How laser light slows an atom

Imagine following one atom as it flies through a vacuum chamber. A laser beam meets it head-on. The atom absorbs a photon, and its forward motion changes by a very small amount. One such encounter barely matters. Repeat the cycle many times, with the light tuned so that atoms moving in a chosen direction are more likely to absorb from the beam facing them, and light becomes a brake.

Slowing an atomic beam changes its average forward motion; cooling a gas narrows the spread of random velocities around that motion. A cloud can drift quickly while its atoms share nearly the same velocity, or have no net drift while its atoms move rapidly in opposite directions. Temperature describes the random spread after the common drift is set aside.

The push from one photon

Light carries momentum even though photons have no rest mass. A photon with wavelength $\lambda$ carries momentum $p=h/\lambda$, where $h$ is Planck's constant. When an atom absorbs that photon, it receives the photon's momentum in the direction the light was travelling. If the atom has mass $m$, the change in its velocity has magnitude $\Delta v=h/(m\lambda)$. For a typical optical photon and an atom, this is a tiny, directional kick that can slow the atom when the beam faces its motion.

The formula also shows why atom mass matters: the same photon momentum produces a smaller change in velocity for a heavier atom. At fixed mass, a shorter wavelength means a larger photon momentum and a bigger speed change. The usable wavelength is still set by the atom's allowed transition.

The absorption briefly excites the atom. It then emits a photon as it returns to a lower internal energy state. This is spontaneous emission because the emission time and direction are not set by a second laser pulse. The emitted photon carries momentum, and its direction varies from one cycle to the next.

In a closed scattering cycle, the atom returns to its original internal state. Fluorescence can then carry away more energy than the laser supplies, with the difference drawn from the atom's kinetic energy. With red-detuned light, an atom moving toward the beam sees its frequency shifted toward resonance and scatters more strongly. Random recoil broadens the velocity distribution. Net cooling occurs when the velocity-dependent energy loss outweighs that heating; at equilibrium the two balance.

Why the laser must be tuned

Atoms absorb light efficiently only near particular frequencies. Each allowed transition between two internal energy states has a resonance frequency. A laser far from resonance is unlikely to drive that transition, so it will produce few of the absorption events needed for a substantial push.

The resonance is a band of frequencies rather than a single perfectly sharp point. Nearer resonance, the transition is driven more often. The two beams do not need to produce an all-or-nothing response: a small Doppler shift can make one beam scatter more strongly than its opposing partner.

Motion changes the frequency an atom sees. This is the Doppler effect, familiar from the change in pitch of a passing siren. An atom moving toward a light beam encounters its wave crests more often, so the light appears shifted to a higher frequency in the atom's frame. An atom moving away sees a lower frequency. A red-detuned laser has a frequency slightly below the resting atom's resonance. For an atom moving toward that beam, the Doppler shift can move the light closer to resonance.

With two beams on opposite sides of a cloud, both slightly red-detuned, an atom drifting right moves toward the leftward beam. That beam is shifted closer to resonance in the atom's frame, while the other shifts farther away. The atom is then more likely to absorb a photon that kicks it left. For motion in the other direction, the favored beam reverses. Near zero velocity the beams nearly balance; at small nonzero velocity their imbalance reduces the motion.

This force depends on velocity because the Doppler shift does. In a simple picture, it resembles drag: motion through the laser field causes a force that opposes motion. The atoms remain far apart in a dilute gas. The name optical molasses refers to the sluggish motion produced by opposing beams. Chu and colleagues demonstrated three-dimensional optical molasses with resonance radiation pressure in 1985 (published 1 July 1985).

Three-dimensional cooling uses opposing beam pairs along three axes. Each pair damps motion along its own axis, so atoms at the intersection can lose random motion in every direction. An atom moving diagonally has a velocity component along each axis, and all three pairs act on it. One pair alone would leave motion in the perpendicular directions largely untouched.

Keeping a decelerating beam resonant

In 1982, Phillips and Metcalf slowed a sodium atomic beam with resonant light sent against its motion. As the atoms lost speed, their Doppler shift changed and a fixed laser would move out of resonance. A magnetic field varied along the beam shifted the atomic transition frequency to keep the atoms interacting with the light (published 1 March 1982). The field changed the resonance; photon absorption supplied the opposing momentum.

Optical molasses reduces small velocity differences because atoms moving one way scatter more strongly from the opposing beam. It does not, by itself, pull atoms back toward a particular point. If an atom drifts away from the center while moving very slowly, the molasses force can also be small. The cloud may slow without staying gathered in one place.

Adding a restoring force

A magneto-optical trap, or MOT, adds a magnetic-field gradient to the opposing laser beams. The gradient means the magnetic field changes with position. Many atomic transitions split or shift slightly in a magnetic field. This is the Zeeman effect. Beam polarization determines which internal transitions are driven.

With polarizations chosen to match the Zeeman shifts, an atom on either side of the trap is more likely to absorb from the beam pointing inward. On the other side, the favored beam reverses. The magnetic field sets where this preference flips; photon momentum supplies the restoring force. The beams also retain velocity damping. Raab and colleagues reported trapping neutral sodium atoms with radiation pressure in 1987 (published 7 December 1987).

