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pulse duration of 10 fs,one expects 1 million modes (or fringes) to appear.

fundamental limit of the width of a single fringe is given approximately by frep/N. For a typical mode-locked laser, this is much smaller than the spectral width of a single pulse. For N = 3 and frep ~ 70 MHz, as used by Witte et al. (3), we expect a fringe width of 70/3 MHz = 23 MHz. Indeed, that is roughly the linewidth observed by the authors [see figure 3 of (3)]. It is still large compared to the requirements of high-resolution spectroscopy, but improvements by many orders of magnitude should be possible.

For these improvements to become a reality, one must shine more pulses on the atoms or molecules. In this case, the fringes turn into sharp spikes that can be as narrow as in a well-stabilized single-mode laser (4). Such a series of delta-shaped spikes is usually called a frequency comb and can be used to measure the frequency of any of the spikes relative to an atomic clock (a very

How to narrow the linewidth.

The spectrum of a train of N pulses, IN(f), is shown schematically for some values of N.The single-pulse spectrum (red curve; repeated as a pink "envelope" in the subsequent spectra) is as broad as the inverse pulse duration. Multiple pulsing causes fringes (blue curves) with a linewidth of frep/N to appear. For a large number of pulses, the spectrum resembles a series of delta-shaped spikes, which are the modes of the frequency comb, that is, the modes of the laser. For a laser with frep = 100 MHz and a f pulse duration of 10 fs,one expects 1 million modes (or fringes) to appear.

precise clock operating in the radio frequency domain).

In principle, it should be possible to apply many pulses in series to an atom or molecule, because a typical mode-locked laser emits ~70 million pulses per second. However, at room temperature, atoms or molecules tend to move out of the laser focus before they can be hit by a large number of pulses. This becomes even more of a problem if a harmonic of a laser is used, because these harmonics are usually of low power and must therefore be focused to a small spot size to obtain a reasonable intensity.

To date, spectroscopy with frequency combs has not reached the resolution of single-mode lasers. In an early experiment, Eckstein et al. reached a resolution of 4 MHz for the sodium 4s-4d transition (natural linewidth 1.6 MHz) (5). More recently, Marian et al. (6) and Snadden et al. (7) have performed comb spectroscopy on the two-photon 5s-5d transition of rubidium. The latter authors laser-cooled and trapped the atoms to keep them within the laser focus. The resulting linewidth approached the natural linewidth of 300 kHz (see the second figure). In contrast to Witte et al., all these authors

Frequency comb position (MHz)

Probing the resonance frequencies with a frequency comb.

The two-photon 5s-5d transition in 85Rb breaks up into several components: For the 5s state, only the F = 3 hyperfine state is used.The 5d state first breaks up into two fine structure states, 5d3/2 and 5d5/2, which in turn break up into hyperfine components (red and blue curves). The black curve is the resonance fluorescence (shifted up for clarity) that is recorded as the frequency comb is scanned across the line. The two-photon excitation becomes possible whenever the frequency of two modes or twice the frequency of one mode coincides with the atomic transition.As a consequence, the two-photon absorption spectrum repeats at an interval of half the laser repetition rate (80.3 MHz in this experiment). Figure adapted from (7).

used the fundamental, not a harmonic, of a frequency comb.

Despite these advances, single-mode lasers remain more suitable than frequency combs for spectroscopy—unless one uses harmonics of frequency combs where single-mode lasers are not readily available. This is what Witte et al. have now demonstrated with a train of three pulses of the fourth harmonic of a Ti:sapphire mode-locked laser (rather than with the femtosec ond laser pulses themselves). Hopefully, we can expect the application of much higher harmonics with many more pulses to interesting atomic or molecular species. A whole new window for high-resolution spec-troscopy thus opens. It might even become possible to use a single laser system to cover all wavelengths from the near-infrared to soft x-rays; this possibility is out of reach for single-mode lasers.

High-resolution spectroscopy in the extreme-ultraviolet regime would be very useful for investigating hydrogen-like ions. For these ions, the quantum electrodynamic contributions to the energy levels (Lamb shifts) become more important and can be determined more precisely. It might even be possible to create an optical clock that operates in the extreme ultraviolet regime. The stability of such a clock is proportional to the transition frequency in use, and would thus be very high.

References

1. E.Peik et al.,Phys. Rev. Lett. 93,170801 (2004).

2. R. J. Rafac et al., Phys. Rev. Lett. 85,2462 (2000).

3. S.Witte, R.Th.Zinkstok,W. Ubachs,W. Hogervorst, K. S. E. Eikema, Science 307,400 (2005).

4. Ye. V. Baklanov, V. P. Chebotayev, Appl. Phys. 12, 97 (1997).

5. J. N. Eckstein, A. I. Ferguson, T.W. Hänsch, Phys. Rev. Lett. 40, 847 (1977).

6. A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, J. Ye, Science 306, 2063 (2004); published online 18 November 2004 (10.1126/science.1105660).

7. M. J. Snadden, A. S. Bell, E. Riis, A. I. Ferguson, Opt. Commun. 125,70 (1996).

10.1126/science.1108159

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