Frequency Combs 
    High Precision 
Measurements for fundamental Physics



We are part of the group of Prof. T. W. Hänsch and located at the Max-Planck Institute for Quantum Optics

Frequency Combs

Frequency combs can be produced by a pulse train of a mode locked laser. One can think of the comb lines as the longitudinal cavity modes of that laser. Frequency combs are simple and compact tools that phase coherently connect the radio frequency domain (below say 100GHz) with the optical domain (above say 200THz). They greatly simplified high precision optical frequency measurements and provide the long awaited clockwork mechanism for an all-optical atomic clock. Optical precision spectroscopy is important to determine fundamental constants like the Rydberg constant and test the underlying theories. The most advanced of it, quantum electrodynamics (QED), allows to calculate energy levels of simple atoms such as the hydrogen atom with 12 digits of accuracy. With the frequency comb it is readily possible to match this precision experimentally. Other spectroscopic applications involve the search for possible slow temporal variations of the fundamental constants that are suggested by some philosophical arguments, tests of special relativity, and the precise calibration of astronomical spectrographs to determine cosmic velocities (see below). In the time domain, the frequency comb allows to stabilize the phase between the carrier and the envelope of a pulse. This capability has been a key element in the generation of attosecond pulses.

First self referenced frequency comb            First octave spanning self referenced frequency comb

The pictures show the first self referenced frequency comb (left) in 1998 and the first octave spanning self referenced frequency comb (right) in 1999 in our lab. Meanwhile fiber based laser systems have taken over most practical applications.

To read more click here: pdf

Broadband Direct Frequency Comb Spectroscopy

There are several possibilities to employ the individual modes of a frequency comb for massive parallel spectroscopy of, say, molecules with their broadband spectra. For highest sensitivity, spectroscopy should be conducted intra cavity to enhance the probing light intensity. In that case one faces the problem of resonating all modes at once. Another problem that arises is that the modes of most mode locked lasers are too dense to be resolved with a common spectrometer. Without resolving the comb lines, the frequency comb is nothing but a broadband lamp in terms of resolution. With our Vernier type comb spectroscopy, we solve both issues at once by using the enhancement cavity also as a filter. If the mode spacing of the frequency comb and the enhancement cavity that contains the sample are in a ratio that is slightly off from an integer, individual modes can be readily selected as sketched below.

Vernier filtering of a frequency comb
A cavity with a spectral power enhancement expressed by an Airy function (blue) is fed with a frequency comb (red). The mode spacing of the comb and the cavities free spectral range are at a ratio of 5:6 such that only every 5th mode of the comb is resonant at a time. The transmitted resonant modes are resolved by a small grating.

As an example, consider a 1GHz repetition rate laser coupled to a cavity whose free spectral range is  adjusted to around 0.99GHz. In this case every 100th mode of the frequency comb (spaced by 100GHz) is resonant, and those modes may be numbered as  0,100,200... Scanning the comb slightly, modes with numbers 1,101,201... become resonant and so on. By flipping a grating synchronized with this scanning all modes of the frequency comb can be mapped on a CCD chip as shown in the figure below.

Transmissions through a cavity whose free spectral range is in close ratio of 1 with the mode spacing of the frequency comb coupled into the cavity. Weak spots caused by absorption lines in the A bands of oxygen are clearly observed.

The 2-dimensional array of spots on the CCD can be ordered uniquely into a single frequency axis using a suitable computer program. Because the spectroscopy cavity will not change the frequency of the transmitted comb modes, each spot of the array can be readily traced to an atomic clock. If necessary, the resolution of the method can be increased beyond the repetition rate by repeating the measurement with different positions of the frequency comb, thereby accessing components that are narrow enough to fit in between the comb modes. The method is sensitive to  the dispersion of the sample while the dispersion of the cavity does not change the frequency of the modes and therefore may be subtracted out. When scanning over molecular resonances, one observes the width of the cavity modes in frequency space. This measurement is the equivalent to highly sensitive cavity ring down measurement because the spectral width is given by the inverse ring down time.

The method therefore:

  • is providing the sensitivity of cavity ring down spectroscopy
  • comes with an accuracy of the clock that controlles the frequncy comb
  • measures dispersion as well as absorption of the sample
  • does not require a high resolution grating or spectrometer
  • require cavity dispersion to be compensated for

