A magneto-optical trap is a device that uses both laser cooling

Laser cooling

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

 with magneto-optical trapping in order to produce samples of cold, trapped, neutral atoms at temperatures as low as several microkelvins, two or three times the recoil limit.
By combining the small momentum

Momentum

In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

 of a single photon

Photon

In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

 with a velocity and spatially dependent absorption cross section

Absorption cross section

Absorption cross section is a measure for the probability of an absorption process. More generally, the term cross section is used in physics to quantify the probability of a certain particle-particle interaction, e.g., scattering, electromagnetic absorption, etc...

 and a large number of absorption-spontaneous emission

Spontaneous emission

Spontaneous emission is the process by which a light source such as an atom, molecule, nanocrystal or nucleus in an excited state undergoes a transition to a state with a lower energy, e.g., the ground state and emits a photon...

 cycles, atoms with initial velocities of hundreds of metres per second can be slowed to tens of centimetres per second.

Although charged particles can be trapped using a Penning trap

Penning trap

Penning traps are devices for the storage of charged particles using a homogeneous static magnetic field and a spatially inhomogeneous static electric field. This kind of trap is particularly well suited to precision measurements of properties of ions and stable subatomic particles which have...

 or a Paul trap using a combination of electric and magnetic fields, these traps do not work for neutral atoms.

Doppler cooling

Photons have a momentum given by ħk (where ħ is the reduced Planck constant and k the photon wavenumber

Wavenumber

In the physical sciences, the wavenumber is a property of a wave, its spatial frequency, that is proportional to the reciprocal of the wavelength. It is also the magnitude of the wave vector...

), which is conserved in all atom-photon interactions. Thus, when an atom absorbs a photon, it is given a momentum kick in the direction of the photon before absorption. By detuning

Laser detuning

In optical physics, laser detuning is the tuning of a laser to a frequency that is slightly off from a quantum system's resonant frequency. Lasers can be detuned in the lab frame so that they are Doppler shifted to the resonant frequency in a moving system, which allows lasers to affect only...

 a laser beam to a frequency less than the resonant frequency (also known as red detuning), laser light is only absorbed if the light is frequency up-shifted by the Doppler effect

Doppler effect

The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...

; which occurs whenever the atom is moving towards the laser source. This applies a friction force to the atom whenever it moves towards a laser source.

For cooling to occur along in all directions, the atom must see this friction force along all 3 cartesian axis; this is most easily achieved by illuminating the atom with 3 orthogonal laser beams, which are then reflected back along the same direction.

Magnetic trapping

Magnetic trapping is created by adding a spatially varying magnetic quadrupole field to the red detuned optical field needed for laser cooling. This causes a Zeeman shift

Zeeman effect

The Zeeman effect is the splitting of a spectral line into several components in the presence of a static magnetic field. It is analogous to the Stark effect, the splitting of a spectral line into several components in the presence of an electric field...

 in the magnetic-sensitive m_f levels, which increases with the radial distance from the centre of the trap. Because of this, as an atom moves away from the centre of the trap, the atomic resonance is shifted closer to the frequency of the laser light, and the atom becomes more likely to get a photon kick towards the centre of the trap.

The direction of the kick is given by the polarisation of the light, which is either left or right handed circular giving different interactions with the different m_f levels. The correct polarisations are used so that photons moving towards the centre of the trap will be on resonance with the correct shifted atomic energy level, always driving the atom towards the centre.

Atomic structure necessary for magneto-optical trapping

As a normal atom has many thousands of times the momentum of a single photon, the cooling of an atom must involve many absorption-spontaneous emission cycles, with the atom losing up to ħk of momenta each cycle .
Because of this, if an atom is to be laser cooled, it must possess a specific energy level structure known as a closed optical loop, where following an excitation-spontaneous emission event, the atom is always returned to its original state.
⁸⁵Rubidium, for example, has a closed optical loop between the 5S_1/2 F=3 state and the 5P_3/2 F=4 state. Once in the excited state, the atom is forbidden from decaying to any of the 5P_1/2 states, which would not conserve parity

Parity (physics)

In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...

, and is also forbidden from decaying to the 5S_1/2 F=2 state, which would require an angular momentum change of −2, which can not be supplied by a single photon.

Many atoms that do not contain closed optical loops can still be laser cooled, however, by using repump lasers which re-excite the population back into the optical loop after it has decayed to a state outside of the cooling cycle. The magneto-optical trapping of rubidium 85, for example, involves cycling on the closed 5S_1/2 F=3 → 5P_3/2 F=4 transition. On excitation, however, the detuning necessary for cooling gives a small, but non-zero overlap with the 5P_3/2 F=3 state. If an atom is excited to this state, which occurs roughly every thousand cycles, the atom is then free to decay either the F=3, light coupled upper hyperfine state, or the F=2 "dark" lower hyperfine state. If it falls back to the dark state, the atom stops cycling between ground and excited state, and the cooling and trapping of this atom stops. A repump laser, which is resonant with the 5S_1/2 F=2 → 5P_3/2 F=3 transition is used to recycle the population back into the optical loop so that cooling can continue.