An experiment needs atoms with suitable transitions, lasers at the right frequencies, control of beam polarization and magnetic field, and a vacuum good enough that collisions with background gas do not quickly disrupt the cloud. A low collision rate lets the atoms scatter many photons and later expand freely for measurement. This selectivity is why shining light on an arbitrary material does not create a laser-cooled atomic sample.

Repeated scattering can move an atom into another hyperfine ground level, one of the closely spaced internal states of its ground state. If the cooling laser does not address that level, the atom stops absorbing cooling light and the directed force disappears. Enough such events can drain atoms from the active scattering cycle. A repumping laser drives a separate transition that lets spontaneous emission return the atom to the cooling cycle. Repumping keeps atoms available to scatter; the opposing cooling beams and magnetic gradient still set the damping and restoring forces. Phillips's review explains this leakage and repumping in its discussion and Fig. 2 (PDF, p. 2).

Optical pumping also has a role in sub-Doppler cooling, where it transfers atoms among sublevels as they move through the changing light pattern. Without a change of sublevel, an atom descending the same optical potential could recover much of the energy it lost while climbing. Pumping to a lower-energy state lets the cycle remove kinetic energy instead.

Beyond the two-level Doppler model

The Doppler limit comes from a simplified model that treats the atom as having two internal levels and balances velocity damping against random photon recoil. A real MOT uses several internal sublevels, whose response to light polarization can open additional cooling paths. The limit is a benchmark for that model rather than a universal floor for laser cooling.

Polarization describes the orientation of the light's electric field. Atomic sublevels respond differently to that field. With suitable beam polarizations, interference can make the polarization vary across space. Each sublevel has transition rules that determine which polarization can drive it. Optical pumping is light-driven redistribution among these sublevels. As an atom moves through the pattern, it can enter a sublevel with a different light-induced energy landscape. An optical potential is an effective energy that depends on position because of the light; the atom does not climb a physical surface. It loses kinetic energy while climbing this potential, then pumping can transfer it to a lower-energy sublevel and restart the cycle. This route allows cooling beyond the two-level prediction. Phillips reviews these multilevel routes to sub-Doppler cooling in his Nobel lecture (published 1 July 1998).

In 1988, Lett and colleagues reported sodium at $43 \pm 20\,\mu\mathrm{K}$, below the $240\,\mu\mathrm{K}$ Doppler prediction for that transition (published 11 July 1988). A microkelvin is one millionth of a kelvin. These values describe that experiment and transition.

Measuring temperature from expansion

For a dilute classical gas, temperature tracks the average kinetic energy of random motion around the cloud's mean velocity. Lett's group measured it after releasing the atoms from the molasses, using several complementary ballistic-motion methods (published 11 July 1988). Ballistic motion means following the atoms after the laser forces are switched off. One way to see how expansion can reveal temperature is to consider the width of a released cloud. This illustrates the principle, rather than reconstructing the specific measurements in the 1988 paper. Random velocities make the cloud's width grow, and a wider velocity spread produces faster growth. The cloud also has a width before release, so a single image cannot tell whether a broad cloud began large or expanded quickly. If $\sigma_x(t)$ is its width after flight time $t$ and $\sigma_v$ is the spread of velocities, then for uncorrelated positions and velocities $\sigma_x^2(t)=\sigma_x^2(0)+\sigma_v^2 t^2$. This follows by tracking each atom's position as its starting point plus its velocity multiplied by flight time. A plot of width squared against time squared separates the starting-size contribution from the expansion term; its slope gives the velocity variance. For an isotropic cloud, the variance along one axis gives the corresponding thermal energy scale through $k_B T=m\sigma_v^2$. Gravity shifts the cloud's centre as it falls; its shared motion can be tracked separately from the growth in width. An anisotropic cloud would require measuring velocity spread in each direction.

What the method makes possible

By reducing the velocity spread, cooling lets atoms drift apart more slowly during free flight and remain available for measurement longer. It also reduces the range of Doppler shifts seen by a probe beam. Atoms moving at different speeds can make a spectral line appear broader; a narrower spread makes that contribution smaller and helps precision spectroscopy. The transition itself has not changed. Rather, atoms moving toward and away from the probe see slightly different frequencies, so a scan sums responses across a wider range. Atomic clocks use stable transitions as frequency references, while laser-cooled samples also make experiments on quantum behavior possible.

Sources

• Phillips and Metcalf, “Laser Deceleration of an Atomic Beam,” Physical Review Letters 48, 596, published 1 March 1982. Article
• Chu et al., “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Physical Review Letters 55, 48, published 1 July 1985. Article
• Lett et al., “Observation of Atoms Laser Cooled below the Doppler Limit,” Physical Review Letters 61, 169, published 11 July 1988. Article
• Raab et al., “Trapping of Neutral Sodium Atoms with Radiation Pressure,” Physical Review Letters 59, 2631, published 7 December 1987. Article
• Phillips, “Nobel Lecture: Laser cooling and trapping of neutral atoms,” Reviews of Modern Physics 70, 721, published 1 July 1998. Article
• Cover photograph: Purple Laser Beam Slowing Erbium Atoms, NIST, image 06PHY018 (2006).