If you want to read more about Vernier type spectroscopy click here: pdf

Astronomical Frequency Combs

Frequency combs can also be useful to calibrate astronomical spectrographs, significantly improving the calibration accuracy over existing calibration methods. This has several fundamental implications: Using periodically varying Doppler shifts of a distant recoiling star, one can detect extraterrestrial planets in their orbits. Also, by observing the variation of the cosmic red shift, it would be possible to measure the dynamics of the Universe in real time. This would allow to verify cosmological expansion without invoking assumptions from an underlying model like General Relativity. Moreover, measurements of gravitational red shifts on the surface of the sun would benefit as well as the limits for a possible temporal variation of the fine structure constant that could be improved by observing distant quasars. In all of these examples, accuracies on the order of parts in 1010 are required. As such an accuracy can be readily supplied by a frequency comb, the challenge is to transfer it to astronomical spectra. A prerequisite is that the modes can be resolved by the spectrograph. This requires mode separations in the 10GHz range which are difficult to reach for a fundamentally mode locked laser with the required optical bandwidth of about one octave. Currently, our research is aiming at achieving these goals in a system that can run autonomously at a remote controlled telescope such as the Very Large Telescope of the European Southern Observatory.

Fraunhofer lines super imposed with a frequency comb

The picture shows a section of a solar spectrum that we recorded at the Vacuum Tower Telescope at Tenerife which is superimposed with a 15GHz frequency comb. The solar Fraunhofer lines appear in dark while the comb lines are the shorter bright vertical lines.

To learn more about our recent work here.

XUV Frequency Combs

We believe that XUV frequency combs will enable high resolution laser spectroscopy at wavelengths shorter than, say, 205nm which is about the shortest wavelength that can be produced in nonlinear crystals (BBO) by second harmonic generation. In order to be useful for this application the XUV frequency comb must posses a mode spacing larger than the linewidth of the investigated transition and posses enough power for a detectable excitation rate. In the meantime we have experimentally met both of the above requirements: The XUV frequency combs are produced from a fs mode locked laser in the infrared (IR) by enhancing its pulse train in a cavity that contains a Xe gas target for intracavity high harmonic generation (HHG). The mode spacing in our apparatus is between 10 and 100MHz. By using the exciting pulse train as a frequency comb we can, at the same time, determine the absolute frequency of each mode of the XUV frequency comb. The traditional approach to produce XUV with pulsed lasers (CPA + HHG) uses a repetition rate around 1kHz. Such a dense frequency comb is basically useless  for high resolution spectroscopy, hence we would not even speak of a "comb" in that context.

Enhancement cavity for XUV generation

The picture shows one of our  femtosecond enhancement cavities used to generate an XUV frequency comb that has been loaded with an infrared pulse before evacuation with dust particles.

Click here to read more.

Hydrogen like Helium

The 1s-2s transition in hydrogen-like helium is one of the most interesting candidates for high precision tests of quantum electrodynamics (QED). Hydrogen-like 4He is an even simpler atom than hydrogen as it shows no hyperfine structure. QED contributions to the energy levels scale with the nuclear charge Z as Z4, thus providing a much more sensitive probe than hydrogen. Even more interesting for theoreticians are higher order contributions. The large uncertainty in the nuclear charge radius of the proton is currently preventing meaningful comparisons between QED and experimental data for hydrogen. Since the uncertainty of the charge radius of the alpha particle is smaller than that of the proton, this problem is greatly reduced for hydrogen-like helium. Last but not least, hydrogen-like He+ is charged and can therefore be trapped and sympathetically laser cooled. We hope to be able to excite the 60.8nm 1s-2s transition with our XUV frequency comb and determine its absolute frequency.

Linear quadrupole ion trap

The picture shows a linear radio frequency ion trap that we are currently investigating to store magnesium ions that we want to use for sympathetic cooling of helium ions.

Fiber Frequency Combs

Frequency combs based on Er and Yb doped fiber mode locked lasers have very few adjustable parts and can therefore operate autonomously for a very long time. This property is essential for running an optical clock. In our group we operate two self-referenced fiber laser combs that are referenced to a hydrogen maser and distributed to several experiments throughout the institute. Besides re-locking them maybe once a month or so, these combs need very little attention. The hydrogen maser is continuously compared to the time signals broadcasted by the Global Positioning System (GPS). Together with data from similar comparisons at the Physikalisch- Technische Bundesanstalt (PTB) we can calibrate our frequency comb relative to the cesium fountain clock there. Curently we are confident to perform this calibration with a relative uncertainty of 10-14.  

Optical Time Transfer

Long haul time transfer is currently done within the radio frequency domain via GPS Common View or two-way satellite links. With the frequency combs at hand, we can always transfer signals from the optical to the radio frequency domain and back. Due to its much higher frequency, two-way time transfer at the optical carrier should significantly improve stability. For this project we acquired a 1000km fiber link connecting the MPQ with the Physikalisch-Technische Bundesanstalt (PTB). We will transmit a narrowband cw laser through this fiber to encode timing signals via the optical carrier. The main challenge there is to compensate the fiber loss of about 190dB and additional losses of optical components with optical amplifiers, i.e. without converting to electronic signals, while maintaining the round trip phase coherence.

last change September 14 2008