Using light as a tool

With the aid of light we can get a fantastic picture of the world of atoms. This field is called spectroscopy and is a way of investigating the energy-level structure in atoms and molecules. Here the laser, with its carefully determined wavelength (colour or frequency), is a very powerful tool.

The finest comb

John Hall and Theodor Hänsch have made important contributions in the field of precision spectroscopy that make it possible to measure the light frequency with an accuracy of 15 digits. Stable lasers with extreme colour definition can be constructed, and the frequency comb technique enables us to measure extremely accurately the frequency of light of all colours. This allows us to measure both time and distance more accurately than before.

The light frequency, f, that we want to determine is too high to be measured directly. Instead we have to use an indirect technique by which we compare the unknown frequency to a measuring stick – the frequency comb. The comparison between two light frequencies is made with a beat technique that shows the difference in frequency low enough to be measured.

We create this frequency comb by means of a mode-locked laser that emits a train of very short pulses of light. The laser light consists of a long series of different frequencies, like the teeth of a comb. The distance between two teeth, f_p, is determined by the time between the pulses.

What we measure are the beats, f_b, between the unknown light and the closest tooth on the comb. By approximately determining the optical frequency we can also find out which tooth lies closest (n=5).

For the measurement to be good, the measuring stick, that is, the frequency comb, has to be carefully calibrated. Unfortunately, the first tooth on the comb is not at the frequency of 0 Hz but at the distance f₀. The first three teeth in the schematically drawn frequency comb (numbered 0, 1 and 2; in practice there can be a million teeth) contain no light, so a trick is needed to measure f₀. Take the first tooth with light (No. 3) and double the frequency. It then stands at the distance f0 from the tooth with twice the number (No. 6), and it is that distance that can be measured.

We then get the unknown frequency: f = n · f_p + f_b + f₀