Laser cooling

Laser cooling reduces the velocity spread of atoms, ions or molecules by repeated momentum exchange with laser light. Each absorbed photon gives the atom a kick $\hbar k$ along the beam; the photon is then re-emitted by spontaneous emission in a random direction, so the emission kicks average to zero over many cycles while the absorption kicks add up. When the light is tuned slightly below the atomic resonance, the Doppler shift makes atoms moving toward a beam absorb more than atoms moving away, and the net force opposes the motion. A vapor of rubidium atoms at room temperature, with an rms speed near 290 m/s, can be cooled this way to about 146 µK, where the rms speed along each axis is about 12 cm/s, and to a few microkelvin with sub-Doppler techniques. Steven Chu, Claude Cohen-Tannoudji and William D. Phillips received the 1997 Nobel Prize in Physics for the development of these methods.

Scattering force and slowing

An atom driven hard on a transition with natural decay rate $\Gamma$ scatters at most $\Gamma/2$ photons per second, so the largest radiation-pressure acceleration is

$$a_\text{max} = \frac{\hbar k\,\Gamma}{2m}.$$

For the rubidium-87 D2 line at 780 nm, with $\Gamma/2\pi$ = 6.07 MHz, this is $1.1 \times 10^5$ m/s², about 11,000 times the acceleration of gravity. The recoil velocity from a single photon is

$$v_r = \frac{\hbar k}{m} = 5.9\ \text{mm/s},$$

so stopping an atom moving at 300 m/s takes about 51,000 absorption cycles; at half the maximum deceleration this takes 5.3 ms over 0.80 m. A Zeeman slower uses a tapered magnetic field to keep the transition resonant as the Doppler shift falls.

Optical molasses and the Doppler limit

Three orthogonal pairs of counterpropagating, red-detuned beams produce a viscous damping force along every axis, called optical molasses. The damping competes with heating from the random recoils, and the balance gives a minimum temperature, reached at a detuning of $\Gamma/2$ below resonance:

$$T_D = \frac{\hbar\,\Gamma}{2 k_B}.$$

For rubidium-87 ($\Gamma/2\pi$ = 6.07 MHz) the Doppler limit is 146 µK; for the cesium D2 line at 852 nm ($\Gamma/2\pi$ = 5.23 MHz) it is 125 µK. The limit depends only on the linewidth, so narrow intercombination lines in strontium and ytterbium give much lower Doppler temperatures.

A lower scale is set by the recoil of a single photon. The recoil temperature, defined as $T_r = \hbar^2 k^2/(m k_B)$, is 362 nK for rubidium-87 and 198 nK for cesium; some texts define it with an extra factor of 1/2.

Magneto-optical traps and sub-Doppler cooling

Molasses damps motion but does not confine. A magneto-optical trap (MOT) adds a quadrupole magnetic field, zero at the center, and gives the beams opposite circular polarizations; the Zeeman shift then makes an atom displaced from the center scatter preferentially from the beam pushing it back. A vapor-cell MOT captures atoms from the slow tail of the room-temperature velocity distribution and typically holds millions to billions of atoms in a millimeter-size cloud.

Experiments in 1988 found molasses temperatures well below $T_D$. The explanation, polarization-gradient or Sisyphus cooling, involves ground-state light shifts that vary in space with the polarization of the interfering beams: atoms climb potential hills and are optically pumped to the bottom of the next, losing energy at each step. With larger detuning and lower intensity, rubidium and cesium reach a few microkelvin, approaching ten or so recoil temperatures.

Uses and equipment

Laser-cooled atoms and ions are the references in cesium fountain clocks and optical atomic clocks, where slow atoms allow long interrogation times. Further evaporative cooling in a magnetic or optical dipole trap, the same dipole force used in optical tweezers, produced the first Bose-Einstein condensates in 1995, at temperatures near 100 nK. Atom interferometers also start from a MOT.

The lasers need linewidths well below $\Gamma$, a few hundred kilohertz to around 1 MHz for the alkali D lines. A common setup locks an external-cavity laser to a saturated-absorption spectrum, sets the detuning with an acousto-optic modulator in double pass, and boosts the power with a tapered amplifier. Alkali atoms also need a repumping laser for the other hyperfine ground state.

Laser cooling of solids

A solid absorbing on the long-wavelength side of a band and fluorescing, on average, at shorter wavelengths loses the energy difference from its lattice vibrations. This anti-Stokes fluorescence cooling is the quantum defect with the opposite sign: pumping at 1020 nm a material with a mean fluorescence wavelength of 1000 nm removes at most 2.0% of the absorbed power, and only with near-unity fluorescence quantum efficiency and low parasitic absorption. Ytterbium-doped glasses and crystals are the main materials.

Common questions

How cold can laser cooling get?

Doppler cooling reaches $\hbar\Gamma/2k_B$, typically 100–250 µK for alkali atoms. Polarization-gradient cooling gives a few microkelvin, and specialized methods such as velocity-selective coherent population trapping and Raman cooling reach below the recoil temperature. Evaporative cooling, usually after laser cooling, goes to nanokelvin.

References: H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer, 1999); P. D. Lett, R. N. Watts, C. I. Westbrook, W. D. Phillips, P. L. Gould and H. J. Metcalf, "Observation of atoms laser cooled below the Doppler limit," Phys. Rev. Lett. 61, 169 (1988); J. Dalibard and C. Cohen-Tannoudji, "Laser cooling below the Doppler limit by polarization gradients: simple theoretical models," J. Opt. Soc. Am. B 6, 2023 (1989); R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell and C. E. Mungan, "Observation of laser-induced fluorescent cooling of a solid," Nature 377, 500 (1995).