Laser

All magneto-optical traps require at least one trapping laser plus any necessary repumper lasers (see above). These lasers need stability, rather than high power, requiring no more than the saturation intensity, but a linewidth much less than the Doppler width, usually several megahertz. Because of their low cost, compact size and ease of use, laser diodes are used for many of the standard MOT species while the linewidth and stability of these lasers is controlled using servo

Servomechanism

thumb|right|200px|Industrial servomotorThe grey/green cylinder is the [[Brush |brush-type]] [[DC motor]]. The black section at the bottom contains the [[Epicyclic gearing|planetary]] [[Reduction drive|reduction gear]], and the black object on top of the motor is the optical [[rotary encoder]] for...

 systems, which stabilises the lasers to an atomic frequency reference by using, for example, saturated absorption spectroscopy

Saturated spectroscopy

Saturated spectroscopy is the method by which the exact energy of the hyperfine transitions within an atom can be found. When a monochromatic light is shone through an atom, the Absorption cross section is broadened due to Doppler broadening...

 and the Pound-Drever-Hall technique

Pound-Drever-Hall technique

The Pound–Drever–Hall technique is an application of FM spectroscopy to detect the resonances of the optical cavity by demodulating the beam reflected from the cavity. The PDH technique is often part of a control system which regulates the frequency of a laser to match the resonance condition of...

 to generate a locking signal.

Vacuum chamber

The MOT cloud is loaded from a background of thermal vapour. However, the trapping potential in a magneto-optical trap is small in comparison to thermal energies of atoms and most collisions between trapped atoms and the background gas supply enough energy to the trapped atom to kick it out of the trap. If the background pressure is too high, atoms are kicked out of the trap faster than they can be loaded, and the trap does not form. This means that the MOT cloud only forms in a vacuum chamber with a background pressure of less than 10 micropascals (10⁻¹⁰ bar).

The limits to the magneto-optical trap

The maximum temperature and density of a cloud in a magneto-optical trap is limited by the spontaneously emitted photon in cooling each cycle. While the asymmetry in atom excitation gives cooling and trapping forces, the emission of the spontaneously emitted photon is in a random direction, and therefore contributes to a heating of the atom. Of the two ħk kicks the atom receives in each cooling cycle, the first cools, and the second heats: a simple description of laser cooling which enables us to calculate a point at which these two effects reach equilibrium, and therefore define a lower temperature limit, known as the Doppler cooling limit

Doppler cooling limit

Doppler temperature is the minimum temperature achievable with Doppler cooling, one of the methods of laser cooling.When a photon is absorbed by an atom moving in the opposite direction, its velocity is decreased according to the laws of momentum conservation. Accordingly, when a photon is emitted...

.

The density is also limited by the spontaneously emitted photon. As the density of the cloud increases, the chance that the spontaneously emitted photon will leave the cloud without interacting with any further atoms becomes non-zero. The absorption, by a neighboring atom, of a spontaneously emitted photon gives a 2ħk momentum kick between the emitting and absorbing atom which can be seen as a repulsive force, similar to coulomb repulsion, which limits the maximum density of the cloud.

Application

As a result of low densities and speeds of atoms achieved by optical cooling, the mean free path

Mean free path

In physics, the mean free path is the average distance covered by a moving particle between successive impacts which modify its direction or energy or other particle properties.-Derivation:...

 in a ball of MOT cooled atoms is very long, and atoms may be treated as ballistic

External ballistics

External ballistics is the part of the science of ballistics that deals with the behaviour of a non-powered projectile in flight. External ballistics is frequently associated with firearms, and deals with the behaviour of the bullet after it exits the barrel and before it hits the target.-Forces...

. This is useful for quantum information experiments where it is necessary to have long coherence time

Coherence time

For an electromagnetic wave, the coherence time is the time over which a propagating wave may be considered coherent...

s ( the time an atom spends in a defined quantum state). Because of the continuous cycle of absorption and spontaneous emission, which causes decoherence

Quantum decoherence

In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...

, any quantum manipulation experiments must be performed with the MOT beams turned off. In this case, it is common to stop the expansion of the gasses during quantum information experiments by loading the cooled atoms into a dipole trap

Dipole trap

A dipole trap is a system in which a laser are used to polarize an individual atom for study. The set-up is similar to a Magneto-optical trap except that there is no magnetic field and a reduced number of lasers....

.

A magneto-optical trap is usually the first step to achieving Bose-Einstein condensation. Atoms are cooled in a MOT down to a few times the recoil limit, and then evaporatively cooled which lowers the temperature and increases the density to the required phase space density.

A MOT of ¹³³Cs was used to make some of the best measurements of CP violation

CP violation

In particle physics, CP violation is a violation of the postulated CP-symmetry: the combination of C-symmetry and P-symmetry . CP-symmetry states that the laws of physics should be the same if a particle were interchanged with its antiparticle , and left and right were swapped...

.