# Laser cooling

Laser cooling refers to a number of techniques in which atomic and molecular samples are cooled down to near absolute zero through the interaction with one or more laser fields.

Simplified principle of Doppler laser cooling:
1 A stationary atom sees the laser neither red- nor blue-shifted and does not absorb the photon. An atom moving away from the laser sees it red-shifted and does not absorb the photon. An atom moving towards the laser sees it blue-shifted and absorbs the photon, slowing the atom. The photon excites the atom, moving an electron to a higher quantum state. The atom re-emits a photon. As its direction is random, there is no net change in momentum over many absorption-emission cycles.

The first example of laser cooling, and also still the most common method (so much so that it is still often referred to simply as 'laser cooling') is Doppler cooling. Other methods of laser cooling include:

## How it works

A laser photon hits the atom and causes it to emit photons of a higher average energy than the one it absorbed from the laser. The energy difference comes from thermal excitations within the atoms, and this heat from the thermal excitation is converted into light which then leaves the atom as a photon. This can also be seen from the perspective of the law of conservation of momentum. When an atom is traveling towards a laser beam and a photon from the laser is absorbed by the atom, the momentum of the atom is reduced by the amount of momentum of the photon it absorbed.

$\frac{\Delta p}{p} = \frac{p_{photon}}{mv} = \frac{\Delta v}{v}$
$\Delta v = \frac{p_{photon}}{m}$

Momentum of the photon is

$p = \frac{E}{c} = \frac{h}{\lambda}$

Suppose you are floating on a hovercraft, moving with a significant velocity in one direction (due north, for example). Heavy metallic balls are being thrown at you from all four directions (front, back, left, and right), but you can only catch the balls that are coming from directly in front of you. If you were to catch one of these balls, you would slow down due to the conservation of momentum. Eventually, however, you must throw the ball away, but the direction in which you throw the ball away is completely random. Due to conservation of momentum, throwing the ball away will increase your velocity in the direction opposite the ball's. However, since the "throw-away" direction is random, this contribution to your velocity will vanish on average. Therefore your forward velocity will decrease (due to preferentially catching the balls in front) and eventually your movements will entirely be dictated by the recoil effect of catching and throwing the balls.[1]

$\eta_{cooling} = \frac{P_{cooling}}{P_{electric}}$

$\eta_{cooling} =$ cooling efficiency

$P_{cooling} =$ cooling power in the active material

$P_{electric} =$ input electric power to the pump light source

$\frac{h}{\lambda} = p = mv$

$h =$ Planck's constant $(h = 6.626 \cdot 10^{-34}$ Js)

$\lambda =$ de Broglie's wavelength

$p =$ momentum of the atom

$m$ = mass of the atom

$v$ = velocity of the atom

Example: $\lambda = \frac{h}{mv} = \frac{\lambda_{photon}}{x}$

$x$ = number of photons needed to stop the momentum of an atom with mass m and at velocity $v$

Na atom

$m_{Na} = 3.818 \cdot 10^{-26}$ kg/atom

$v_{Na} \approx 300$ meters/second

$\lambda_{photon} = 600$ nm

$\frac{\lambda_{photon}}{x} = \frac{h}{m_{Na} v_{Na}} \Rightarrow x = 10372$

Conclusion: A total of 10372 photons are needed to stop the momentum of one sodium atom with a velocity of about 300 m/s. Experiments in laser cooling have yielded a number of $10^7$ photons to be emitted from a laser per second. This sodium atom could be stopped in space in just a matter of 1 millisecond.

## Doppler cooling

Main article: Doppler cooling

Doppler cooling, which is usually accompanied by a magnetic trapping force to give a magneto-optical trap, is by far the most common method of laser cooling. It is used to cool low density gases down to the Doppler cooling limit, which for Rubidium 85 is around 150 microkelvin. As Doppler cooling requires a very particular energy level structure, known as a closed optical loop, the method is limited to a small handful of elements.

In Doppler cooling, the frequency of light is tuned slightly below an electronic transition in the atom. Because the light is detuned to the "red" (i.e., at lower frequency) of the transition, the atoms will absorb more photons if they move towards the light source, due to the Doppler effect. Thus if one applies light from two opposite directions, the atoms will always scatter more photons from the laser beam pointing opposite to their direction of motion. In each scattering event the atom loses a momentum equal to the momentum of the photon. If the atom, which is now in the excited state, then emits a photon spontaneously, it will be kicked by the same amount of momentum, but in a random direction. Since the initial momentum loss was opposite to the direction of motion, while the subsequent momentum gain was in a random direction, the overall result of the absorption and emission process is to reduce the speed of the atom (provided its initial speed was larger than the recoil speed from scattering a single photon). If the absorption and emission are repeated many times, the average speed, and therefore the kinetic energy of the atom will be reduced. Since the temperature of a group of atoms is a measure of the average random internal kinetic energy, this is equivalent to cooling the atoms.

## Other methods of laser cooling

Several somewhat similar processes are also referred to as laser cooling, in which photons are used to pump heat away from a material and thus cool it. The phenomenon has been demonstrated via anti-Stokes fluorescence, and both electroluminescent upconversion and photoluminescent upconversion have been studied as means to achieve the same effects. In many of these, the coherence of the laser light is not essential to the process, but lasers are typically used to achieve a high irradiance.

## Uses

Laser cooling is primarily used for experiments in quantum physics to achieve temperatures of near absolute zero (0K, −273.15 °C, −459.67 °F). This is done to observe the unique quantum effects that can only occur at this heat level. Generally, laser cooling has only been used on the atomic level to cool down elements, but progress is being made on larger scales. In 2007, an MIT team successfully laser-cooled a macro-scale (1 gram) object to 0.8 K.[2] In 2011, a team from the California Institute of Technology and the University of Vienna became the first to laser-cool a (10 μm x 1 μm) mechanical object to its quantum ground state.[3]