field. The absorption and stimulated counts stay at zero.

2. 02

   #### Start at transparency

   Choose Equal populations before running. Compare the absorption and stimulated rates at that instant, then step.

   **What to observe:** The two driven rates start out equal. Spontaneous decay then breaks the balance, and the ensemble absorbs more than it emits, yet stimulated events keep happening.

3. 03

   #### Use up a prepared inversion

   Choose Inverted sample and run. Watch the upper population, the signed photon exchange with the mode, and how the two driven rates compete later on.

   **What to observe:** Without a pump, the initial gain does not last. The population settles toward a steady mean with no inversion.

4. 04

   #### Look at many runs, not one lucky trace

   Repeat with the same settings and different random seeds. Also compare running on resonance with a detuning of one half-width.

   **What to observe:** The event counts change from run to run, but the exact mean comes out the same every time. Detuning changes the driven rates, and spontaneous decay still happens.

Physical conclusion

The driving field pushes emitters both up and down. For gain to last, a pump has to keep enough emitters in the upper state.

## Related experiments and articles

Continue exploring

### Events and their average

How do random transition counts approach a smooth population curve?

1. [Lab **Absorption, Spontaneous & Stimulated Emission** Send a probe through an excited gas and watch gain turn into absorption.](https://sandboxphysics.com/labs/absorption-spontaneous-stimulated-emission/)
2. [You are here **Three Light–Matter Transitions** Count individual stochastic events and compare with the expected population.](https://sandboxphysics.com/labs/light-matter-transitions/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

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