---
title: "Optomechanical Sideband Cooling Interactive Lab | Sandbox Physics"
description: "How can light cool a vibrating mirror? A laser tuned below the cavity resonance scatters more often by taking energy from the mirror than by giving it energy."
canonical_url: "https://sandboxphysics.com/labs/optomechanical-sideband-cooling/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/optomechanical-sideband-cooling/"
---

FR12-A · Light carries mechanical energy away

# Optomechanical Sideband Cooling

**How can light cool a vibrating mirror?** A laser tuned below the cavity resonance scatters more often by taking energy from the mirror than by giving it energy. The outgoing light carries away that difference. A narrow cavity suppresses the reverse process and allows a lower final vibration energy.

Tune a laser below the cavity resonance and watch a suspended mirror settle. Broaden the cavity or tune above resonance to see cooling give way to heating.

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

Model assumptions

A weak-coupling secular rate equation describes one high-quality mechanical mode and a driven optical mode with a vacuum optical bath. Frequencies are divided by the mechanical angular frequency; the cavity linewidth is its energy decay rate. The drive holds the enhanced coupling fixed as detuning changes. Mirror motion is a positive-Wigner Gaussian sample of symmetrized fluctuations, not a measurement record. Displacement and time are magnified; optical absorption, static bistability, strong coupling and nonlinear saturation are omitted. Above the instability threshold only early growth is shown.

Rate-equation predictions · synthetic motion

## Where the energy goes

### The cavity selects a sideband

$(\omega-\omega_L)/\Omega_m$

Cyan removes a phonon. Coral adds one. The curve shows the cavity response, normalized to its peak.

### The mirror settles or grows

$\Omega_m t\quad\longrightarrow\qquad\bar n(t)$

Cyan is the rate-equation prediction. The dashed line is the bath occupation. The moving dot gives the current animation time.

Displacement sample and spectral conventions

The sample is generated by the Gaussian dynamics of the same secular model. It represents symmetrized fluctuations, not a detected optical record. Its seed and exact transition are saved with the parameters.

$\Omega_m t\quad\longrightarrow\qquad x/x_{\mathrm{zpf}}$

$\int_{-\infty}^{\infty}\frac{d\omega}{2\pi}\bar S_{xx}(\omega)=x_{\mathrm{zpf}}^2(2\bar n+1)$

Angular-frequency, double-sided, symmetrized spectra. A stationary spectrum exists only for positive total damping. The cavity rate model assumes weak coupling and a high mechanical quality factor.

[Aspelmeyer, Kippenberg & Marquardt · quantum cooling, equations 80–90](https://arxiv.org/html/1303.0733v1#S7.SS1)

[Study quantum optomechanics from moving mirrors to single photons](https://sandboxphysics.com/stories/quantum-optomechanics/)

Physics tutorial

## Optomechanical Sideband Cooling

**Background** Tune a laser below the cavity resonance and watch a suspended mirror settle. Broaden the cavity or tune above resonance to see cooling give way to heating.

**Why it matters** A photon can leave a cavity with a little more energy than it arrived with. The extra energy comes from the vibrating mirror.

Start with the essentials

- **Focus question**: How can light cool a vibrating mirror?
- **One-sentence intuition**: Cooling depends on the imbalance between phonon-removing and phonon-adding scattering.

### Core mathematical model

#### Two scattering rates

$$
A_- = \frac{g^2\kappa}{(\kappa/2)^2+(\Delta+\Omega_m)^2},\qquad A_+ = \frac{g^2\kappa}{(\kappa/2)^2+(\Delta-\Omega_m)^2}
$$

The detuning is laser frequency minus cavity frequency. The linewidth is an energy decay rate. Anti-Stokes scattering removes a phonon; Stokes scattering adds one.

#### Occupation changes by competing transitions

$$
\frac{d\bar n}{dt}=-(\Gamma_m+A_--A_+)\bar n+\Gamma_m\bar n_{\mathrm{th}}+A_+
$$

A stable steady state needs positive total damping. In the blue-detuned case the occupation grows, until omitted nonlinear effects matter.

### Common difficulties

#### Cold does not mean motionless

**Typical misconception** A ground-state mirror should stop moving.

**Better mental model** The displacement variance still contains vacuum fluctuations. The displayed sample represents the positive Wigner distribution of a Gaussian state.

#### Keep the drive convention in mind

**Typical misconception** The slider compares equal incident powers at different detunings.

**Better mental model** The enhanced coupling is held fixed. The laser drive would need adjustment as detuning changes.

### Run the experiment

1. 01

   #### Predict which photon wins

   Choose Remove a phonon. Compare the two scattering rates and follow the occupation curve.

   **What to observe:** The anti-Stokes rate is larger, and the mirror approaches a smaller but finite fluctuation amplitude.

2. 02

   #### Let heating leak through

   Choose A cavity too broad, then reduce the linewidth while leaving the enhanced coupling fixed.

   **What to observe:** A broad cavity accepts both sidebands. A narrow cavity selects the phonon-removing transition more strongly.

3. 03

   #### Reverse the energy flow

   Choose Light amplifies motion, then turn off the light. Export the model and the Gaussian motion sample.

   **What to observe:** Blue-detuned light supplies mechanical energy. With the drive off the thermal bath alone sets the equilibrium.

Physical conclusion

Light cools a mirror when it carries away more mechanical energy than it returns.

## Related experiments and articles

Quantum optomechanics · Reading path

### From a moving mirror to quantum measurement

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

1. [Article **How a moving mirror changes light**](https://sandboxphysics.com/stories/quantum-optomechanics/moving-mirror-and-cavity/)
2. [Article **How strong light enhances a weak interaction**](https://sandboxphysics.com/stories/quantum-optomechanics/linearization-and-sidebands/)
3. [Article **Why cooling needs a cavity that stores light**](https://sandboxphysics.com/stories/quantum-optomechanics/cooling-and-instability/)

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)