A brief discussion of laser cooling

Laser Cooling

Laser cooling is a process by which kinetic energy is removed from the motion of charged particles in a trap. This is done by the use of radiation pressure of a laser beam. Each time an ion absorbs a photon, it absorbs also the momentum associated with that photon, so if we ensure that the absorption always takes place when the ion is moving towards the laser beam, the ion is always slowed down by the interaction with the laser. The limiting temperature is in the region of millikelvin and is limited by the natural width of the laser cooling transition, which is typically the resonance line of the ion.

For ions in a Penning trap, the laser beam has to be offset from the centre of the trap in order for the laser cooling to be effective for both magnetron and cyclotron motions simultaneously. The laser also has to be tuned slightly below the transition frequency (ie. to the red side of the transition) so that the ions are brought into resonance when they are moving towards the laser, as a result of the Doppler effect. In the rf trap the laser beam is not offset. The theory of laser cooling in the Penning trap is a rich area which has been looked at by many authors. We have also made some contributions in this area.

In our own experiments we use either Mg⁺ or Be⁺ ions, for which the laser cooling wavelengths are at 280 and 313 nm respectively. We generate these wavelengths by frequency doubling of a dye laser using an intra-cavity frequency doubling crystal. For the new work on quantum information processing we are working with Ca⁺ ions which can be laser cooled using diode lasers at 397 nm and 866 nm.

Quantum Jumps

In the simplest case laser cooling is performed with a two-level ion. In this case the ion continually absorbs radiation when it is tuned close to the resonance frequency, resulting in a level of fluorescence which under certain circumstances is high enough that even a single ion can be continuously monitored optically in a trap using photon counting techniques. If the ion has an additional, long-lived state, then it may be possible for the ion to enter this state. If this happens, then the ion fluorescence in a single-ion experiment must drop to zero because the ion cannot absorb the incident radiation when it is not in the ground state. Eventually the ion will return to the ground state, at which point the fluorescence will return. This happens typically after a period of the order of the lifetime of the state.

The result of this is that the fluorescence level becomes a so-called "random telegraph signal", switching randomly on and off as the ion makes quantum jumps between the ground state and the long-lived state. The signal is characteristic of a single particle and can be used as a diagnostic to "count" how many particles there are in the trap. In our own experiment on ²⁴Mg⁺ the third level arises from the effect of the magnetic field on the ground state of the ion, splitting it into two Zeeman sub-levels. The transitions into and out of this "metastable" level are spontaneous Raman transitions driven by the laser cooling beam. As a result, for this particular set-up the ratio of the "on" times to the "off" times is 16:1. This ratio is modified for different isotopes of Mg and for Be due to the presence of hyperfine structure.