Measuring the Frequency of Light using Femtosecond Laser Pulses (2001)

In the course of this work a new technique to measure the frequency of light has been developed, implemented and refined. For all time and frequency measurements the SI second defined by the cesium ground state hyperfine splitting near 9.2 GHz is the defined standard of reference. Therefore in precision optical frequency measurements optical frequencies on the order of several 100 THz – too fast to be counted with any electronics – have to be compared with radio frequencies on the order of a few GHz. The basic idea here is to measure dierences between optical frequencies with the help of frequency combs generated by the periodic pulse trains of femtosecond lasers. The output spectrum of such a laser consists of modes equally spaced by the repetition frequency of the pulses and forms a convenient ruler in frequency space. Extending this principle to the intervals between harmonics of the same optical frequency f, in the most simple case the interval between f and 2f, allows the absolute measurement of an optical frequency f = 2f − f. To bridge the interval between an optical frequency f and its second harmonic 2f a broad frequency comb with a width of several 100 THz is needed. This can be achieved with very short pulses (on the order of 5 fs) or with moderately short pulses on the order of a few 10 fs via self phase modulation in an optical fiber. Especially suited for such massive broadening are so called photonic crystal fibers. Here the light is guided in a very small core (1-2 µm) surrounded by air holes. This development culminates in the “single laser frequency chain” linking the radio frequency domain with the optical domain with the help of just one fs laser, a piece of fiber and some optics. Our optical frequency synthesizer can be used to measure not only one but almost any optical frequency with the same compact apparatus. Originally this project has been initiated to perform precision spectroscopy on the 1S- 2S transition in atomic hydrogen, a project with a long tradition in our group, and yielded what is thus far the most precise optical frequency measurement with a relative uncertainty of 1.8×10−14. Hydrogen as the most simple bound system served and still serves as an important cornerstone for tests of quantum physics, the measurement of the 1S Lamb shift represents one of the most accurate QED tests. Furthermore the Rydberg constant can be determined very precisely from optical frequency measurements in hydrogen. Soon it became obvious that this technique has a broad applicability. In this work transition frequencies in cesium, indium and molecular iodine have been measured. Besides that principle tests on this technique have been conducted. The direct comparison of two such frequency chains showed agreement on the level of 5 × 10−16. Further applications besides precision spectroscopy can be found in the time domain. There it is now possible with this technique to control the phase evolution of ultra short light pulses and perform optical waveform synthesis. As optical clock work for future all optical clocks a fs frequency chain transfers stability and accuracy from the optical to the rf domain.