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.

Mean phonon number now $0.9$

Total damping / mechanical frequency $0.00308$

Anti-Stokes rate / mechanical frequency $0.00300$

Stokes rate / mechanical frequency $1.68\times10^{-5}$

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

Study quantum optomechanics from moving mirrors to single photons

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 misconceptionA ground-state mirror should stop moving.

Better mental modelThe 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 misconceptionThe slider compares equal incident powers at different detunings.

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

Run the experiment

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.
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.
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.

Optomechanical Sideband Cooling

Where the energy goes

The cavity selects a sideband

The mirror settles or grows