Frequency Combs and Astrophysics

Clifford Johnson is pointing to a pair of stories about extrasolar planets. One is a news piece about the "flood" of new discoveries, and the other is a Top 10 list from space.com (warning: irritating web design).

This provides a good excuse to roll out a blog suggestion from Ron Walsworth, who pointed out a possible connection to the ultra-stable lasers that Jun Ye and Jim Bergquist talked about on the first day of last week's conference. He suggested that, in the future, these ultra-stable lasers may be useful not only for comparing clocks on Earth, but as a crucial reference to help detect planets around other stars.

The connection here is that one of the main methods used to detect planets relies on measuring the tiny Doppler shifts caused by the gravitational tug of the planet orbiting a star. The star exerts a gravitational force on the planet, but the interaction goes both ways, so a force of the same magnitude is exerted on the star by the planet. Stars are vastly more massive than planets, so the resulting acceleration is very small, but it is there.

The orbiting planet thus produces a periodic force on the star, which leads to a very small oscillation in the position of the star. We can detect this through the Doppler shift of the light emitted by the star-- the frequency gets very slightly higher as the star moves toward us, and very slightly lower as it moves away. If we identify a particular line, and track it over time, we can watch it wobble back and forth, and thus detect the presence of a planet. The period of the wobble tells us how long it takes the planet to complete one orbit, and the amplitude tells us the mass of the planet (bigger planets cause bigger forces, which lead to higher velocities and bogger shifts).

The shift involved is really tiny, and Ron pointed out that it's limited in part by the availability of reference sources. To measure a really tiny Doppler shift of some spectral feature, we need a really accurate measurement of where that line is supposed to be. And in order to do a really good job with this, we need to measure lines in many different regions of the spectrum, as a cross-check, which means we need lots of reference lines, over a very wide range.

Which is where the femtosecond frequency comb comes in. A comb laser consists of an extremely large number of laser modes, spaced by a regular and well known interval. These modes can span the entire spectrum, from the ultraviolet to the infrared.

If we know the frequency of one mode very well, we can know the frequency of all the others to the same precision. And, as Jun Ye and Jim Bergquist noted at DAMOP (and others have demonstrated in labs all over the world), we can measure the frequency of those modes to something like a part in 10¹⁷.

This would, at least in principle, enable you to use a frequency comb source as a reference for measuring Doppler shifts to really ridiculous precision over the entire spectrum. Which, in turn, translates to measuring extremely tiny stellar velocities, which would let us detect planets with very low masses.

Ron's other suggestion for an astrophysical application of frequency combs was in cosmology. The basic idea is the same-- using the comb as a reference to measure the Doppler shift of some spectral feature, in this case a line from a distant galaxy. If you could measure the shift well enough, he pointed out, you could detect velocity changes on the level of centimeters per second. In which case you could track the spectrum of a single distant source over some time, and measure the acceleration of the universe directly from the change in the velocity of that source. And how cool would that be?

Either of these measurements would, of course, be a long way off, and there may very well be some technical limitation that would keep them from working. But it's fun to think about this sort of stuff all the same. When you can measure things at the 10^-17 level, all sorts of improbable measurements start to look possible.