Macroscopic Laser Trapping

An All-Optical Trap for a Gram-Scale Mirror

Thomas Corbitt, et alii

PRL 98, 150802 (2007)

URL: http://link.aps.org/abstract/PRL/v98/e150802

This experimental group has demonstrated laser cooling and trapping of a large object: a 1 gram mirror. (That doesn't sound large, but its 10^25 atoms --- a lot larger than the typical atomic and molecular clouds in these types of experiments.)

The authors were able to achieve an effective temperature of 0.8 K along the direction of the beams. (Temperature is a scalar quantity, so how can it have a direction? What the authors really measured were the mean-square fluctuations in the direction of the beam. The equipartition theorem allow one to turn this quantity into an effective temperature.)

It's not hard to point a laser at a mirror, so why hadn't someone done this before? The authors point out that there are two types of radiation pressure effects: damping forces and restoring forces. A damping force slows things down. It leads to effects like optical molasses. A restoring force keeps objects in a certain region, like in optical tweezers.

For a mirror in an optical cavity, both effects can be implemented by detuning a laser from the resonant frequency of the cavity, but not simultaneously. If the laser is above resonance, it will produce a restoring force, but also an anti-damping force. If the laser is below resonance, it gives rise to a damping force, but also an anti-restoring force. It is impossible to trap a mirror and damp its motion with a single laser. (Sounds like Heisenberg: you can't fix the momentum and position simultaneously. If you had a laser beam tuned to resonance, but with fluctuations above and below, could you achieve both effects with the same beam? Would the spread in momentum and position obey some uncertainty principle? Or would the whole system be totally unstable?)

The authors get around this difficulty by using two beams. One is tuned above resonance, the other below. The frequencies are chosen so that one gives a large restoring force with small anti-damping and the other a large damping force with small anti-restoring. The result is a very stable, rigid localizing force.

What caught my attention in this article was the rigidity. The authors imagine replacing the laser beam with a rigid rod of the same diameter. To achieve the same stiffness (spring constant) as their trap, you would need a material 20% stiffer than diamond!

The caveat of all this work is that the confinement is only to one dimension. The mirror still shows room temperature (or higher) fluctuations in the directions perpendicular to the beam. Perhaps a cubic mirror could be cooled and trapped just as effectively in all three directions.